Discussion Paper No. 524

GROWTH OR STAGNATION:
ECONOMIC CONSEQUENCES OFSTATUS PREFERENCE

Yoshiyasu Ono

January 2001

The Institute of Social and Economic Research
Osaka University
6-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan

January 2001

Growth or Stagnation:
Economic Consequences of Status PreferencebyYoshiyasu Ono*
Osaka University

Abstract
Using a dynamic optimization model with status preference this paper shows that
depending on the object of people’s status preference an economy exhibits a completely
opposite performance; permanent growth or persistent stagnation. If the object is a
producible asset (viz. real capital), new employment is created and extra production isinvested in capital, which generates permanent growth even under decreasing returns tocapital. If it is an unproducible asset (viz. money), commodity demand is not created
and deflation occurs. Full employment is never reached under nominal wage
sluggishness although prices and wages continue to adjust.
Keywords: Status Preference, Long-Run Growth, Persistent Unemployment.
JEL Classifications: E12, E24, O41
Correspondence: Yoshiyasu Ono, The Institute of Social and Economic Research,
Osaka University, 6-1, Mihogaoka, Ibaraki-shi, Osaka, 567-0047, Japan.
e-mail: ono@iser.osaka-u.ac.jp*

The author is indebted to Ryo Horii, Shinsuke Ikeda, and Akihisa Shibata for their valuable comments.

1. Introduction“Why do the rich save so much?” (Carroll, 2000). It is naturally attributed toVeblen’s