# Socioeconomic Measure: A Relativist Perspective on Debt Crisis Management

John D Pappas

► To cite this version:

John D Pappas. Socioeconomic Measure: A Relativist Perspective on Debt Crisis Management. International Journal of Economics and Finance, 2025, 17 (6), pp.86. 10.5539/ijef.v17n6p86. hal-05085283

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# Socioeconomic Measure: A Relativist Perspective on Debt Crisis Management

John D. Pappas

Correspondence: Author, AGM Legal & Financial Consulting Co., 3 Skylitsi Str., Athens 11473, Greece. Tel: 30-210-653-2674. E-mail: pappas.research@gmail.com

Received: March 26, 2025

Accepted: May 14, 2025

Online Published: May 25, 2025

doi:10.5539/ijef.v17n6p86

URL: https://doi.org/10.5539/ijef.v17n6p86

## Abstract

This paper introduces a concrete definition of the concept of *measure* in human interaction, highlighting its parallels with the principles of moderation and aesthetic balance—the latter traditionally symbolized by the golden ratio in art and architecture. By applying this definition to socioeconomic behavior, the paper proposes a model to help prevent or mitigate future debt crises. To this end, the model aligns with the IMF's balance sheet approach for assessing the net worth of economic sectors or national economies. Adopting a relativist perspective in this context, the paper identifies key conditions for implementing alternative policies for debt crisis management. These policies offer a potential pathway for distressed economies to escape debt traps while preserving their socioeconomic class structure and protecting creditors' interests.

**Keywords:** growth theory, mathematical economics, net worth, public sector, debt spiral, sovereign indebtedness, socioeconomic sustainability

**JEL classification:** C03, C30, F43, H63, O10, P20, P51.

## 1. Introduction

The classical concept of *measure*, often linked to moderation, balance, equilibrium, harmony and beauty, has been symbolized by the golden ratio (φ) in architecture and the arts. However, in the realm of human interaction, an exact definition of measure remains elusive. To date, no universally accepted formula or “magic number” has been established for defining measure in human behavior and interaction.

Despite the insights of great thinkers from Homer to Kant and Nietzsche, a comprehensive and precise definition of measure has yet to be articulated. Consequently, the persistent ambiguity surrounding the concept of measure, coupled with the human impulsive tendency toward excess, has left individuals, societies, and nations vulnerable to extreme deviations from measure. Such deviations, which often manifest as hubris, have contributed to the downfall of economies, states, and empires.

This paper seeks to address this indeterminacy by proposing a concrete definition of the classical concept of measure that is applicable to human behavior. The proposed definition is both quantitative and qualitative: it is mathematically precise yet intuitively understandable. It aligns with Aristotle's specifications, being subjective at the individual level, cultural at the macrosocial level, and adaptable to changing circumstances.

To demonstrate the applicability of this definition, the paper applies it to a socioeconomic context, showing how measured economic behaviour and organization can protect an economy from both debt traps and prolonged stagnation. To this end, the proposed definition implies a normative policy orientation that avoids the extremes of protectionist autarky and unregulated globalization. As to economies that deviate excessively—or *hubristically*—from measure, the model highlights their heightened vulnerability to future debt crises. It also provides analytical tools to help a distressed economy escape its debt trap while preserving social cohesion and minimizing creditor losses, and thus accounting for political economy constraints and distributional conflicts.

## 2. Analytical Method

The definition of measure is derived by dynamically modeling socioeconomic interactions within a simplified Aristotelian dyadic (two-sector or two-class) socioeconomic structure (Note 1). The model's state variables align
with the IMF's balance sheet approach (Note 2) for assessing the net worth and sustainability of economic sectors or national economies. In this model, the net worth ($N_i$) of each sector ($i$) in an open mixed economy changes over time ($t$) according to a system of differential equations of the following general form:

$$ \dot{N}_i = F_i(N_i, N_j, t) \quad (i, j) \in \{(1, 2), (2, 1)\} \quad (1) $$

where $\dot{N}_i$ is the derivative of $N_i$ with respect to time ($t$). In a closed economy, or an open laissez-faire economy, the net worth changes according to the dynamics of the following autonomous system:

$$ \dot{N}_i = \Phi_i(N_i, N_j) \quad (i, j) \in \{(1, 2), (2, 1)\} \quad (2) $$

The definition of socioeconomic measure, derived from these systems, ensures that the net worth of each sector and the broader economy grows over time along a sustainable development path. Thus, this definition presents a promising policy tool for preventing recessions and avoiding future debt traps driven by excessive indebtedness. With regard to economies that are exposed to the risk of future debt crises, this model specifies the necessary conditions for effective debt crisis management, which may include a minimal yet sufficient debt reduction, as summarized in a perspectivist algorithm of conditionalities (Appendix B, Figure B5).

In this framework, the main text of the paper presents a descriptive, metaphorical storyline as a comprehensive theory that incorporates qualitative phase-plane analysis, making it accessible to a general interdisciplinary readership. Source material is included in the Notes, as well as Appendices A and C, to maintain the streamlined nature of the narrative in the main text. The former appendix (A) includes philosophical background information on the concept of measure, while the latter (C) summarizes the ongoing academic debate on shock therapy and gradualist adjustment. The underlying mathematical details, along with statistical data, have been relegated to Appendix B for readers who are more mathematically inclined. A glossary of the model's variables and parameters is presented in the last appendix (D).

### 3. Structure of the Model

We consider a simplified economy with only two members, a prince and a pauper, who may be perceived as representing the two sectors, such as the public and private sectors, of a two-sector economy (Note 3). In this model, the net worth of each member ($i$) at any given time ($t$) changes depending not only on the member's own net worth, $N_i(t)$, but also on the net worth, $N_j(t)$, of the other member ($j$) at that time. The model is defined by the following equations, where $\dot{N}_i(t)$ is the derivative of $N_i(t)$ with respect to time ($t$):

$$ \dot{N}_i(t) = (w_i - l_i)N_i(t) + b_i N_j(t) + \gamma_i e^{\rho t} + g_i \quad (i, j) \in \{(1, 2), (2, 1)\} \quad (1') $$

where: $N_i(t), \rho \in \mathbb{R}$; $w_i, l_i, b_i, g_i > 0; \gamma_i \ge 0$;

$N_i(t)$: net worth of member ($i$) at time $t$;

$w_i$: work coefficient of member ($i$);

$l_i$: leisure coefficient of member ($i$);

$b_i$: interaction coefficient of member ($i$);

$\gamma_i$: international information coefficient of member ($i$);

$\rho$: policy factor, determined exogenously by the government;

$g_i$: teleonomial term of member ($i$);.

This system is based on the following considerations:

#### 3.1 Work and Leisure Coefficients

Each member ($i$) has a work coefficient ($w_i$) and a leisure coefficient ($l_i$), which reflect the member's view on the trade-off between work and leisure. These coefficients are assumed to be positive; even in a Robinson-Crusoe economy, where there is no social interaction ($N_i(t) = 0, \forall t$), the member engages in some work ($w_i > 0$) and enjoys some leisure ($l_i > 0$), because work is necessary to replace depreciating capital, while leisure is considered “the end” of work from an Aristotelian perspective (Note 4). The difference between these coefficients is denoted as $a_i$ (where $a_i \in \mathbb{R}$ and $a_i = w_i - l_i$) and termed the intrinsic coefficient of this member (Appendix B, section B1). The member is leisure-oriented if $a_i$ is negative, work-oriented if $a_i$ is positive (Note 5), or intrinsically neutral if $a_i$ is zero (Appendix B, section B2). The product of the intrinsic coefficients represents the economy's intrinsic effect, $a_i a_j$.

#### 3.2 Interaction Coefficient ($b_i$)

The reaction coefficient $b_i$ of each member ($i$) is referred to as the member's interaction coefficient, which reflects the impact of interpersonal comparisons on the member. Each member ($i$) is disposed competitively
towards the other member (j) (Note 6). The higher the net worth of the other member at a time, the more motivated the former member is to increase his/her own net worth by an amount $b_iN_i(t)$ at that time. The product of the interaction coefficients represents the economy's demonstration effect, $b_ib_j$ (Note 7).

### 3.3 International Impact ($\gamma_i e^{\rho t}$)

In an open economy, the term $\gamma_i e^{\rho t}$ accounts for the international influence on the change in the net worth of each member (i) at a time (t). The international information coefficient, $\gamma_i$, represents the degree of access that this member has to international information on consumption standards and investment opportunities (Note 8). The policy factor, $\rho$, is determined exogenously by the government (Note 9).

### 3.4 Teleonomial Term ($g_i$)

The significance of $g_i$ becomes apparent in the context of a closed economy, where information borders are closed ($\gamma_i = 0$). In this scenario, the above dynamic system (relation (1')) takes the reduced form of the following autonomous system of linear differential equations:

$$ \dot{N}_i - a_i N_i - b_i N_j = g_i \quad (i, j) \in \{(1, 2), (2, 1)\} \quad (2') $$

By setting $\dot{N}_i$ equal to zero in relation (2') (that is also stated in matrix form in Appendix B, section B3) and solving for $N_i$, we find:

$$ N_i = -(g_i/a_i) = G_i \quad (i=1, 2) \quad (2'') $$

<figure><img src="image_2.png" /><figcaption>Figure 1. Closed High-Motivation Leisure-Oriented economy</figcaption></figure>

Note. The economy is vulnerable to a future debt crisis. A potential debt trap is illustrated by the grey-shaded "hubris zone" to the left of the systems's saddle path (section 4.1.1).

Ratio $G_i$, termed the autarky net worth of member (i), specifies the level of net worth of each member (i) that, in the absence of social interaction ($N_i = 0$), would satisfy all the needs of that member so that no further change in that member's net worth is desirable ($\dot{N}_i = 0$). Consequently, $g_i$ is termed the teleonomial term of member (i) and reflects this member's fundamental life goals—such as building a house or creating an artwork—even in isolation, as in a Robinson-Crusoe economy (Note 10).

## 4. Theoretical Analysis

Based on these considerations, we specify the following categorizations of an economy regarding its motivation structure:
— Overall Motivation: In a high-motivation economy, the demonstration effect is higher than the intrinsic effect ($b_ib_j > a_ia_j$); in a low-motivation economy, it is lower than the intrinsic effect ($b_ib_j < a_ia_j$); in a balanced-motivation economy it is equal to the intrinsic effect ($b_ib_j = a_ia_j$).

— Prevailing Work Ethic: The economy is characterized as leisure-oriented if both intrinsic coefficients are negative ($a_i, a_j < 0$), work-oriented if both these coefficients are positive ($a_i, a_j > 0$), or heterogenous if one of these coefficients is negative but the other is positive ($a_i < 0 < a_j$), i.e., if the members are conversely predisposed regarding work and leisure, with one member (i) being leisure-oriented and the other (j) work-oriented. In rather exceptional cases, if both of these coefficients are zero, the economy is characterized as totally neutral; if either of these coefficients is zero, the economy is considered partially neutral.

In accordance with these categorizations, the dynamic behavior of an economy and its exposure to a future debt crisis depends not only on its motivation structure, but also on whether it is a closed ($\gamma_i = 0$), open laissez-faire ($\gamma_i > 0, \rho = 0$), or open mixed ($\gamma_i > 0, \rho \neq 0$) economy, as specified below:

## 4.1 Closed Economy.

A closed economy, where information borders are closed and each member may borrow from and lend to foreigners only indirectly, through the country's banking system, can be graphically outlined by setting $\dot{N}_i = 0$ in equations (2') and solving for $N_i$ at $\dot{N}_i = 0$:

$$N_i = G_i + B_i N_i \quad (i, j) \in \{(1, 2), (2, 1)\} \quad (3)$$

$$\text{where } B_i = -(b_i/a_i) \quad (i = 1, 2) \quad (3')$$

Ratio $B_i$, termed the status coefficient of member (i), represents the percentage of the other member's net worth that, in addition to the former member's autarky net worth, would satisfy all the needs of this member, such that no further change in the member's net worth is desirable. The product, $B_iB_j$, of the two status coefficients is termed the status effect of the economy.

Relation (3) defines a demarcation line, labeled "$\dot{N}_i = 0$" in Figures 1-3, for each member (i). The intercept of this line equals the member's autarky net worth, while its slope is equal to the member's status coefficient (Note 11). In this context, the dynamics of the system depend on the motivation structure of the economy, as follows:

### 4.1.1 Closed High-Motivation Leisure-Oriented Economy

Figure 1 illustrates a high-motivation economy that is closed and where its members are both leisure-oriented. The horizontal axis measures the net worth of the pauper ($N_1$), while the vertical axis measures the net worth of the prince ($N_2$). Initially, at $t = 0$, each member (i) has an endowment, $N_i(0)$, whose net worth is a real number. The endowment of the prince has a higher value than that of the pauper: $N_2(0) > N_1(0)$. The pair of the endowments maps to a point, termed *endowment point*, in the $N_1N_2$-plane (e.g., point W in Figure 1).

The two demarcation lines ("$\dot{N}_1 = 0$" and "$\dot{N}_2 = 0$" respectively) intersect at the system's stationary point (E), that lies in the third quadrant: negative net worth of the public sector is statistically a standard phenomenon even in developed economies (Appendix B, section B4). The value of $N_i$ at the stationary point is denoted as $\tilde{N}_i$, termed the stationary net worth of member (i), and specified as follows:

$$\tilde{N}_i = (b_ig_j - a_jg_i)/(a_ia_j - b_ib_j) \quad (i, j) \in \{(1, 2), (2, 1)\} \quad (4)$$

The numerator in equations (4) is positive, because $a_j < 0$, but the denominator is negative because $b_ib_j > a_ia_j$, implying $\tilde{N}_i < 0$. Furthermore, system 2' entails that for each member (i):

$$\frac{\partial \dot{N}_i(t)}{\partial N_i(t)} \text{ is} \quad \begin{bmatrix} < 0 & \text{if this member } (i) \text{ is leisure-oriented} & (a_i < 0) \\ > 0 & \text{if this member } (i) \text{ is work-oriented} & (a_i > 0) \\ = 0 & \text{if this member } (i) \text{ is intrinsically neutral} & (a_i = 0) \end{bmatrix} \quad (5)$$

This information enables us to draw a set of directional arrows (Note 12), such as the small vertical (green) and horizontal (blue) arrows in Figure 1. Consistent with the directional arrows, we may sketch a series of streamlines, also known as phase paths, depicted by solid (red) curved arrows in Figure 1, each mapping out the dynamic movement of the system from a selected initial point (e.g., the endowment point W in Figure 1). The net worth of each member at any time, depicted by a point on a streamline, can be determined by solving the autonomous system of a closed economy (as specified in Appendix B, section B5).

The stationary point has a pair of stable branches (HE and H'E in Figure 1) that flow consistently and directly toward this point, and also has a pair unstable branches (ED and ED' in Figure 1) that flow consistently and directly away from it. These stable branches comprise the (convergent) saddle path (depicted as HH' in Figure 1,
and specified algebraically in Appendix B, section B6). The saddle path passes through this point, which therefore is characterized as a *saddle point*, i.e., it behaves as an *attractor* for some trajectories and a *repeller* for others. Specifically:

- If the endowment point lies on a stable branch, the economy will head directly and consistently toward the stationary point. Once it reaches this point, equilibrium prevails, i.e., $N_i(t) = \bar{N}_i$ for each member (i) for all t thereafter.

- If the endowment point lies on the unstable branch northeast [southwest] of the stationary point, the economy will move along this branch in a northeastern [southwestern] direction, causing the net worth of the economy, $N_1(t) + N_2(t)$, to be increasing [decreasing] in the long run.

<figure><img src="image_3.png" /><figcaption>Figure 2. Closed Low-Motivation Leisure-Oriented economy</figcaption></figure>

*Note.* The economy is not vulnerable to a debt crisis—no hubris zone is embedded in the system—but it faces the risk of long-run stagnation at the stable node (section 4.1.2).

- If the endowment point lies to the right of the saddle path *and* to the right or left of *both* demarcation lines (such as point W in Figure 1), the streamline starting at this point initially flows closer to the stationary point. However, once it crosses a demarcation line (as at point p in Figure 1) it flows in a northeastern direction converging to the unstable branch (ED'), indicating that the net worth of the economy will ultimately be increasing in the long run (see Appendix B, section B7 for necessary conditions for such increase).

- Conversely, if the endowment point lies to the left of the saddle path *and* to the right or left of *both* demarcation lines (such as point W' in Figure 1), the streamline initially flows closer to the stationary point, effecting a *temporary* increase in the net worth of one member and a simultaneous decrease in the net worth of the other member (as in the segment W'p' of the streamline in Figure 1). However, as soon as the streamline crosses a demarcation line (as at point p') it flows in a southwestern direction, converging to the unstable branch (ED), indicating that the net worth of the economy will ultimately be decreasing in the long run (Appendix B, section B8).

In this context, the area to the left of the saddle path is termed the economy's *debt-overhang zone* or *hubris zone* (the grey area in Figure 1). This zone depicts the specter of a debt crisis: once the economy is caught within this zone, it follows an irreversible debt-overhang process (Jeffrey Sachs, 1990); as consequence, the net worth of both members deteriorates in the long run (in the grey-grid part of the hubris zone below the stationary point in Figure 1), although the net worth of one member *may* increase temporarily as shown above.

A shock to stock variables, e.g., a withdrawal of investor confidence, might entrap the economy in the hubris
zone (e.g., by repositioning it from W to W' in Figure 1), especially if the economy is initially positioned outside but close to this zone (as at point W in Figure 1). Consequently, this economy is exposed to the risk of a future debt crisis.

### 4.1.2 Closed Low-Motivation Leisure-Oriented Economy

Figure 2 illustrates a low-motivation economy that is closed and where its members are both leisure-oriented. The stationary point lies in the first quadrant, as both the numerator and the denominator on the right side of equations (4) are positive. Moreover, all branches are convergent, because both eigenvalues derived from the characteristic equation of the system are negative (Appendix B, section B5). Thus, this point is a globally *stable node*, as all streamlines flow towards it: all initial vectors converge directly or asymptotically to the equilibrium vector, which serves as the *attractor* in an infinite *basin of attraction*, i.e., in the entire two-dimensional space of potential initial vectors.

Consequently there is no hubris zone in this system, meaning this economy is not exposed to the risk of a future debt crisis. For instance, even if this economy is initially a net debtor (as at points W and W' in Figure 2), it will reverse its debt status (from net debtor to net creditor) in the long run.

However, once the stationary point is reached in the first quadrant, the same weak impact of the demonstration effect that shields the economy from overborrowing will prevent it from expanding any further—e.g., as happened to the USSR during the Cold War, when the Soviet economy was characterized by a combination of low indebtedness and technological and economic stagnation in consumer goods production.

<figure><img src="image_4.png" /><figcaption>Figure 3. Closed Positively-Balanced economy</figcaption></figure>

*Note.* The economy is not vulnerable to a debt crisis—no hubris zone is embedded in the system—and attains long-run growth irrespective of initial conditions or subsequent shocks to stock variables (section 4.1.3).

### 4.1.3 Closed Positively-Balanced Economy

Inspection of equations (4) reveals that the stationary point of the system vanishes to infinity as the demonstration effect approaches the intrinsic effect. Specifically, when $a_i, a_j < 0$:

$$ \text{If } b_i b_j > a_i a_j, \quad \text{then } \tilde{N}_i \to -\infty \quad \text{as } b_i b_j \to a_i a_j \quad (i, j) \in \{(1, 2), (2, 1)\} \qquad (6.a) $$

$$ \text{If } b_i b_j < a_i a_j, \quad \text{then } \tilde{N}_i \to +\infty \quad \text{as } b_i b_j \to a_i a_j \quad (i, j) \in \{(1, 2), (2, 1)\} \qquad (6.b) $$

Statement (6.a) implies that a high-motivation leisure-oriented closed economy may avoid a future debt spiral if the demonstration effect is sufficiently close (from above) to the intrinsic effect. Graphically, the closer the demonstration effect is to the intrinsic effect, the further the convergent branches are from the origin in a
southwestern direction, and thus the further the hubris zone is from the origin in this direction.

Similarly, statement (6.b) implies that a low-motivation leisure-oriented economy may avoid economic stagnation if the demonstration effect is sufficiently close (from below) to the intrinsic effect. Graphically, the closer the demonstration effect is to the intrinsic effect, the further the stationary point is from the origin in a northeastern direction.

In the limiting case where the demonstration effect is equal to the intrinsic effect, or equivalently where the status effect equals unity (i.e., where the stationary point vanishes to infinity, as depicted in Figure 3), the economy is not exposed to the risk of a future debt crisis: a hubris zone does not appear in this case. Moreover, the forces of the system result in long-term growth in the economy's net worth, regardless of the endowment of each member and irrespectively of future shocks to stock variables. The economy will absorb such shocks (e.g., like one that might shift the economy from point W to point W' in Figure 3) and will immediately follow a new path of economic growth. In this context, the degenerate-equilibrium case of a leisure-oriented economy represents an economy that is perfectly shielded from both indebtedness and stagnation. Such positively balanced motivation structure serves as a reminder that both the debt and stagnation traps can be avoided if a leisure-oriented economy is marked by motivational balance, such that $b_i b_j \cong a_i a_j$.

### 4.1.4 Closed Exposed Economies

All other types of closed economies—whether work-oriented, heterogeneous, partially neutral, or totally neutral—share a common characteristic: they are all exposed to the risk of a future debt spiral, indicated by the presence of a hubris zone in their graphical depiction. This exposure exists even in cases where the motivation is balanced ($b_i b_j = a_i a_j$) in work-oriented closed economies (Note 13).

## 4.2 Open Laissez-Faire Economy

In a laissez-faire economy, where information borders are open ($\gamma_i > 0$) and there is no government intervention ($\rho = 0$), the dynamic system 1' simplifies to the following autonomous system:

$$ \dot{N}_i - a_i N_i - b_i N_j = g_i + \gamma_i \quad (i, j) \in \{(1, 2), (2, 1)\} \quad (7) $$

By setting $\dot{N}_i = 0$ in equations (7)—which are specified in matrix form in Appendix B, section B10—and solving for $N_i$ we derive the equations of the demarcation lines of a laissez-faire economy:

$$ N_i = G_i + \Gamma_i + B_i N_j \quad (i, j) \in \{(1, 2), (2, 1)\} \quad (8) $$

$$ \text{where } \Gamma_i = -(\gamma_i / a_i) \quad (i = 1, 2) \quad (8') $$

Ratio $\Gamma_i$, termed the information effect on member (i), represents the impact of information ($\gamma_i$) on this member, internalized according to the member's perception ($a_i$) of the trade-offs between work and leisure.

These equations (8) are analogous to the equations (3) for the demarcation lines in a closed economy. Therefore, from the analytical viewpoint of the transformation of a closed economy into an open laissez-faire economy, the slope of each member's demarcation line is the same before and after the transformation. Additionally, in open laissez-faire economies, the partial derivative of $\dot{N}_i$ with respect to $N_i$ is negative if they are leisure-oriented, and positive if they are work-oriented, as in closed economies (by relation (5)). Therefore, the dynamics, as depicted by directional arrows in both types of economies, are similar (Note 14). Consequently, all inferences drawn from the phase-plane analysis for closed economies also apply to open laissez-faire economies.

The only difference between these economies lies in the intercept of the demarcation line of each member (i). In a closed economy, the intercept equals the member's autarky net worth according to equations (3). In a laissez-faire economy, however, the intercept is equal to the member's autarky net worth augmented by the information effect on this member ($G_i + \Gamma_i$) per equations (8).

Therefore, the transformation of a closed economy into an open laissez-faire economy entails the following alternative effects: (1) reduction of its exposure to the risk of a future debt crisis if it is a high-motivation leisure-oriented economy, because the transformation shifts the saddle path—the rightmost border of the hubris zone—in a southwestern direction; (2) increase in the stationary net worth of each sector if it is a low-motivation leisure-oriented economy, because the transformation shifts the stationary point in a northeastern direction; (3) no effect if it is a positively-balanced economy, because the demarcation lines remain parallel.

The exposure of all other types of closed economies to the risk of future debt crisis, will be reduced if they open their information borders; the only exception is a totally neutral economy—also marked by the presence of a hubris zone—whose exposure to a future debt crisis remains unchanged before and after the opening of its information borders.
In general, if a closed economy is exposed to a future debt crisis, it will remain exposed to such crisis after its transformation to an open laissez-faire economy, but such exposure will be reduced as a result of opening its information borders.

## 4.3 Open Mixed Economy

An open mixed economy, with open information borders ($γ_i > 0$) and government intervention ($ρ ≠ 0$), is described by relation (1'). By setting $N_i(t) = 0$ in this relation and solving for $N_i(t)$, we derive the equations of the demarcation lines at a point in time (t):

$$N_i(t) = G_i + \Gamma_i e^{\rho t} + B_i N_i(t) \quad (i, j) \in \{(1, 2), (2, 1)\} \quad (9)$$

As shown in equations (9), the slope ($B_i$) of the demarcation line of each member ($i$) is the same as in both closed economies (equations (3)) and open laissez-faire economies (equations (8)).

However, in an open mixed economy, the $N_i$-axis intercept ($G_i + \Gamma_i e^{\rho t}$) is a function of time, causing the demarcation line of each member ($i$) to shift in the direction of the $N_i$-axis over time (Note 15). Such an economy's stationary point moves progressively further away from the origin over time (Note 16). In general, the following inferences are drawn regarding open mixed economies:

### 4.3.1 Contractionary Policy ($ρ < 0$)

If $ρ < 0$ in an open mixed economy, its dynamics will eventually converge to those of a closed economy (where $\Gamma_i e^{\rho t} = 0$), because $ρ < 0$ implies that $\lim (G_i + \Gamma_i e^{\rho t}) = G_i$, as $t \to \infty$.

### 4.3.2 Expansionary Policy ($ρ > 0$)

The effects of expansionary policy in an open mixed economy are summarized below, from the analytical viewpoint of the transformation of an open laissez-faire economy into an open mixed economy:

(a) Risk of Future Debt Crisis: If an open laissez-faire economy is exposed to the risk of a future debt crisis, its exposure will diminish after its transformation into an open mixed economy. The saddle path, which forms the rightmost border of the hubris zone, will be continuously repositioned further away from the origin over time in a leftward—or southwestern or downward direction, depending on the structure of the economy—if the policy is expansionary.

(b) Risk of Future Stagnation: If an open laissez-faire economy is exposed to the risk of future stagnation in the economy's net worth, this exposure may diminish over time after its transformation into an open mixed economy: its stationary point will be continuously repositioned further from the origin in a northeastern direction over time.

(c) Shielding from Indebtedness and Stagnation: If an open laissez-faire economy is positively balanced, its transformation into an open mixed economy does not affect its (zero) exposure to the risks of debt crisis and stagnation. However, an expansionary policy will determine the economy's growth rate, which tends toward $ρ$ in the long run.

## 4.4 Definition of Socioeconomic Measure

In general, an economy can be effectively shielded from both indebtedness and stagnation if it is positively balanced, i.e., if it fulfills two key conditions: (1) its demonstration effect is equal to its intrinsic effect, and (2) the economy is leisure-oriented.

Descriptively, an economy will be safeguarded against these risks if (1) in economic decisions, the sectors of the economy consider equally socioeconomic standards (representing extrinsic patterns of behaviour) and their intrinsic dispositions (reflecting deeply-rooted personal and cultural traits)—i.e., if the demonstration effect equals the intrinsic effect—and (2) the economy is uniformly leisure-oriented, meaning that the society values leisure time highly for culturally cohesive activities, with all sectors' intrinsic coefficients being negative.

Respectively, at a national level, the optimal condition for shielding an economy from indebtedness and recession is termed socioeconomic measure, which is defined as follows: Socio-economic measure is a condition of valuing national traits and international standards equally in socioeconomic behavior in a country that is uniformly committed to cultural development (Note 17).

The application of this definition to economic behavior and institutional organization implies a policy orientation that deliberately avoids the extremes of protectionist autarky, on one hand, and unregulated global integration, on the other. Within this framework, a motivationally balanced economy remains internationally engaged while safeguarding domestic priorities, synthesizing national sovereignty with global cooperation—that is, aligning economic conduct with both internal cohesion and responsible international participation.
# 5. Discussion and Applications

## 5.1 Sustainability

From socioeconomic and environmental perspectives, a positively balanced economy may be sustainable with respect to equity and resource utilization, as outlined below.

### 5.1.1 Equity

In a positively balanced economy, the relative net worth of each member (i), as a percentage of the net worth of the other member, tends to align with the former's status coefficient in the long run (Note 18): this ratio, $N_i(t)/N_j(t)$, approaches asymptotically this coefficient ($B_i$) as $t \to \infty$. Therefore the share of each member (i) in the economy's net worth in the long run can be expressed in terms of this member's status coefficient ($B_j$): this share tends to the ratio $B_i/(B_i + 1)$ as $t \to \infty$ (Appendix B, section B16).

These limits, termed equity shares, demonstrate that, over time, the distribution of the economy's net worth increasingly reflects the personal value system ($w_i, l_i, a_i, b_i$), represented by the status coefficient of each member (i). In Aristotelian terms, this "proportionate equality" (Appendix A, section A3) in the distribution of the net worth in a positively balanced economy—as proportionality is subjectively perceived by each member—is achieved in the long run, regardless of whether the economy is closed, or open laissez-faire, or open mixed.

### 5.1.2 Resource Utilization

In positively balanced economies, whether they are closed, or open laissez-faire, or open mixed with contractionary or neutral government policy, the growth rate remains positive and asymptotically approaches zero from above over time (Note 19).

However, in an open mixed economy with expansionary government policy, the growth rate approaches asymptotically the policy factor ($\rho$), which represents the long-term rate of change in the economy's net worth (Appendix B, section B17). This type of growth increases the demand for natural resource utilization across the economy's sectors continuously and exponentially.

<figure><img src="image_5.png" /><figcaption>Figure 4. Cohesively effective wealth redistribution</figcaption></figure>

*Note.* Under these conditions, wealth redistribution repositions the entrapped economy from point W to point W', outside the hubris zone, while preserving the existing socioeconomic class structure (section 5.3).

## 5.2 Effective Wealth Redistribution

The preceding analysis focuses on positively balanced economies that are perfectly shielded from both indebtedness and stagnation. In reality, however, most economies exhibit motivation structures that are not positively balanced and are thus vulnerable to the risk of future debt crises.

When a high-motivation economy becomes entrapped within its hubris zone, wealth redistribution can serve as a policy tool to reposition the economy outside of this zone. The key policy questions surrounding such redistribution are:
* Is *effective* wealth redistribution economically feasible?

* Which sector should be favored?

* What is the appropriate amount of wealth redistribution?

* Should the implementation of the redistribution be gradual (as in policies of mild adjustment) or instantaneous, as in shock therapy (Appendix C)?

In an entrapped high-motivation economy, effective wealth redistribution (as from W' to W'' in Figure 1), such that it enables the economy to exit the hubris zone, is economically feasible only if the slope of the saddle path differs from -1 (Appendix B, section B19). While this condition is necessary for such redistribution, it is not sufficient on its own.

Beyond this feasibility condition, the choice between populist or liberal wealth redistribution policies—favoring the pauper or the prince, respectively—depends on the economy's motivation structure (Appendix B, section B20): If the slope of the saddle path is steeper (i.e., less than -1) with respect to the axis of member (i) (i.e., the $N_1$-axis), wealth redistribution should favor this member (e.g., the pauper in Figure 1); conversely, if the slope is greater than -1, the wealth redistribution should favor the other member (j) (e.g., the prince in Figure B3).

These conditions highlight the relativist nature of the model. In either case—*populist* or *liberal* policies—the redistribution should be of sufficient magnitude (Appendix B, section B21) and implemented instantaneously (Note 20) to be effective.

## 5.3 Socioeconomic Cohesion

Effective wealth redistribution is also contingent on the political will to implement such a policy, which may need to be drastic and executed in a single phase. However, in the absence of debt restructuring, political economy constraints may obstruct such redistribution, due to its potential to destabilize the existing class structure. For example, in Figure 1, after effective wealth redistribution repositions the entrapped economy from point W' inside the hubris zone to point W'' outside it, the pauper becomes the new “prince” (the wealthier sector).

However, in Figure 4, where the saddle path is relatively steep with respect to the $N_1$-axis, the effective populist wealth redistribution—in favor of the pauper—from point W to point W' does not entail a reversal of the class structure. This is because the saddle path is positioned to the right of the intersection (η) of the *wealth-redistribution* line with the *egalitarian-distribution* line. The former passes through the economy's position (W) and forms a 135° angle with the $N_1$-axis, while the latter passes through the origin at a 45° angle with the same axis. Such redistribution is characterized as *cohesively effective* (Note 21).

## 5.4 Comprehensive Debt Reduction

If the saddle path of an entrapped economy is relatively steep with respect to the $N_1$-axis and is positioned to the right of the intersection of the wealth-redistribution line and the egalitarian-distribution line (as depicted in Figure 5), then an effective wealth redistribution in favor of member (i) (as from point W to point W'' in Figure 5) would not be socioeconomically cohesive.

Under these conditions, a policy mix of wealth redistribution and debt reduction may enable the economy to escape its debt trap without disrupting its socioeconomic class structure, while simultaneously minimizing creditor losses due to the reduction.

As shown in Figure 5, this policy mix, termed *comprehensive debt reduction* (or, equivalently, *conditional debt restructuring*), would reposition the economy from point W inside the hubris zone to point W' outside this zone, just above the intersection of the saddle path and the egalitarian-distribution line. This intersection (point $\delta$ in Figure 5), termed the *saddle-path egalitarian point* (Note 22), is central to this policy, which includes the following three actions (specified algebraically in Appendix B, section B25):

- *Wealth redistribution*, in favor of the underprivileged sector, that repositions the economy from point W to point $\xi$ on the wealth-redistribution line within the hubris zone. Both point $\xi$ and the saddle-path egalitarian point share the same coordinate ($\xi_2$ and $\delta_2$ respectively) on the axis of the other sector ($N_2$-axis in the figure).

- *Debt reduction*, also in favor of the underprivileged sector, by an amount represented by the horizontal distance (the red-dashed line segment in Figure 5) between points $\xi$ and $\delta$, which repositions the economy horizontally from the former to the latter point.

- *Debt reduction*, in favor of the other (privileged) sector, by a relatively small amount $u$, that repositions the economy vertically from the saddle-path egalitarian point to point W' outside the hubris zone.

These three components of comprehensive debt reduction must all be implemented in a single
phase—simultaneously and instantaneously, as in the macroeconomic adjustments of FRG (1951), Bolivia (1985), Poland (1991) and Russia (2000) (Appendix C)—so that there is no time for the system’s dynamics to distort the policy’s implementation (as they do in Figure B4). Only then will the policy be cohesively effective *and* minimize creditor losses due to debt reduction (Appendix B, section B26). As a result, the *transitional egalitarian* structure of comprehensive debt reduction (Appendix B, section B27) serves the interests of both creditors and debtors in the economy (Note 23).

<figure><img src="image_6.png" /><figcaption>Figure 5. Comprehensive debt reduction</figcaption></figure>

*Note.* Under these conditions, comprehensive debt reduction repositions the entrapped economy from point W to point W', outside the hubris zone, while preserving the existing socioeconomic class structure and minimizing creditor losses. Specifically, redistribution shifts the system from W to ξ, debt restructuring moves it from ξ to δ, and marginal debt reduction completes the transition from δ to W' (section 5.4).

# 6. Concluding Remarks, Policy Recommendations and Further Research

## 6.1 *Conclusion*

A positively balanced economy ensures long-term socioeconomic cohesion, as the distribution of net worth across sectors aligns with each sector's value system. It also fosters sustainable economic growth with zero exposure to future debt and recession crises, and with minimal natural resource utilization, as the growth rate asymptotically approaches zero from above over time.

However, when the government adopts an expansionary economic policy to raise the growth rate, this rate stabilizes in the long run at a constant level, determined by policy choices. This leads to exponential, unbounded growth, which continually increases demand for natural resource utilization across all sectors.

## 6.2 *Policy Recommendations*

In the absence of a positively balanced motivation structure, an economy becomes vulnerable to sovereign debt crises. If creditor confidence is abruptly lost, then such an economy may fall into a debt trap, triggering a full-scale crisis. The model outlines specific policy alternatives for managing such crisis effectively, enabling the economy to exit the debt trap while preserving its underlying socioeconomic class structure and at the same time minimizing creditor losses. These alternatives are context-specific, i.e., *wealth redistribution* (without debt reduction); *unconditional debt reduction* (Appendix B, section B28); *wealth redistribution with insignificant debt reduction* (Appendix B, section B29); and *comprehensive debt reduction*, which combines wealth redistribution with significant but minimized debt relief (Note 25).

To be effective, each alternative must be implemented in a single phase—instantaneously in this dynamic
model—which, from a political economy perspective, requires democratic consensus and broad public support for such reform, ideally resembling the Polish paradigm of the 1990s (Appendix C, section C2). Moreover, the model’s relativist logic determines whether the policy should be liberal, populist, or even temporarily egalitarian, depending on the economy’s structural conditions. In this context, comprehensive debt reduction entails a transitional (temporary) egalitarian restructuring, which aims at protecting creditor interests by minimizing creditor losses. Under specific conditions, this kind of reset aligns with temporary egalitarian policies historically employed during the transformation from a peace economy to a war economy in periods of total warfare (Appendix B, section B30).

### 6.3 Recommendation for Further Research

Beyond its normative prescriptions, the dynamic model developed in this paper also contributes a diagnostic tool that may complement the IMF's static balance sheet approach. By offering a dynamic lens for identifying financial distress, this model enhances the interpretation of key stock variables—particularly the net worth of the public sector—as potential indicators of sovereign debt risk. When analyzed dynamically, such variables may offer more reliable signals than when viewed in static terms. Consequently, empirical research is needed for each economy to determine not only whether these values are negative, but whether they position the economy within or outside a debt trap or hubris zone (Appendix B, section B31). To this end, comparative dynamic analysis that would involve tracking the dynamic behavior of key stock variables across economies with differing institutional structures and policy responses could further validate the model's predictive capacity and refine its application in real-world policy contexts.

### Acknowledgments

The author expresses gratitude to (a) Prof. George Babiniotis, former Rector of the National and Kapodistrian University of Athens, for his encouragement and academic support on the author's interdisciplinary research on "*the highly nuanced and complex concept of measure*," (b) the late Ronald Finlay, former Rargar Nurkse Professor of Economics at Columbia University, for his invaluable comments on an earlier draft of this paper, (c) the Department of Economics at Columbia University for a doctoral fellowship that was conducive to the research leading to this article. The author thanks the anonymous reviewers and editors at the International Journal of Economics and Finance for their valuable comments that improved this work.

### Author Contributions

The author independently conceived the model and carried out the research that led to this paper.

### Funding

No financial support accompanied this research.

### Competing interests

The author declares that he has no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

### References

Alesina, A., Omar, B., Carlo, F., Francesco, G., & Matteo, P. (2017). The Effects of Fiscal Consolidations: Theory and Evidence. *NBER Working Paper 23385*. https://doi.org/10.3386/w23385

Allen, M., Christoph, R., Christian, K., Brad, S., & Nouriel, R. (2002). A Balance Sheet Approach to Financial Crises. *IMF Working Paper 2210*.
Retrieved from https://www.imf.org/external/pubs/ft/wp/2002/wp02210.pdf

Araujo, R. A., & Joanílio, R. T. (2004). Structural Economic Dynamics: an Alternative Approach to North-South Models. *Cambridge Journal of Economics*, 8(5), 705-717. https://doi.org/10.1093/cje/beh031

Asonuma, T., & Christoph, T. (2016). Sovereign Debt Restructurings: Preemptive or Post-Default. *Journal of the European Economic Association*, 14(1), 175-214. https://doi.org/10.1111/jeea.12156

Booth, A. J. (1869). *Robert Owen: The Founder of Socialism in England* (p. 181). London, UK: Trübner.

Budina, N., & Norbert, F. (2005). *Public Debt and its Determinants in Market Access Countries: Results from 15 Country Case Studies*. Washington, DC: World Bank. Retrieved from:
https://www publicdebtnet org pdm/content/PaginaInternaConDocuments/ECONOMIC-ANALYSES-AND-POLICIES/Macroeconomic-Analysis-/Documents/DOCUMENT_20090129122945.html

Burgess, M. G., Amanda, R. C., Steven, D. G., Alessandro, P., & Steve, V. (2021). Prepare developed
democracies for long-run economic slowdowns. *Nature Human Behaviour*, 5, 1608-1621.
https://doi.org/10.1038/s41562-021-01229-y

Cochran, & Thomas, C. (1971). The Entrepreneur in Economic Change. In Peter Kilby (Ed.), *Entrepreneurship and Economic Development* (pp. 95-107). New York, NY: The Free Press.

Cones, R. (1992). *Duality and Modern Economics*. Cambridge, UK: Cambridge University Press.
https://doi.org/10.1017/CBO9780511571725

Daniel, J., Jeffrey, D., Manal, F., & Caroline, V. R. (2006). Fiscal Adjustment for Stability and Growth. *IMF Pamphlet Series*, 55, 58-59. International Monetary Fund.
Retrieved from https://www.imf.org/external/pubs/ft/pam/pam55/pam55.pdf

Darwish, M. A. (2023). Optimal workday length considering worker fatigue and employer profit. *Computers & Industrial Engineering*, 179. https://doi.org/10.1016/j.cie.2023.109162

Das, U. S., Michael, G. P., & Christoph, T. (2012). Sovereign Debt Restructurings 1950–2010: Literature Survey, Data, and Stylized Facts. *IMF Working Paper 12/203*. https://doi.org/10.5089/9781475505535.001

De Grazia, S. (1962). *Of Time, Work and Leisure*. New York, NY: Twentieth Century Fund.

Duesenberry, J. (1949). *Income, Savings and the Theory of Consumer Behavior*. Cambridge, MA: Harvard University Press.

Edgerton, D. (2011). *Britain's War Machine: Weapons, Resources, and Experts in the Second World War* (pp. 168-176). Oxford, UK: Oxford University Press.

Edmonds, G. W., Goldberg, L. R., Hampson, S. E., & Barckley, M. (2013). Personality stability from childhood to midlife: Relating teachers' assessments in elementary school to observer- and self-ratings 40 years later. *Journal of Research in Personality*, 47, 505-513. https://doi.org/10.1016/j.jrp.2013.05.003

Elder, M. (2008). *How the State Got a Grip on Energy*. Moscow Times (March 14).

Fisher, I. (1892). *Mathematical Investigations in the Theory of Value and Prices*. New Haven, CN: Yale University Press.

Freeman, K. (1976). The Significance of McClelland's Achievement Variable in the Aggregate Production Function. *Economic Development and Cultural Change*, 24(2), 815-824. https://doi.org/10.1086/450921

Guinnane, T. W. (2004). Financial Vergangenheitsbewaeltigung: The 1953 London Debt Agreement. *YUEGC Research Paper 880*. Yale University Economic Growth Center http://dx.doi.org/10.22004/ag.econ.28387

Guzman, M., & Joseph, E. S. (2016). Creating a Framework for Sovereign Debt Restructuring That Works. In M. Guzman, J. A. Ocampo, & J. E. Stiglitz (Eds.), *Too Little, Too Late: The Quest to Resolve Sovereign Debt Crises* (pp. 3-32). New York Chichester, West Sussex: Columbia University Press.
https://doi.org/10.7312/guzm17926-003

Hagen, E. E. (1963). How Economic Growth Begins: A Theory of Social Change. *Journal of Social Issues*, 19, 20-24. https://doi.org/10.1111/j.1540-4560.1963.tb00428.x

Hampson, S. E., & Goldberg, L. R. (2006). A first large cohort study of personality trait stability over the 40 years between elementary school and midlife. *Journal of Personality and Social Psychology*, 91, 763-779.
https://doi.org/10.1037/0022-3514.91.4.763

Hemingway, J. L. (1988). Leisure and Civility: Reflections on a Greek Ideal. *Leisure Sciences*, 10, 179-191.
https://doi.org/10.1080/01490408809512188

Hemingway, J. L. (1996). Emancipating Leisure: The Recovery of Freedom in Leisure. *Journal of Leisure Research*, 28(1), 27-43. https://doi.org/10.1080/00222216.1996.11949759

Hoselitz, B. F. (1963). Entrepreneurship and Traditional Elites. *Explorations in Entrepreneurial History (Second series)*, 1, 36-49.

International Monetary Fund. (2005). Bolivia: Ex-Post Assessment of Longer-Term Program Engagement. *IMF Country Report 5-139* (p. 39). https://doi.org/10.5089/9781451970500.002

Janssen, J. (2001). New Zealand's Fiscal Policy Framework: Experience and Evolution. *Treasury Working Paper* 01/25. New Zealand Treasury. https://doi.org/10.2139/ssrn.2095164

Kahneman, D. (2011): Thinking, Fast and Slow. *Statistical Papers*, 55, 915.
https://doi.org/10.1007/s00362-013-0533-y
Kant, I. (1785). *Groundwork of the Metaphysics of Morals* (trans. Mary Gregor), AK 4:421, 31. Cambridge, UK: Cambridge University Press (1998). https://doi.org/10.1017/CBO9780511809590

Kant, I. (1786). *Metaphysical Foundations of Natural Science* (trans. & ed. Jonathan Bennett) ch. 2, 20-22. British Columbia, Canada: Early Modern Texts (2017).

Keen, M., Yitae, K., & Ricardo, V. (2006). The ‘flat taxes’: Principles and Evidence. *IMF Working Paper 6/218*. International Monetary Fund.

Kotlikoff, L. J. (2010). Is Uncle Sam Bankrupt? *NCPA Brief Analysis No. 689*.
Retrieved from https://www.ncpathinktank.org/pdfs/ba689.pdf

Krugman, P. (1988). Financing vs. Forgiving a Debt Overhang. *NBER Working Paper 2486*.
https://doi.org/10.3386/w2486

Lindbeck, A., Nyberg, S., & Weibull, J. (1999). Social norms and economic incentives in the welfare state.
*Quarterly Journal of Economics, 114*(1), 1-35. https://doi.org/10.1162/003355399555936

Livio, M. (2002). *The Golden Ratio: The Story of Phi, the World's Most Astonishing Number* (p. 6). New York, NY: Broadway Books.

Locke, J. (1690). *Two Treatises on Government* (ch. II(V), pp. 115-126). London, UK: Thomas Tegg et al. (1823).

Maridal, H. J. (2013). Cultural impact on national economic growth. *The Journal of Socio-Economics, 47*, 136-146. https://doi.org/10.1016/j.socec.2012.08.002

Mayer, T., & Gunther, S. (2021). How to Escape from the Debt Trap: Lessons from the Past. *CESifo Working Paper* 9078. Center for Economic Studies and Ifo Institute (Munich). https://doi.org/10.2139/ssrn.3848340

McClelland, D. C., Atkinson, J. W., Clark, R. A., & Lowell, E. L. (1953). *The Achievement Motive*. New York, NY: Appleton-Century-Crofts. https://doi.org/10.1037/11144-000

Mian, A., Ludwig, S., & Amir, S. (2021). Indebted Demand. *BIS Working Paper* 968, 27-30. Bank of International Settlements (Switzerland). https://doi.org/10.1093/qje/qjab007

Moyer, J. D. (2023). Modeling transformational policy pathways on low growth and negative growth scenarios to assess impacts on socioeconomic development and carbon emissions. *Scientific Reports, 13*, 15996. https://doi.org/10.1038/s41598-023-42782-y

Nietzsche, F. W. (1873). *Philosophy in the Tragic Age of the Greeks* (trans. Marianne Cowan, p. 61).
Washington, DC: Regnery Gateway (1962).

Nurkse, R. (1952). Some International Aspects of the Problem of Economic Development. *American Economic Review, 42*, 570-600.

Oudemans, Th. C. W., & André, P. M. H. L. (1987). *Tragic Ambiguity - Anthropology, Philosophy and Sophocles' Antigone* (p. 203). Leiden, Nederlands: E.J. Brill. https://doi.org/10.1163/9789004246539

Pappas, J. D. (2014). The Concept of Measure and the Criterion of Sustainability. *The St. John's Review, 56*(1), 74-94. https://doi.org/10.5281/zenodo.15465422

Patel, K., & Horacio, S. (2023). *Policies for Improving Sovereign Debt Restructurings* (Economic Brief 23-04).
Federal Reserve Bank of Richmond.
Retrieved from https://www.richmondfed.org/publications/research/economic_brief/2023/eb_23-04

Pigou, A. C. (1903). Some Remarks on Utility. *Economic Journal, 13*, 58-68. https://doi.org/10.2307/2956866

Piketty, T. (2014). *Capital in the Twenty-First Century* (trans. Arthur Godlhammer). Cambridge, MA: Harvard University Press. https://doi.org/10.4159/9780674369542

Reinhart, C. M., & Kenneth, S. R. (2010). Growth in a Time of Debt. *American Economic Review, 100*(2), 573-578. https://doi.org/10.1257/aer.100.2.573

Robinson, T. M. (1987). *Heraclitus: Fragments* (p. 185). Toronto, Canada: University of Toronto Press.

Rockoff, H. (1998). The United States: from ploughshares to swords. In Mark Harrison (Ed.), *The Economics of World War II: Six Great Powers in International Comparison* (pp. 81-121). Cambridge, UK: Cambridge University Press. https://doi.org/10.1017/CBO9780511523632

Rodrik, D. (2006). Goodbye Washington Consensus, Hello Washington Confusion? A review of the World Bank's Economic Growth in the 1990s: Learning from a Decade of Reform. *Journal of Economic Literature,*
44(4), 973-987. https://doi.org/10.1257/jel.44.4.973

Rosenberg, C., Ioannis, H., Brett, H., Christian, K., Jens, N., Alexander, P., & Brad, S. (2005). Debt Related Vulnerabilities and Financial Crises. An Application of the Balance Sheet Approach to Emerging Market Countries. *IMF Occasional Paper 240*. International Monetary Fund.
https://doi.org/10.5089/9781589064256.084

Rutland, P. (2008). Putin's Economic Record: Is the Oil Boom Sustainable? *Europe-Asia Studies*, 60(6), 1051-1072. https://doi.org/10.1080/09668130802180975

Sachs, J. (2002). Measure, Moderation, and the Mean. *The St. John's Review*, 46(2), 7. Retrieved from
http://digitalarchives.sjc.edu/files/original/2b69b2ce561c611b2fc3cefb8e8bdaec.pdf

Sachs, J. D. (1990). A strategy for efficient debt reduction. *The Journal of Economic Perspectives*, 4(1), 19-29.
https://doi.org/10.1257/jep.4.1.19

Sachs, J. D. (1993). Poland's Jump to the Market Economy. *Lionel Robbins Lectures*. Cambridge, MA: MIT Press.
https://doi.org/10.7551/mitpress/5430.001.0001

Sachs, J. D. (1994). Shock Therapy in Poland: Perspectives of Five Years. *The Tanner Lectures on Human Values* (pp. 275-276 and 281-282). Salt Lake City, UT: University of Utah. Retrieved from
https://tannerlectures.org/lectures/shock-therapy-in-poland-perspectives-of-five-years/

Soldz, S., & Vaillant, G. E. (1999). The Big Five personality traits and the life course: A 45-year longitudinal study. *Journal of Research in Personality*, 33, 208-232. https://doi.org/10.1006/jrpe.1998.2235

Stephenson, J. (2023). Cultural Stability. In: *Culture and Sustainability* (pp. 118-119). Cham, Switzerland: Palgrave Macmillan. https://doi.org/10.1007/978-3-031-25515-1

Stiglitz, J. E. (2002). Globalization and its Discontents. *Economic Notes*, 32(1), 123-142.
https://doi.org/10.1046/j.0391-5026.2003.00107.x

Theobald, R. (1960). *The Rich and the Poor; a Study of the Economics of Rising Expectations*. New York, NY: C. N. Potter.

Thiessen, G. G. (2001). *Canada's Economic Future: What Have We Learned from the 1990s?* (Remarks by the Governor of the Bank of Canada). Bank of Canada.
Retrieved from https://www.bankofcanada.ca/wp-content/uploads/2010/01/sp01-1.pdf

Traa, B., & Alina, C. (2007). A Government's Net Worth. *Finance and Development*, 44(2).
http://dx.doi.org/10.5089/9781451866584.087

Veblen, T. (1899). *The Theory of the Leisure Class* (introd. John Kenneth Galbraith). Boston, MA: Houghton Mifflin (1973).

Vinton, L., & Ben, S. (1994). Bad Debts and the Polish Restructuring Program. *MOCT-MOST: Economic Policy in Transitional Economies*, 4(3), 85-108. https://doi.org/10.1007/BF00993831

Weber, M. (1905). *The Protestant Ethic and the Spirit of Capitalism*. New York, NY: Taylor & Francis.
https://doi.org/10.4324/9781315063645

Young, F. (1971). A Macrosociological Interpretation of Entrepreneurship. In Peter Kilby (Ed.), *Entrepreneurship and Economic Development* (pp. 139-149). New York, NY: The Free Press.

## Notes

Note 1. According to Aristotle, "*politically organized societies (poleis) consist of two classes, the people with no economic resources and those in control of the resources*" (Aristotle, *Politics*, V.1315a: 32-33). In this context, this paper might be considered a "Leibnitzian" footnote to Aristotle's work on measure: by using mathematical tools of dynamic analysis—invented simultaneously by Pascal and Leibnitz two millennia after Aristotle—the paper presents a dynamic model of basic theoretical constructs of measured socioeconomic interaction, in a context laid out by Aristotle.

Note 2. This paper presents a qualitative theory aligned with the IMF's quantitative *balance sheet approach* for diagnosing vulnerabilities in national and regional economies (Traa & Carare, 2007; Allen et al., 2002; Rosenberg et al., 2005). Still, in lieu of the IMF's term *net worth*, the term *net wealth* (i.e., total *net* value of assets) may be used in order to avoid logical, historical and ethical pitfalls associated with the accounting term "net worth" when applied to human beings at any level (individual, social, national, regional, or global).
Note 3. The two members (prince and pauper) in this dyadic economy can represent not only the sectors of a two-sector economy but also two antagonistic countries, or groups of countries in a regional economy (e.g., the G7 versus the rest of the world), and so on. In general, the present (dyadic) model builds analytically on two-sector models (Theobald, 1960; Cones, 1992; Araujo & Teixeira, 2004). The methodology of using metaphors from the behavior of a single individual or a small group of individuals (e.g., a family) to draw inferences about the socioeconomic dynamics or political affairs of a state, was employed by Aristotle (*Ethics*, 1100a4-9; *Economics*, 1.1343a, 2.1345b).

Note 4. According to Aristotle, "*Nature herself... requires that we should be able, not only to work properly, but also to use leisure well... Both are required, but the ultimate choice is for leisure rather than work, because the former is the natural end of the latter.*" (Aristotle, *Politics*, 8.1337b:30-35). In the Aristotelian worldview, work is a means to leisure or *scholē* (σχολή, which is the Greek root of the English word *school*), meaning well-used free time that allows one to pursue non-material or idealistic goals (Hemingway, 1988 and 1996) such as advancing one's intellect or attaining virtue in civic affairs (De Grazia, 1962). Thus, leisure is not necessarily recreational and should not be confused with idleness or "conspicuous leisure" (Veblen, 1899).

Note 5. A work-oriented individual may find inherent value in work itself, not merely as a means to acquire material possessions (Weber, 1905). Such an individual may even live in a Lockean world, where one must constantly strive to create property and value through creative labor (Locke, 1690).

Note 6. In the context of national economies, the terms "intrinsic coefficient" ($a_i$) and "interaction coefficient" ($b_i$) can be adapted to "intrasectoral coefficient" and "intersectoral coefficient" respectively for modeling two economic sectors, or "national coefficient" and "international coefficient" respectively for modeling interactions between two countries.

Note 7. The first attempt to incorporate interpersonal comparisons of consumption levels into utility theory was made by Pigou (1903), who specified a utility function that included as dependent variable a (weighted by a "social distance" factor) sum of others' possessions, as suggested by Fisher (1892). Duesenberry (1949) linked these comparisons to the savings ratio, and Nurkse (1952) extended them to economic growth by applying Duesenberry's approach (interclass comparisons) to international comparisons. Regarding the positive impact of the demonstration effect on productivity, this model assumes that social status is based on material wealth (Hoselitz, 1963), drawing on theories of the intergroup relations' impact on motivation (Hagen, 1963; Young, 1971; Cochran, 1971) and their potential effect on welfare policies (Lindbeck, Nyberg, & Weibull, 1999). Concerning a country's overall motivation, Freeman (1976), following McClelland's (1953) earlier work, found a significant correlation between economic growth and societal motivation. In this model, socioeconomic interaction plays a crucial role in the system's dynamic behavior.

Note 8. In a closed economy, like the former USSR or present-day North Korea, the international information coefficient ($\gamma_i$) is nearly zero ($\gamma_i \cong 0$). In an isolated economy, such as the Robinson Crusoe economy, that coefficient is exactly zero ($\gamma_i = 0$).

Note 9. In a purely laissez-faire economy with no government intervention, the policy factor equals zero ($\rho = 0$). However in reality, fiscal policies can significantly affect the value of this factor, e.g., through tariffs, taxation, and investment incentives. In this model, it is assumed that these policies remain stable over time, meaning this factor is constant in the medium term within an intragenerational period.

Note 10. The autarky net worth ($G_i$) reflects the $i^{th}$-member's perception of the trade-offs between teleonomial needs for net-wealth accumulation ($g_i$) and intrinsic needs for both work and leisure time ($a_i$). A notable literary example is Robinson Crusoe, who worked constructively on his island only until he achieved a net worth equal to $G_i$, which represents the net value of his living quarters and surroundings necessary for sustaining an autarkic life in isolation.

Note 11. As depicted in Figure 1, the angle ($h_i$) of the demarcation line ("$\dot{N}_i = 0$") of each member ($i$) with the (dashed) vertical line to the $N_i$-axis at intersection point $G_i$ is equal the arctangent of the member's status coefficient: $h_i = \arctan(B_i)$.

Note 12. The negative partial derivative of $\dot{N}_i$ with respect to $N_i$ in leisure-oriented economies (where $a_i < 0$) implies that as we move from west [south] to east [north] in Figure 1, i.e., as $N_1[N_2]$ increases, $\dot{N}_1[N_2]$ decreases, so that the sign of $\dot{N}_1[N_2]$ passes through three stages, in the order +, 0, -. Therefore, we append the plus sign on the left [below] and the minus sign on the right of [above] the "$\dot{N}_1 = 0$" ["$\dot{N}_2 = 0$"] demarcation line. Based on these plus and minus signs, a set of directional arrows—like the blue [green] horizontal [vertical] arrows in Figures 1-3—can be drawn to indicate the intertemporal movement of $N_1[N_2]$ in the four areas delineated on the
phase plane by the two intersecting demarcation lines (Figures 1-2), or in the three areas delineated by the two parallel demarcation lines (Figure 3).

Note 13. The term “*positively balanced*” is attributed to balanced economies whose (parallel) demarcation lines are positively (upward) sloped, as in Figure 3. On the contrary, if a balanced economy is work-oriented (where $b_i b_j = a_i a_j$, but $a_i, a_j > 0$), then the demarcation lines are still parallel but they are negatively (downward) sloped. Consequently, the latter economies are characterized as “*negatively balanced*” and are marked by a hubris zone.

Note 14. In the present version of the model, a change in the economy's motivation structure—specifically, an increase in the interaction coefficient ($b_i$) of each member (i)—resulting from opening the country's information borders is assumed to be absent, as specified in relation (1') and discussed in Appendix B, section B11.

Note 15. For a review and graphical depiction of the movement of each demarcation line (which, as it moves over time, forms a *demarcation surface*) in the three-dimensional space (where the third dimension is time *t*), and the concomitant movement of the stationary point (which, as it moves over time, delineates a *stationary path*, where the two demarcation surfaces intersect), see Appendix B, section B13.

Note 16. For the algebraic expression of the stationary point over time in an open mixed economy, see Appendix B, section B14 (relations (B10) and (B11)). For the general solution of the non-autonomous system of an open mixed economy, see Appendix B, section B14 (relation (B13)).

Note 17. In line with the definition of *socioeconomic measure* (section 4.4), the general definition of measure is articulated epigrammatically as: *Measure is a condition of balancing internal trends and external influences, fostering an environment conducive to cultural development*. This definition reflects: (1) a fundamental law of nature, whereby a system's internal forces (e.g., blood pressure) balance out the environment's qualitatively similar forces (e.g., atmospheric pressure) exerted on the system, which ceases to exist as soon as it deviates from such balancing equilibrium beyond a quantifiable range of variation (Kant, 1786); (2) the Aristotelian view of leisure for personal and cultural development as a precondition for the realization of the potential of both the individual and the society (Aristotle, *Politics*, 8.1338a:1-45;8.1338b:1-4).

Note 18. As summarized in Appendix B, section B15, in a closed or open laissez-faire economy that is positively balanced, the attractor is the demarcation line “$\dot{N}_i = 0$” of the member (i) with the *lower* status coefficient ($B_i < B_j$). Likewise, in a positively balanced open mixed economy, the attractor is the demarcation surface “$\dot{N}_i(t) = 0$” of the member (i) with the *lower* status coefficient.

Note 19. In recent bibliography, the phenomenon of economic slowdowns of (positive) growth rates in advanced and highly indebted economies in the long run, is analyzed from different perspectives (Burgess, 2021; Moyer, 2023; Piketty, 2014). The long-term growth rate in the economy's net worth is derived in Appendix B, section B17.

Note 20. The importance of instantaneity in wealth redistribution—as opposed to *gradual* or *mild* adjustment—is shown in Appendix B, section B22 (Figure B4). The argument for large-scale, instantaneous wealth redistribution, as a policy tool to escape a debt trap, aligns with the economic literature on fiscal adjustment for debt crisis resolution (Alesina et al., 2017; Daniel et al., 2006; Mayer & Schnabl, 2021; Mian et al., 2021).

Note 21. The socio-political feasibility conditions for *cohesively effective* wealth redistribution are specified algebraically in Appendix B, section B23.

Note 22. The net worth of each sector when the economy is positioned on the *saddle-path egalitarian point* is specified algebraically in Appendix B, section B24.

Note 23. Minimizing creditor losses through *comprehensive debt restructuring* serves the interests not only of creditors—considering the tradeoff between financing a debt overhang and forgiving it (Krugman, 1988)—but also those of debtors: evidence suggests that while credit markets may “forgive,” they rarely “forget” (Cruses, 2013).

Note 24. Comprehensive debt reduction aligns with economic literature on the importance of swift debt restructuring with significant haircuts, combined with fiscal consolidation—either directly or indirectly through wealth redistribution—to restore fiscal stability and improve growth trajectories post-crisis (Asonuma & Trebesch, 2016; Das et al., 2012; Patel & Sapriza 2023).

Note 25. This model's relativist approach to debt crisis management is summarized algorithmically in Figure B5.
# Appendix A

## Classical Concepts of Measure, Justice and Equity

### A1 Measure

The economic concept of *equilibrium* differs from the philosophical concept of *measure*. Historical examples show that equilibrium can sometimes lead to hubris. For instance, in 1930s the German economy attained macroeconomic equilibrium, marked by massive rearmament at the time, but deviated perilously from measure, ultimately leading Germany to national ruin and intertemporal infamy.

In recorded world history, the concept of measure was initially perceived about three millennia ago: It appears 12 times in *Odyssey* (e.g, Bk. 2, l. 231, Bk. 5, l. 9, Bk. 7, l. 310, Bk. 14, l. 434, Bk. 15, l. 71, Bk. 17, l. 321, Bk. 21, l. 294, and Bk. 22, l. 46). Homer uses the word *aisima* (αἴσιμα) for *measure*, related to Aisa (Αἴσα), the Greek goddess personifying human destiny. In the Homeric context, human actions are *measured* if they remain within predestined bounds.

Half a millennium later, Aristotle's defined measure (μέτρον) as a "mean" between deficiency (ἔλλειψις) and excess (ύπερβολή). Such a mean suggests a balance that is closer to one extreme than the other. Unlike the arithmetic mean, the Aristotelian mean is subjective ("the mean relative to us") and applies dynamically to human interaction. Therefore it is not the same for different people, as it is perceived subjectively, nor does it remain static, as it evolves with changes in internal states and external conditions (Aristotle, *Nichomachean Ethics*, *Ethics*, 1106a25-35).

But the Aristotelian definition of measure raises a critical question: *how much* closer to one extreme should this balance be? Likewise, in contemporary lexicography, measure is defined as "due proportion; due restraint," and so on; however, such tautological definitions are of limited utility as they immediately raise the question: what exactly is "due"?

From a traditional academic perspective, defining measure in human affairs may be impossible; even the golden ratio (Euclid, *Elements*, Book 6, Definition 3) is an irrational number, defying complete mathematical precision. This ratio ($φ ≅ 1.6180339...$), which is the asymptotic limit of the Fibonacci sequence $F_{n+1}/F_n$, has inspired thinkers across disciplines like no other number in the history of mathematics (Livio, 2002). Still, "numbers are too crude an instrument by which to know something our eyes know at a glance" (Joe Sachs, 2002). As a consequence, in the social sciences, measure is a fuzzy concept (Pappas, 2014).

### A2 Hubris and Nemesis

Heraclitus', the Great Tragedians' and Nietzsche's view of hubris as significant deviation from measure (Nietzsche, 1873) has limited utility without a precise definition of measure to determine ex ante—before the intervention of retributive Nemesis—whether the deviation is indeed significant (hubristic).

Such deviations from measure are intertwined with of even embedded in human nature, because "*Nature and man have boundaries apportioned to them, but finite beings are unable to stay within these boundaries. They are 'hybrid'. . . From their perspective, they have to stay within their boundaries, but they have to transcend them as well. It is both necessary and impossible to avoid transgression*" (Oudemans & Lardinois, 1987).

In this context, the nemesic effects of transcending such boundaries may be catastrophic, because "*[Heraclitus'*] unified, ordered world of balanced change is also a world in which the 'laws' or norms of justice prevail... *Justice that is cosmic law is the justice of disruption and revolution, of war and violence, not that of balm and healing'*" (Robinson, 1987). Indicatively, it is noteworthy that Kant articulated his categorical imperative—i.e., "*act only according to that maxim whereby you can at the same time will that it should become a universal law*" (Kant, 1785)—without reference to the concept measure, a cornerstone of classical civilization. As a consequence, the Kantian imperative has been used (and abused) hubristically by totalitarian regimes in the 20th century to the detriment of Western civilization.

### A3 Proportionate Equality

In light of the aforementioned "hybrid" human nature and the retributive and often catastrophic intervention of Nemesis, Aristotle theorized that "proportionate equality" ("τὸ κατ' ἀναλογίαν ἴσον") is a necessary condition for sociopolitical cohesion and economic progress (Aristotle, *Politics*, V.1301a:26-27). In fact, the concept of equity (proportionate equality) aligns with Aristotle's zero tolerance for injustice: "*it is important that both [classes] are committed to avoiding any act of injustice against each other*" ("μάλιστα μὲν ἀμφοτέρους ὑπολαμβάνειν δεῖ... τοὺς ἐτέρους ὑπὸ τῶν ἐτέρων ἀδικεῖσθαι μηδέν") (Aristotle, *Politics*, V.1315a:35).
<table><caption>Table B1. Intertemporal Net Worth of Public Sector in EU-27</caption><thead><tr><th rowspan="2">Rank*</th><th rowspan="2">Country</th><th colspan="2">Intertemporal net worth (% of GDP)</th></tr><tr><th>Finite</th><th>Infinite</th></tr></thead><tbody><tr><td>1</td><td>Cyprus</td><td>- 494</td><td>- 1,793</td></tr><tr><td>2</td><td>Greece</td><td>- 418</td><td>- 1,385</td></tr><tr><td>3</td><td>Luxembourg</td><td>- 383</td><td>- 1,745</td></tr><tr><td>4</td><td>Spain</td><td>- 307</td><td>- 986</td></tr><tr><td>5</td><td>Slovenia</td><td>- 287</td><td>- 1,262</td></tr><tr><td>6</td><td>Czech Rep.</td><td>- 256</td><td>- 996</td></tr><tr><td>7</td><td>Romania</td><td>- 252</td><td>- 1,097</td></tr><tr><td>8</td><td>Lithuania</td><td>- 250</td><td>- 857</td></tr><tr><td>9</td><td>Slovak Rep.</td><td>- 243</td><td>- 981</td></tr><tr><td>10</td><td>Netherlands</td><td>- 218</td><td>- 697</td></tr><tr><td>11</td><td>Ireland</td><td>- 213</td><td>- 812</td></tr><tr><td>12</td><td>Estonia</td><td>- 200</td><td>- 595</td></tr><tr><td>13</td><td>Malta</td><td>- 188</td><td>- 790</td></tr><tr><td>14</td><td>Austria</td><td>- 173</td><td>- 514</td></tr><tr><td>15</td><td>UK</td><td>- 172</td><td>- 558</td></tr><tr><td>16</td><td>Belgium</td><td>- 156</td><td>- 427</td></tr><tr><td>17</td><td>Germany</td><td>- 152</td><td>- 484</td></tr><tr><td>18</td><td>France</td><td>- 148</td><td>- 339</td></tr><tr><td>19</td><td>Finland</td><td>- 130</td><td>- 552</td></tr><tr><td>20</td><td>Italy</td><td>- 110</td><td>- 129</td></tr><tr><td>21</td><td>Portugal</td><td>- 106</td><td>- 273</td></tr><tr><td>22</td><td>Poland</td><td>- 72</td><td>- 140</td></tr><tr><td>23</td><td>Latvia</td><td>- 20</td><td>- 28</td></tr><tr><td>24</td><td>Denmark</td><td>- 2</td><td>87</td></tr><tr><td>25</td><td>Bulgaria</td><td>0</td><td>- 212</td></tr><tr><td>26</td><td>Sweden</td><td>43</td><td>- 25</td></tr><tr><td>27</td><td>Hungary</td><td>43</td><td>21</td></tr><tr><td colspan="2">Average (weighted) EU27</td><td>- 153</td><td>- 472</td></tr></tbody></table>

# Appendix B

## Mathematical and Statistical Remarks

### B1 Non-Autonomous System

The intrinsic coefficient ($a_i$) of each member ($i$) is constant in this (intragenerational) model, consistent with research on the stability of personality traits (Edmonds et al., 2013; Hampson & Goldberg, 2006; Soldz & Vaillant, 1999) and cultural traits (Maridal, 2013; Stephenson, 2023). The constancy of these coefficients is also aligned with the *intertemporal consistency* assumption in consumer choice theory.

In this context, setting $a_i = w_i - l_i$, the system of differential equations (1'), can be expressed in the following matrix form:

$$ \dot{\mathbf{N}}(t) - \mathbf{A}\mathbf{N}(t) = \mathbf{g} + \gamma\mathbf{e}^{\rho t} \quad (B1) $$

$$ \text{where } \mathbf{N}(t) = \begin{bmatrix} N_1(t) \\ N_2(t) \end{bmatrix} \quad \mathbf{A} = \begin{bmatrix} a_1 & b_1 \\ b_2 & a_2 \end{bmatrix} \quad \mathbf{g} = \begin{bmatrix} g_1 \\ g_2 \end{bmatrix} \quad \gamma = \begin{bmatrix} \gamma_1 \\ \gamma_2 \end{bmatrix} $$

### B2 Balancing Work and Leisure

The 40-hour workweek movement, which began as early as 1817 with the guiding ideal "Eight hours labour. Eight hours recreation, Eight hours rest" (Booth, 1869; Darwish, 2023), indicates a societal shift toward balancing work and leisure. Economies where most of the labor force works more than 40 hours per week are work-oriented, such as Japan (75.9%), the US (67.6%) and Switzerland (66.9%). In contrast, economies where less than 20% of the labor force works beyond 40 hours per week, like Finland (16.0%) and Norway (15.8%), may be considered leisure-oriented (ILO, Key Indicators – Data is for 2000).

### B3. Autonomous System

The autonomous system of differential equations for modeling a closed economy (relation (2')) can be

<footnote>*Rank order: top is worst (most indebted).</footnote>

<footnote>Source: IMF (2010)</footnote>
represented in the following matrix form:

$$ \dot{\mathbf{N}} - \mathbf{A}\mathbf{N} = \mathbf{g} \qquad (B2) $$

where $\mathbf{N} = \begin{bmatrix} N_1 \\ N_2 \end{bmatrix}$, and $\mathbf{A}$ and $\mathbf{g}$ are specified in relation B1 above.

## B4 Stationary Net Worth

According to IMF calculations, the net worth of the public sector in most EU27 countries is negative (Table B1). Furthermore, by 2010 the fiscal gap of the U.S. exceeded $77 trillion, i.e., more than five times country's GDP in that year (Kotlikoff, 2010).

## B5 Solution of the Autonomous System

In matrix form, the general solution of the autonomous system of a closed economy, is specified as follows:

$$ \begin{bmatrix} N_1(t) \\ N_2(t) \end{bmatrix} = \begin{bmatrix} \tilde{N}_1 \\ \tilde{N}_2 \end{bmatrix} + \begin{bmatrix} \beta_{11} & \beta_{12} \\ 1 & 1 \end{bmatrix} \begin{bmatrix} n_1 e^{r_1 t} \\ n_2 e^{r_2 t} \end{bmatrix} \qquad (B3) \\ \begin{bmatrix} n_1 \\ n_2 \end{bmatrix} = (r_1 - r_2)^{-1} \begin{bmatrix} (a_1 - r_2) / \beta_{11} & -(a_1 - r_1) \\ -(a_1 - r_2) / \beta_{11} & a_1 - r_1 \end{bmatrix} \begin{bmatrix} N_1(0) - \tilde{N}_1 \\ N_2(0) - \tilde{N}_2 \end{bmatrix} $$

where $r_k$ ($k = 1, 2$) are the system's two characteristic roots, also called eigenvalues, and $\beta_{ik}$ ($k = 1, 2$) are the adjusted status coefficients of each member (i):

$$ \beta_{ik} = -b_i/(a_i - r_k) \qquad (i, k) = (1, 2) \qquad (B3') $$

Each $\beta_{ik}$ represents the adjustment of the intrinsic coefficient ($a_i$) of each member (i)—and consequently (by relation (3')) of the member's status coefficient ($B_i$)—by eigenvalue $r_k$ so that the characteristic equation of the reduced linearization of the autonomous system (relation (B2)) is equal to zero, making the two equations of the reduced (homogenous) system linearly dependent:

$$ \begin{vmatrix} r-a_1 & -b_1 \\ -b_2 & r-a_2 \end{vmatrix} = r^2 - (a_1 + a_2)r + a_1 a_2 - b_1 b_2 = 0 \qquad (B4) $$

Solving this quadratic equation (B4) yields two distinct real eigenvalues ($r_1, r_2 \in \mathbb{R}$), given our assumption of positive interaction coefficients ($b_1, b_2 > 0$). Notably, the above general solution (relation (B3)) is expressed primarily in terms of the variables (or “value system”) of the first member (1). It may also be expressed primarily in terms of the variables (or “value system”) of the second member (2) as follows:

$$ \begin{bmatrix} N_1(t) \\ N_2(t) \end{bmatrix} = \begin{bmatrix} \tilde{N}_1 \\ \tilde{N}_2 \end{bmatrix} + \begin{bmatrix} 1/\beta_{21} & 1/\beta_{22} \\ 1 & 1 \end{bmatrix} \begin{bmatrix} n_1 e^{r_1 t} \\ n_2 e^{r_2 t} \end{bmatrix} \qquad (B3) \\ \begin{bmatrix} n_1 \\ n_2 \end{bmatrix} = (r_2 - r_1)^{-1} \begin{bmatrix} -b_2 & -(a_2 - r_2) \\ b_2 & a_2 - r_2 \end{bmatrix} \begin{bmatrix} N_1(0) - \tilde{N}_1 \\ N_2(0) - \tilde{N}_2 \end{bmatrix} $$

## B6 Saddle Path

If one eigenvalue ($r_1$) is positive and the other ($r_2$) is negative, then from relation (B3) we can derive the algebraic expression of the saddle path in terms of the adjusted status coefficient ($\beta_{i2}$) of each member (i) for the economy's negative eigenvalue ($r_2$). To this end, by setting $n_1 = 0$ in relation (B3)—this condition ($n_1 = 0$) neutralizes the (divergent) effect of the positive root ($r_1$) on the state variables and thus implies that the economy moves along the (convergent) saddle path of the system—we derive the following expression of the saddle path:

$$ N_i = \tilde{N}_i + \beta_{i2} (N_j - \tilde{N}_j) \qquad (i, j) \in \{(1, 2), (2, 1)\} \qquad (B6) $$

The expression in parentheses is termed the wealth privilege, denoted as $\hat{W}_j$, of member j: $\hat{W}_j = N_j - \tilde{N}_j$

## B7 Endowment Privilege

By equations (B6), we infer the necessary initial condition for a high-motivation leisure-oriented economy to grow in the long run:
$$N_i(0) > \tilde{N}_i + \beta_{i2}(N_i(0) - \tilde{N}_i) \quad (i, j) \in \{(1, 2), (2, 1)\} \quad (B7.a)$$

where $\beta_{i2} > 0$ for each member (i), because $r_2 < 0$. The difference inside the brackets, $N_i(0) - \tilde{N}_i$, is termed the endowment privilege, denoted as $\hat{W}_i(0)$, of member (j). In this context, relation (B7.a) implies that for a high-motivation leisure-oriented economy to grow in the long run, the endowment privilege of each member (i) must be higher than the product of this member's adjusted status coefficient ($\beta_{i2}$)—for the economy's negative eigenvalue ($r_2 < 0$)—and the other member's endowment privilege:

$$\hat{W}_i(0) > \beta_{i2} \hat{W}_i(0) \quad (i, j) \in \{(1, 2), (2, 1)\} \quad (B7.b)$$

## B8 Temporary Improvement within a Debt Trap

A historical example of temporary improvement in an economy's indebtedness before it worsens over the long term is the EU27 economy from 2005 to 2022: The government debt-to-GDP ratio in the EU27 decreased from 42% in 2005, to 39% in 2006, to 35% in 2007, and then increased to 38% in 2007, to 47% in 2008, to 53% in 2009 (IMF 2010), and so on, until reaching an all-time high of 90.8% in 2022 (Eurostat 2024), which is 150% higher than the 60% threshold for this ratio according to the Maastricht criterion.

## B9 Structural Stagnation

A well-known example of a closed low-motivation leisure-oriented economy is that of the USSR during the Cold War, when its economy was characterized by a combination of low indebtedness and technological and economic stagnation in consumer goods production—despite notable achievements in athletics, the performing arts, and other leisure (cultural) activities. Another example is the barter-based closed economies of continental Europe in the Middle Ages, characterized by economic intertemporal stagnation within the spiritually (religiously) oriented medieval kingdoms of that era.

## B10 Open Laissez-faire Economy

The autonomous system of differential equations for modeling an open laissez-faire economy (relation (7)) can be expressed in the following matrix form:

$$\dot{N} - AN = g + \gamma \quad (B8)$$

where matrix N is specified in relation (B2), and A, g and $\gamma$ are specified in relation (B1).

## B11 Information Borders

In a closed, low-motivation, leisure-oriented economy (Figure 2) that is opening its information borders, the effects of foreign consumption, investment and management standards are both direct and indirect, as described below:

- **Direct Effect:** As shown in Figure B1.a, the impact of the (positive) international information coefficient ($\gamma_i$)—which represents the degree of access each member (i) has to these foreign standards—is illustrated by a shift in the intercept of the member's demarcation line ("$\dot{N}_i = 0$") with the $N_i$-axis, from $G_i$ to $G_i + \Gamma_i$ (per relations (3) and (8), respectively). This results in a shift of the demarcation line in the positive direction along the $N_i$-axis. Consequently, in Figure B1.a, the stationary point moves from $E^A$ (a stable node) to $E^B$ (also a stable node) in a northeastern direction. At the new stationary point, the stationary net worth of each member is higher than it was before the opening of the country's information borders.

- **Indirect Effect:** Moreover, as depicted in Figure B1.b, the opening of information borders may also lead to a significant change in the economy's motivation structure and particularly to an increase in the interaction coefficient ($b_i$) of each member (i). This increase alters the slope of the member's demarcation line (per relation (8)), making it steeper with respect to the $N_i$-axis. If the increase is big enough, the stationary point may shift into the third quadrant, e.g., from $E^B$ (a stable node in the first quadrant) to $E^C$ (a saddle point in the third quadrant), as shown in Figure B1.b. Therefore, this indirect effect can result in a fundamental change in the economy's motivation structure, from low-motivation to high-motivation, thus exposing the economy to the risk of a future debt crisis: after the opening of information borders, a hubris zone may emerge in the graphical depiction of the economy.

In summary, opening the information borders of a closed, low-motivation, leisure-oriented economy increases the stationary net worth of both members (sectors) if they maintain their existing motivation structure, as shown in Figure B1.a—e.g., as occurred in the economies of China, Qatar, and Dubai since 1980s. However, this opening may expose the economy to a future debt crisis if it leads to a fundamental change in the economy's motivation structure, as shown in Figure B1.b. In a worse-case scenario, the economy may enter a debt spiral if it is positioned at a point (such as W in Figure B1.b) inside the hubris zone that will emerge right after the opening
(as happened in the Russian economy in the 1990s). It is important to note, however, that such a change in the economy's motivation structure, from low-motivation to high-motivation, will not significantly impact its growth trajectory if the economy is safely positioned outside the hubris zone (as at point W' in Figure B1.b) just prior to opening its information borders.

The indirect effect depicted in Figure B1.b, however, is beyond the scope of this paper due to the assumption of constant reaction coefficients, as specified in relation (1'). Socioeconomic structures with changing reaction coefficients are addressed in a follow-up paper, which employs comparative dynamics methodology.

<figure><img src="image_7.png" /><figcaption>Figure B1(a). Direct effect of opening the information borders</figcaption></figure>

*Note.* Opening the information borders of a closed economy shifts the intercept of the demarcation line of each sector (i) with the *N*-axis from *G*₁ to *G*₁+*Γ*₁ (Appendix B, section B11).

<figure><img src="image_8.png" /><figcaption>Figure B1(b). Indirect effect of opening the information borders</figcaption></figure>

*Note.* Opening the information borders of a closed economy increases the slope of the demarcation line of each sector (i) with respect to the other sector's axis (*N*'-axis) (Appendix B, section B11).
<figure><img src="image_9.png" /><figcaption>Figure B2. Mapping the stationary path in the $N_1N_2$ plane</figcaption></figure>

Note. In the three-dimensional $N_1N_2t$ space of an open mixed economy, the stationary net worth point over time traces a stationary path, which is mapped as a reddish line in the two-dimensional $N_1N_2$ plane (Appendix B, section B13).

In general, a useful insight implied by the current model is that preserving a closed economy's motivation structure (reflecting its cultural value system) may be essential for shielding the economy from potential negative consequences of internationalization.

## B12 Increase in the Stationary Net Worth

Due to the above direct effect (Appendix B, section B11), opening the information borders of a closed low-motivation leisure-oriented economy causes per se—without government intervention—the following increase in the economy's stationary net worth:

$$ \Delta(\tilde{N}_1 + \tilde{N}_2) = \frac{(b_1 - a_1)\gamma_2 + (b_2 - a_2)\gamma_1}{a_1a_2 - b_1b_2} \quad (B9) $$

This equation (B9) is derived by calculating the economy's stationary net worth ($\tilde{N}_1 + \tilde{N}_2$) before and after the opening of the economy's information borders—according to relations (4) above and (B12) below, respectively—and subtracting the former (before) from the latter (after).

## B13. Stationary Path

Figure B2 plots in the (two-dimensional) $N_1N_2$-plane—the third dimension is time ($t$), not depicted in the figure—the shifts in the demarcation lines and the concomitant movement of the stationary point $E(t)$ in an open mixed low-motivation leisure-oriented economy that is subject to an expansionary policy ($\rho > 0$). The stationary point moves over time—from $E(0)$, $E(1)$, $E(2)$,... at $t = 0, 1, 2, ...$ respectively—progressively further from the origin in a northeastern direction.

In open mixed economies, each demarcation line at a specific time $t^*$ is the locus of all $[N_i(t^*), N_i(t^*)]$ combinations that satisfy relation (9) at that time ($t = t^*$). In Figure B2, this locus is plotted in the $N_1N_2$-plane for $t = 0, 1, 2, ...$: The intercepts of the “$\tilde{N}_1 = 0$” line along the $N_1$-axis are at $G_1 + \Gamma_1$, $G_1 + \Gamma_1 e^\rho$, $G_1 + \Gamma_1 e^{2\rho}$, ..., and those of the “$\tilde{N}_2 = 0$” line along the $N_2$-axis are at $G_2 + \Gamma_2$, $G_2 + \Gamma_2 e^\rho$, $G_2 + \Gamma_2 e^{2\rho}$, ..., respectively.

In three-dimensional space $N_1N_2t$, where the third dimension represents time ($t$), the set of all demarcation lines intersecting the $N_1$-axis over time in such an (open mixed) economy forms a concave demarcation surface (not shown in Figure B2). This surface intersects the $N_1t$-plane along a concave curve. The three-dimensional domain $N_1N_2t$ is divided into four subspaces by two such surfaces (one for each member ($i$), or equivalently, one for each $N_1t$-plane). These surfaces intersect along an upward-sloping concave curve in a northeastern direction. This curve is termed the economy's stationary path.

In the three-dimensional $N_1N_2t$-space, the stationary net worth point over time—mapped as $E(0)$, $E(1)$, $E(2)$,
and so on, in the two-dimensional $N_1N_2$-space in Figure B2—traces out the economy’s stationary path, which is mapped as a (reddish) line in the $N_1N_2$-space in this figure.

To visualize the dynamics of an open mixed economy in three-dimensional $N_1N_2t$-space, one can apply the principle of motion pictures. Just as a film consists of sequential still frames of a moving object, the movement of the demarcation lines and the stationary point of an open mixed economy can be broken down into “frames” observed “one by one”. For instance, in an open mixed economy that has a low-motivation leisure-oriented structure, each frame, placed successively one upon the other, resembles Figure 2 and differs from adjacent frames by the intercept of each demarcation line and also by the stationary point (where these lines intersect). Consequently, the stationary point can be treated as a moving point tracing the stationary path of the system through space. Thus, by “freezing the action,” one can determine the exact value of the stationary net worth, $\tilde{N}_i(t)$, for each member (i) at a specific time (t), as detailed in equations (B10-B11) below.

## B14. Solution of the Non-Autonomous System

In an open mixed economy, the stationary net worth, $\tilde{N}_i(t)$, of each member (i) at time t, is specified as follows:

$$ \tilde{N}_i(t) = \frac{b_i g_j - a_i g_j}{a_i a_j - b_i b_j} + \frac{b_i \gamma_j - (a_j - \rho) \gamma_i}{(a_i - \rho)(a_j - \rho) - b_i b_j} e^{\rho t} \quad (i, j) \in \{(1, 2), (2, 1)\} \quad (B10) $$

or equivalently in compact form:

$$ \tilde{N}_i(t) = \tilde{N}_i + P_i(\rho) e^{\rho t} \quad (i, j) \in \{(1, 2), (2, 1)\} \quad (B11) $$

where $\tilde{N}_i$ is specified in relation (4)—the stationary point of a closed economy—and $P_i(\rho)$ is the coefficient (a ratio) of $e^{\rho t}$ in relation (B10). In an open mixed economy, the stationary point moves over time as specified by relations (B10-B11). The first term ($\tilde{N}_i$) on the right-hand side of equations (B11) indicates that in an open mixed economy, a sufficient condition for the stationary net worth of each member over time to approach infinity is that the demonstration effect equals the intrinsic effect. It is noteworthy that if we set $\rho = 0$ in relation (B10), these equations reduce to the equations for the stationary point in open laissez-faire economies, i.e.:

$$ \tilde{N}_i = \frac{b_i(g_j + \gamma_j) - a_j(g_i + \gamma_i)}{a_i a_j - b_i b_j} \quad (i, j) \in \{(1, 2), (2, 1)\} \quad (B12) $$

The general solution of the non-autonomous system of an open mixed economy (relations (1') and (B1)) may be expressed as follows:

$$ \begin{bmatrix} N_1(t) \\ N_2(t) \end{bmatrix} = \begin{bmatrix} \tilde{N}_1(t) \\ \tilde{N}_2(t) \end{bmatrix} + \begin{bmatrix} \beta_{11} & \beta_{12} \\ 1 & 1 \end{bmatrix} \begin{bmatrix} n_1(t) e^{r_1 t} \\ n_2(t) e^{r_2 t} \end{bmatrix} \quad (B13) $$

$$ \begin{bmatrix} n_1(t) \\ n_2(t) \end{bmatrix} = (r_1 - r_2)^{-1} \begin{bmatrix} (a_1 - r_2) / \beta_{11} & -(a_1 - r_1) \\ -(a_1 - r_2) / \beta_{11} & a_1 - r_1 \end{bmatrix} \begin{bmatrix} N_1(0) - \tilde{N}_1(t) \\ N_2(0) - \tilde{N}_2(t) \end{bmatrix} $$

where $\tilde{N}_1(t)$ and $\tilde{N}_2(t)$ are specified in relations (B10-11).

## B15 The Attractor in Positively Balanced Economies

If a closed or open laissez-faire economy is positively balanced, the basin of attraction is the entire two-dimensional space of potential initial vectors. The attractor is the demarcation line “$\dot{N}_i = 0$” of the member (i) with the lower status coefficient ($B_i < B_j$). Every trajectory will converge asymptotically to this line, whose slope is $B_i$. If the two status coefficients are equal ($B_i = B_j$), then the attractor is the equidistant line between the two demarcation lines of the system, i.e., the line $N_i = 0.5(G_i + S_i) + B_i N_j$ in a closed economy, or the line $N_i = 0.5(G_i + S_i + \Gamma_i) + B_i N_j$ in an open laissez-faire economy, where:

$$ S_i = -(g_i / b_i) \quad (i, j) \in \{(1, 2), (2, 1)\} \quad (B14) $$

Graphically, $S_i$, termed socioteleonomial standard of member (j), is represented by a point on the $N_j$-axis at which the “$\dot{N}_i = 0$” demarcation line intersects this axis.

Similarly, if an open mixed economy is positively balanced, the basin of attraction is the entire three-dimensional space of potential vectors [$N_i(t) N_j(t)$]' where the third dimension is time (t). The attractor in such an economy is the demarcation surface (Appendix B, section B13) of the member with the lower status coefficient.

## B16. Equity in Positively Balanced Economies

In positively balanced economies the relative net worth of each member (i) is a percentage that over time tends to the member’s status coefficient, or, equivalently, to the slope of the member’s demarcation line:
$$ \lim_{t \to \infty} \left( \frac{N_i(t)}{N_j(t)} \right) = B_i \quad (i, j) \in \{(1, 2), (2, 1)\} \quad (B15.a) $$

By this relation (B15.a), the (percentage) share of each member (i) in the economy's net worth, tends over time to the ratio $B_i/(B_i+1)$, given that $B_iB_i = 1$ in such economies:

$$ \lim_{t \to \infty} \left( \frac{N_i(t)}{N_i(t) + N_j(t)} \right) = \lim_{t \to \infty} \left( \frac{\frac{1}{1 + \frac{N_i(t)}{N_j(t)}}}{1 + \frac{N_i(t)}{N_j(t)}} \right) = \frac{1}{1 + B_i} = \frac{B_i}{B_i + 1} \quad (B15.b) $$

## B17 Long-Term Growth Rate in Positively Balanced Economies

By relation (B13), we may derive the rate of change in the economy's net worth at a point in time (t) as follows, where $(N_i(t) + N_j(t))'$ is the derivative of $N_i(t) + N_j(t)$ with respect to time:

$$ \frac{(N_i(t) + N_j(t))'}{N_i(t) + N_j(t)} = \frac{\rho [P_i(\rho) + P_j(\rho)] e^{\rho t} + r_1(\beta_{i1} + 1) n_1 e^{r_1 t} + r_2(\beta_{i2} + 1) n_2 e^{r_2 t}}{N_i + N_j + [P_i(\rho) + P_j(\rho)] e^{\rho t} + (\beta_{i1} + 1) n_1 e^{r_1 t} + (\beta_{i2} + 1) n_2 e^{r_2 t}} = \quad (B16.a) $$

$$ \frac{\rho [P_i(\rho) + P_j(\rho)] e^{(\rho - r_1)t} + r_1(\beta_{i1} + 1) n_1 + r_2(\beta_{i2} + 1) n_2 e^{(r_2 - r_1)t}}{(N_i + N_j)e^{-r_1 t} + [P_i(\rho) + P_j(\rho)] e^{(\rho - r_1)t} + (\beta_{i1} + 1) n_1 + (\beta_{i2} + 1) n_2 e^{(r_2 - r_1)t}} = \quad (B16.b) $$

If $r_1$ is the higher eigenvalue and is greater than the policy factor (i.e., $r_1 > r_2$, $\rho$), then the limit of this ratio (B16.b), as $t \to \infty$, is equal to that eigenvalue ($r_1$):

$$ \lim_{t \to \infty} \left( \frac{(N_i(t) + N_j(t))'}{N_i(t) + N_j(t)} \right) = \frac{0 + r_1 (\beta_{i1} + 1) n_1 + 0}{0 + 0 + (\beta_{i1} + 1) n_1 + 0} = r_1 \quad (B17) $$

By relation (B4), in positively balanced economies, the higher eigenvalue is equal to zero, i.e., $r_1 = 0$, while the lower eigenvalue is negative, as $r_2$ equals the trace of the matrix ($\mathbf{A}$) of the system's coefficients—the sum of coefficients in the first diagonal of $\mathbf{A}$, which is specified in relation (B1)—i.e., $r_2 = \text{tr}(\mathbf{A}) = a_1 + a_2 < 0$. Therefore, by relation (B17), the growth rate in positively balanced economies, is positive, approaching zero asymptotically (from above) over time, whether they are closed or open laissez-faire economies, or even open mixed economies with contractionary or neutral government policies ($\rho \le 0$):

$$ \lim_{t \to \infty} \left( \frac{(N_i(t) + N_j(t))'}{N_i(t) + N_j(t)} \right) = 0^+ \quad (B18) $$

Regarding open mixed economies with expansionary government policies ($\rho > 0$), if the higher eigenvalue ($r_1$) is less than the policy factor ($\rho > r_1 > r_2$), then the limit on the left-hand side of relation (B17) can be derived similarly. Specifically, by dividing all terms in relation (B16.a) by $e^{\rho t}$ and taking the limit of every term as $t \to \infty$, we find that the rate of growth in the net worth of the economy tends asymptotically to $\rho$.

## B18 Long-Term Growth Rate in Exposed Economies

In the long run, in a positively balanced economy that is closed, open laissez-faire, or open mixed where the government policy is contractionary or neutral ($\rho \le 0$), the values of the state variables increase at the same rate as this rate approaches zero asymptotically from above over time:

$$ \text{As } t \to \infty, \quad \dot{N}_i(t)/N_i(t) \cong \dot{N}_i(t)/N_i(t) \cong (N_i(t) + N_j(t))'/((N_i(t) + N_j(t)) \quad (B19) $$

In contrast, an economy that is exposed to the risk of a future debt crisis, as depicted by the economy's hubris zone, grows at a rate that is equal to the system's higher (positive) eigenvalue ($r_1 > 0$) if the government policy is contractionary or neutral. Consequently, if such an economy is trapped within its hubris zone, then its indebtedness (negative net worth) will worsen exponentially over time at a rate that approaches this eigenvalue, as specified in relation (B17). Only in positively balanced economies the higher eigenvalue is zero ($r_1 = 0$).

## B19 Feasibility Condition for Effective Wealth Redistribution
The feasibility condition for *effective* wealth redistribution is specified as follows:

$$|\beta_{i2}| \neq 1 \qquad (i=1, 2) \qquad (B20)$$

Descriptively, equations (B20) state that the absolute value of the adjusted status coefficient of each member for the economy's negative eigenvalue ($r_2$), must differ from unity in order for *effective* wealth redistribution to be feasible. As the economy moves along the saddle path towards its stationary point, the higher [lower] the value of $|\beta_{i2}|$ for a member (i), the more [less] responsive that member is to changes in the net worth of the other member (j), i.e., the greater [smaller] the absolute value of a change in $N_i$ in response to a change in $N_j$.

## B20 Liberal or Populist Wealth Redistribution?

For an entrapped economy to escape its debt spiral, wealth redistribution should favor the member (sector) with the lower absolute value of the adjusted status coefficient for the economy's negative eigenvalue. For example, in Figure 1, *effective* wealth redistribution, repositioning the economy from point W' to point W'', favors the pauper (the more indebted sector) because $|\beta_{i2}| < 1 < |\beta_{22}|$; however, in Figure B3, such redistribution (from point W to point W') favors the prince (the less indebted sector) because $|\beta_{i2}| > 1 > |\beta_{22}|$.

It is noteworthy that, from relations (B3') and (B4), we have: $b_1b_2 = (r_2 - a_1)(r_2 - a_2) \Rightarrow \beta_{12} = 1/\beta_{22}$. Thus, if $|\beta_{12}|$ is less [greater] than 1, then $|\beta_{22}|$ is greater [less] than 1.

<figure><img src="image_10.png" /><figcaption>Figure B3. Effective liberal wealth redistribution</figcaption></figure>

*Note.* Under these conditions, wealth redistribution favoring the privileged sector—without debt restructuring—is effective in repositioning the entrapped economy from point W to point W', outside the hubris zone (section 5.2; Appendix B, section B20).

## B21 Effective Wealth Redistribution

In a high-motivation economy, the amount of redistributed wealth, $m_i(t)$, from one member (i) to the other member (j) at a point in time (t), in order for the redistribution to be effective—without debt restructuring—should exceed $\Phi_i(t)$, where:

$$\Phi_i(t) = \frac{\hat{W}_i(t) - \beta_{i2} \hat{W}_j(t)}{(1 + \beta_{i2})} \qquad (i, j) \in \{(1, 2), (2, 1)\} \qquad (B21)$$

The economic interpretation of $\Phi_i(t)$ is the amount of wealth redistribution from member (i) to member j (at time t) that would reposition an entrapped economy from inside the hubris zone to a point on the saddle path (as from point W inside the hubris zone, to point $\varphi$ on the saddle path in Figure 4). The point $\varphi$ is the intersection of the saddle path and the *wealth-redistribution* line, which forms a 135° angle with the horizontal axis and passes through the entrapped economy's position (point W in Figure 4). For wealth redistribution to be effective, it must exceed $\Phi_i(t)$ by a marginal amount (u), i.e., $m_i(t) = \Phi_i(t) + u$.

To derive relation (B21), we combine the equation of the saddle path, $N_i = \tilde{N}_i + \beta_{i2}(N_j - \tilde{N}_j)$, from relation (B6), with the equation of the downward-sloping 135°-line, $N_i = N_i(t) + N_j(t) - N_j$, equating the left-hand sides of both
equations, solving for $N_i$ and subtracting $N_i(t)$ from the resulting expression for $N_i$.

The specification of $\Phi_i(t)$ in relation (B21) is applicable to most economies that are exposed to the risk of future debt spirals, i.e., to high-motivation economies, as well as to low-motivation work-oriented economies.

## B22 Debt Trap

If wealth redistribution is relatively mild in an entrapped high-motivation economy—i.e., if $m_i(t) < \Phi_i(t)$, where $\Phi_i(t)$ is specified in relation (B21)—it will fail to extricate the economy from its debt spiral. Figure B4 depicts a sequence of inadequate wealth redistributions, effected gradually in successive stages, such as along the (purple) *charybdisic* path from point W(t) to point W(t + 2v)' inside the hubris zone. This outcome is empirically corroborated by New Zealand's ineffective fiscal adjustment in the 1980s, where inadequate spending cuts and weak institutional support led to social strain without sustained fiscal gains (Janssen, 2001). By contrast, the broadly supported fiscal reforms of Canada in the 1990s combined strategic communication with significant expenditure cuts in the public sector, achieving lasting deficit reduction without undermining social cohesion (Thiessen, 2001). These cases demonstrate that decisive and well-designed action—such as an effective redistribution shifting the economy from point W(t) inside the hubris area to point W(t)'' outside it instantaneously at time t in this figure (B4)—may reposition an economy on a sustainable growth path, outside the hubris zone.

<figure><img src="image_11.png" /><figcaption>Figure B4. Debt spiral</figcaption></figure>

*Note.* A sequence of inadequate wealth redistributions—without accompanying debt restructuring—fails to reposition the economy outside the hubris zone, as shown by the purple *charybdisic* path of entrapment (section 5.4; Note 20; Appendix B, section B22).

## B23. Populist Wealth Redistribution

In an entrapped economy where the adjusted status coefficient ($\beta_{i2}$) of the underprivileged member (i) is lower in absolute value than that of the privileged member (j), a policy of wealth redistribution in favor of the former (i) will be *cohesively effective*—i.e., it will reposition the economy outside the hubris zone, while preserving the economy's *class structure* at time t—provided the following condition holds (as in Figure 4):

$$ \tilde{N}(t) > (\tilde{N}_i - \beta_{i2} \tilde{N}_j) / (1 - \beta_{i2}) \quad (i, j) \in \{(1, 2), (2, 1)\} \quad (B22) $$

where $\tilde{N}(t) = 0.5(N_i(t) + N_j(t))$, i.e., $\tilde{N}(t)$ is the economy's *average net worth* at time t. If the above condition (B22) holds, then:

$$ \Phi_i(t) < \tilde{N}(t) - N_i(t) \quad (B23) $$

where $\Phi_i(t)$ represents the lower limit of redistributed net wealth (equation (B21)). Consequently, if this condition (B22) is satisfied, a *cohesively effective* wealth redistribution will reposition the economy at a point, (such as W' in Figure 4) along the downward-sloping wealth-redistribution line between its intersections ($\phi$) with the *saddle path* and ($\eta$) with the *egalitarian-distribution* line, i.e.:
$$ \Phi_j(t) < m_j(t) < \tilde{N}(t) - N_i(t) \qquad (B23') $$

## B24. Saddle-Path Egalitarian Wealth

The ratios on the right-hand side of relation (B22) represent each member's net worth, termed *saddle-path egalitarian wealth*, corresponding to the *saddle-path egalitarian point* ($\delta$ in Figures 4–5). These ratios are equal:

$$ (\tilde{N}_i - \beta_{i2} \tilde{N}_j) / (1 - \beta_{i2}) = (\tilde{N}_j - \beta_{j2} \tilde{N}_i) / (1 - \beta_{j2}) \qquad (B24) $$

## B25 Comprehensive Debt Reduction

If the condition specified relation (B22) does not hold in an entrapped economy, where the *adjusted status coefficient* of the underprivileged member is lower in absolute value than that of the privileged member, a policy of wealth redistribution alone—without debt reduction—cannot be *cohesively effective*. This is because it would reposition the economy either outside the hubris zone disrupting its class structure at time $t$ (e.g., from point W to point W'' in Figure 5), or inside the hubris zone preserving the class structure but failing to escape the trap (as from point W(t) to point W(t)' in Figure B4). In the first case, the redistribution is effective but not cohesive; in the second, it is cohesive but not effective.

Instead, a specific policy mix—combining wealth redistribution and debt reduction—will be *cohesively effective* with *minimized* loss to creditors, if it implements the following three actions simultaneously and instantaneously at this time ($t$):

(1) Wealth redistribution of net amount $\Psi_j(t)$ from sector ($j$) to sector ($i$), where:

$$ \Psi_j(t) = N_j(t) - \frac{\tilde{N}_j - \beta_{j2} \tilde{N}_i}{1 - \beta_{j2}} \qquad (B25) $$

(2) Debt reduction of amount $\Omega_i(t)$ in favor of sector ($i$), where:

$$ \Omega_i(t) = \frac{2(\tilde{N}_i - \beta_{i2} \tilde{N}_j)}{1 - \beta_{i2}} - 2 \tilde{N}(t) \qquad (B26) $$

(3) Debt reduction of a marginal or symbolic amount $u$ in favor of sector ($j$).

## B26 Creditor Losses

The creditors' total loss due to *comprehensive debt reduction*, amounts to $\Omega_i(t) + u$, where $\Omega_i(t)$ and $u$ are specified above (Appendix B, section B25). This loss is *minimized*: all other alternative combinations of wealth redistribution and debt reduction, that would enable the entrapped economy to escape the hubris zone while preserving its socioeconomic class structure, result in greater total loss for the creditors. Therefore, from their perspective, it is to their interest to forgive (write off) this debt overhang rather than finance it.

## B27 Transitionally Egalitarian Wealth Distribution

As a result of a *comprehensive debt reduction* in a debt-ridden economy at time $t$, where the *adjusted status coefficient* ($\beta_{i2}$) of the underprivileged sector ($i$) is lower in absolute value than that of the privileged sector ($j$), and the economy's *average net worth* falls short of its *saddle-path egalitarian wealth* (specified in Appendix B, section B24 above), the net worth of the former sector, $N_i(t + v)$, and that of the latter sector, $N_j(t + v)$, where $v$ is infinitesimally small, are specified as follows, by relations (B24-B26):

$$ N_i(t + v) = \frac{\tilde{N}_i - \beta_{i2} \tilde{N}_j}{1 - \beta_{i2}} \qquad (B27.a) $$

$$ N_j(t + v) = \frac{\tilde{N}_j - \beta_{j2} \tilde{N}_i}{1 - \beta_{j2}} + u = \frac{\tilde{N}_i - \beta_{i2} \tilde{N}_j}{1 - \beta_{i2}} + u \qquad (B27.b) $$

That is, the net worth of the underprivileged sector becomes exactly equal to the *saddle-path egalitarian wealth* of the economy, and the net worth of the privileged sector exceeds this amount only by a marginal amount ($u$), of rather symbolic significance. Consequently, the economy becomes *temporarily egalitarian* at time $t + v$.

## B28 Unconditional Debt Reduction

The algorithm for relativist debt crisis management (Figure B5) includes the special case of an entrapped economy with $|\beta_{i2}| = 1$, where only unconditional debt reduction (without wealth redistribution) can enable the economy to escape its debt trap at a specific point in time, because the *wealth-redistribution* line and the *saddle path* are parallel. The necessary debt reduction—that minimizes creditor losses—amounts to a total of $\Omega(t) + u$, where $u$ is defined above (Appendix B, section B25) and:
$$ \Omega(t) = -W_i(t) + \beta_{i2}W_j(t) = -W_j(t) + \beta_{j2}W_i(t) \quad (B28) $$

The debt reduction in this case may benefit either sector individually or both sectors in any proportion (including unequal allocations).

## B29 Egalitarian Wealth Redistribution

As specified in the algorithm for relativist debt crisis management (Figure B5), if the saddle path of an entrapped economy passes through the intersection of the wealth-redistribution line with the egalitarian-distribution line (point η in Figures 4-5), then no significant debt reduction is required to enable the economy to escape its debt trap. Instead, an egalitarian wealth redistribution (without debt reduction) of amount $\Psi_i(t)$ from the privileged sector (j) to the underprivileged sector (i) at a specific point in time (t) will reposition the economy on the saddle path—at the intersection (η), termed the economy's egalitarian point—where:

$$ \Psi_i(t) = 0.5(N_i(t) - N_i(t)) \quad (B29) $$

Then only an insignificant debt reduction u in favor of the privileged sector (j) will suffice to reposition the economy outside the hubris zone, while maintaining the class structure of the economy, at a creditor loss that is thus minimal (symbolic).

<figure><img src="image_12.png" /><figcaption>Figure B5. Algorithm for relativist debt crisis management in high-motivation economies</figcaption></figure>
## B30 Temporary Egalitarian Policies in Wartime

Relations (B27.a-b) suggest that, in peacetime, temporary egalitarian policies of wealth redistribution may enable an economy to escape its debt trap at minimized creditor losses. Likewise, in wartime, irrespective of an economy's structure, its transition from a peace economy to a war economy involves significant economic and social restructuring aimed at maximizing resource allocation and public support for the war effort. More specifically in wartime, temporary egalitarian policies—such as horizontal food rationing, progressive taxation, and restrictions on luxury imports during the war—play a critical role in ensuring fairness and social cohesion. These temporary egalitarian measures (a) promote unity and morale, (b) prioritize resource allocation for essential war needs rather than private consumption, and (c) prevent economic inequality and inflation, e.g., as seen in the economies of the Winning Powers during the Second World War (Rockoff, 1998; Edgerton, 2011).

## B31 Operationalization of the Model

To operationalize the model, standard econometric techniques may be employed to estimate the coefficients and terms in equations (1'), according to the following guidelines: (1) First, approximate the time derivative $\dot{N}_i(t)$ using finite differences, (2) introduce an error term $\varepsilon_i(t)$ on the right-hand side; (3) in the resulting discretized two-equation system, estimate parameters via linear regressions using Ordinary Least Squares (OLS), Generalized Least Squares (GLS), or Nonlinear Least Squares (NLS) if the policy factor $\rho$ is to be estimated jointly with $\gamma_i$—when $\rho$ is known or determined exogenously from policy data, treat $e^{\rho t}$ as a known regressor; otherwise, apply nonlinear regression to jointly estimate both $\rho$ and $\gamma_i$ simultaneously—(4) if simultaneity is suspected between the state variables $N_i(t)$ and $\dot{N}_i(t)$, adopt lagged-value estimators; (5) normalize variables when necessary to mitigate multicollinearity or scale-related distortions; (6) after estimation, inspect residuals for autocorrelation and heteroskedasticity.

Thereafter, with the values of the parameters estimated, its is straightforward to conduct stability analysis via eigenvalue decomposition, and delineate the saddle path—and thereby the hubris zone to the left of the saddle path—if the system exhibits a saddle-point equilibrium. The saddle path may be specified algebraically by relations (4) and (B6) for closed economies, or relations (B6) and (B12) for open laissez-faire economies; for open mixed economies, relations (B10)–(B11) may be used to specify the values of $\dot{N}_i(t)$ and $\dot{N}_j(t)$, allowing for the determination of the (moving) saddle path at each time $(t)$ as:

$$N_i(t) = \dot{N}_i(t) + \beta_{iz} (N_j(t) - \dot{N}_j(t)) \quad (B30)$$

It is noteworthy that in closed economies (where $\gamma_i = 0$) and open laissez-faire economies (where $\rho = 0$), the model becomes linear in parameters (i.e., autonomous) and thus more tractable for estimation.

Primary data sources are IMF sectoral balance sheet data and national accounts detailing the net worth of economic sectors such as public/private or export/import sectors. Secondary (auxiliary) sources include national time-use statistics on work and leisure, and household wealth surveys to obtain microeconomic analogs of the “prince” and “pauper.” Within this framework, the net worth of a sector is defined as the aggregate net worth not only of its principal institutions (like the state in the public sector), but also of economic agents whose income is derived primarily from this sector (like public employees, defense contractors, and public enterprises).

# Appendix C

## Shock Therapy

The term shock therapy was initially used to describe the Bolivian economic adjustment of the mid-1980s, the Polish transition of the early 1990s, and Russia's post-default macroeconomic consolidation in the 2000s.

### C1 The Bolivian Adjustment

In 1985, Bolivia eliminated price and interest rate controls, raised public sector prices, enacted tax reform, liberalized trade, and allowed banks to operate in foreign currency. Next year, the government launched an Emergency Social Fund and introduced export tax rebates. As a result, hyperinflation—24,000 percent in mid-1985—was brought under control by early 1986. Between 1986 and 1987, Bolivia's commercial bank debt was reduced by 72% through the Paris Club mechanism, including a buy-back of $253 million at 11 cents on the dollar, funded by foreign donors. Between 1986 and 1995, total debt relief equaled 38% of Bolivia's 1986 sovereign debt stock, reducing the external debt-to-GDP ratio from 115% in 1985 to 70% in 1995 (International Monetary Fund, 2005).

### C2 The Polish Transition

Poland's market transition involved: (a) sweeping economic reform with large-scale reallocation from public to
private sectors; (b) sharp trade levies—in December 1991, tariffs rose by 50–300 percent; and (c) major debt cancellation, halving sovereign debt, backed by Western aid such as the U.S.-sponsored $1 billion zloty stabilization fund (Vinton and Slay, 1994). These reforms coincided with democratic transformation under Solidarity's leadership. The austerity and trade controls in the Balcerowicz Plan gained public support in pursuit of reintegration with Western Europe—the goal of the so-called “Return to Europe.”

As result, inflation dropped from 585.8% in 1990 to 55.2% in 1991, then to 6.4% later in the decade. By 1992, growth resumed. Between 1991 and 2000, Poland's real GDP grew by 3.7% annually, outperforming EEFSU peers—e.g., Bulgaria (–2.6%), Hungary (0.4%), Romania (–2.2%), Russia (–4%), Ukraine (–7.9%)—and the EU11 average (1.9%). Poland thus became a model for democratic, post-communist market reform (Jeffrey Sachs, 1993).

### C3 The Adjustment of Post-Default Russia

In August 2000, Russia secured a 50% reduction of its external commercial debt via the London Club (Budina and Fiess, 2005). A 2001 tax reform replaced progressive income tax with a 13% flat rate (Keen et al., 2006). Simultaneously, state control over oil increased as the Kremlin reasserted control over oligarch-owned assets: state-owned firms' oil output rose from 10% in 2000 to 42% in 2008 (Elder, 2008). By 2008, Russia's Stabilization Fund had accumulated $168 billion from energy windfalls.

As result, between 1999 and 2003, exports surged, while the import-to-export ratio fell from 77.3% to 41.6%. Public debt dropped from 88.7% of GDP in 1999 to 33.4% in 2003. By January 2008, external debt was down to $53 billion (4% of GDP) (Rutland, 2008). From 2000 to 2008, foreign currency reserves rose from $13 billion to $402 billion; total investment increased seven-fold; foreign trade turnover, five-fold; stock market capitalization, over twenty-fold. GDP (PPP) grew by 72%, lifting Russia's global rank from 20th in 1999 to 7th in 2008 (World Bank, 2011).

### C4 The FRG Adjustment

A precursor to shock therapy was the Federal Republic of Germany's adjustment between September 1951 and June 1952—three decades before the term emerged. To resolve its postwar balance-of-payments crisis, the FRG adopted: (a) monetary tightening, (b) resource shifts from imports to exports, (c) OEEC-supported import restrictions, and (d) debt restructuring via the 1952 London Agreements, which canceled about half of its debt (Guinnane, 2004). These policies restored solvency and triggered the German Wirtschaftswunder (economic miracle).

### C5 Misleading Sobriquet

The FRG (1951), Bolivia (1985), Poland (1991), and Russia (2000) combined economic liberalization with significant debt restructuring. In contrast, other reforms in Chile (1975–78), Russia (1992–97), Argentina (1999–2004), and Greece (2010–2015) lacked timely sovereign-debt restructuring—typically “too little, too late.” Nevertheless, all these diverse policies are often labeled as *shock therapy*. As such, the term has frequently functioned as a misleading sobriquet (Jeffrey Sachs, 1994).

### C6 Context-Specific Policies

Shock therapy gained prominence in IMF structural adjustment programs, aiming to restore market confidence rapidly (Reinhart & Rogoff, 2010). In contrast, gradualist approaches prioritize institutional resilience and social cohesion, arguing that abrupt adjustments can undermine long-term stability (Stiglitz, 2002). Central to this debate is fiscal sustainability, i.e., a government's ability to meet obligations without triggering unsustainable debt accumulation. Behavioral economics further enriches this discourse, revealing how cognitive biases, such as overconfidence and loss aversion, can drive pro-cyclical fiscal policies and delay necessary adjustments, even amid deteriorating fundamentals (Kahneman, 2011). These academic debates trace back to classical economic thought. Ricardo's warnings against excessive borrowing and Keynes's advocacy for counter-cyclical policies still define opposing views on debt and state intervention.

Today, synthesizing classical insights with behavioral and institutional perspectives offers a more nuanced understanding of debt dynamics—balancing short-term stabilization with long-term growth and political feasibility. Within this framework, this paper's relativist policy recommendations align with contemporary emphasis on context-specific strategies that account for political economy constraints, social equity, and institutional capacity (Rodrik, 2006). Furthermore, the proposed transitional egalitarian policies for debt crisis management may mitigate distributional conflicts (Guzman & Stiglitz, 2016) by limiting creditor losses while preserving the economy's class structure.
## Appendix D

### Glossary of Variables and Parameters

<table><thead><tr><th>Symbol</th><th>Description*</th><th>Initial Reference (Chapter/Equation)</th></tr></thead><tbody><tr><td>N<sub>i</sub>(t)</td><td>net worth of sector (i) at time t</td><td>Section 3; relation (1')</td></tr><tr><td>w<sub>i</sub></td><td>work coefficient of sector (i)</td><td>Section 3; relation (1')</td></tr><tr><td>l<sub>i</sub></td><td>leisure coefficient of sector (i)</td><td>Section 3; relation (1')</td></tr><tr><td>a<sub>i</sub></td><td>intrinsic coefficient of sector (i)</td><td>Section 3.1</td></tr><tr><td>a<sub>i</sub>a<sub>j</sub></td><td>the economy's intrinsic effect</td><td>Section 3.1</td></tr><tr><td>b<sub>i</sub></td><td>interaction coefficient of sector (i)</td><td>Section 3.2; relation (1')</td></tr><tr><td>b<sub>i</sub>b<sub>j</sub></td><td>the economy's demonstration effect</td><td>Section 3.2</td></tr><tr><td>γ<sub>i</sub></td><td>international information coefficient of sector (i)</td><td>Section 3; relation (1')</td></tr><tr><td>ρ</td><td>policy factor, determined by the government</td><td>Section 3; relation (1')</td></tr><tr><td>g<sub>i</sub></td><td>teleonomial term of sector (i)</td><td>Section 3; relation (1')</td></tr><tr><td>G<sub>i</sub></td><td>autarky net worth of sector (i)</td><td>Section 3.4; relation (2')</td></tr><tr><td>B<sub>i</sub></td><td>status coefficient of sector (i)</td><td>Section 4.1; relation (3')</td></tr><tr><td>B<sub>i</sub>B<sub>j</sub></td><td>the economy's status effect</td><td>Section 4.1</td></tr><tr><td>Ñ<sub>i</sub></td><td>stationary net worth of sector (i)</td><td>Section 4.1.1; relation (4)</td></tr><tr><td>N<sub>i</sub>(t)</td><td>matrix of the state variables in an open economy at time t</td><td>Appendix B, section B2; relation (B1)</td></tr><tr><td>N</td><td>matrix of the state variables in a closed economy</td><td>Appendix B, section B3; relation (B2)</td></tr><tr><td>A</td><td>matrix of the system's coefficients (a<sub>1</sub>, a<sub>2</sub>, b<sub>1</sub>, b<sub>2</sub>)</td><td>Appendix B, section B2; relation (B1)</td></tr><tr><td>g</td><td>matrix of the teleonomial terms (g<sub>1</sub>, g<sub>2</sub>)</td><td>Appendix B, section B2; relation (B1)</td></tr><tr><td>γ</td><td>matrix of the international information coefficients (γ<sub>1</sub>, γ<sub>2</sub>)</td><td>Appendix B, section B2; relation (B1)</td></tr><tr><td>r<sub>k</sub></td><td>characteristic root or eigenvalue k of sector (i) (k = 1, 2)</td><td>Appendix B, section B5; relation (B3)</td></tr><tr><td>β<sub>ik</sub></td><td>adjusted status coefficient of sector (i) with respect to eigenvalue r<sub>k</sub></td><td>Appendix B, section B5; relation (B3')</td></tr><tr><td>N<sub>i</sub>(0)</td><td>endowment of sector (i) at initial time (t = 0)</td><td>Section 4.1.1</td></tr><tr><td>W̃<sub>i</sub>(0)</td><td>endowment privilege of sector (i) at initial time (t = 0)</td><td>Appendix B, section B7</td></tr><tr><td>W̃<sub>i</sub>(t)</td><td>wealth privilege of sector (i) at time t</td><td>Appendix B, section B6</td></tr><tr><td>S<sub>i</sub></td><td>socioteonomial standard of sector (i)</td><td>Appendix B, section B15; relation (B14)</td></tr><tr><td>Ñ̃<sub>i</sub>(t)</td><td>the economy's average net worth at time t</td><td>Appendix B, section B23; relation (B22)</td></tr><tr><td>m<sub>i</sub>(t)</td><td>effective wealth redistribution from sector (i) to sector j at time t</td><td>Appendix B, section B23; relation (B23')</td></tr><tr><td>Φ<sub>i</sub>(t)</td><td>wealth redistribution from sector (i) to sector j (at time t) that repositions an entrapped economy from inside the hubris zone to a point on the saddle path.</td><td>Appendix B, section B21; relation (B21)</td></tr><tr><td>Ψ<sub>i</sub>(t)</td><td>cohesively effective wealth redistribution from sector (i) to sector j at time t</td><td>Appendix B, section B25; relation (B25)</td></tr><tr><td>Ω<sub>i</sub>(t)</td><td>cohesively effective debt reduction in favor of sector (i) at time t</td><td>Appendix B, section B25; relation (B26)</td></tr></tbody></table>

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<footnote>* In this dyadic model (two-sector, two-member, or two-class), the term *sector* (real) is used interchangeably with *member* (symbolic) or *class* (real).</footnote>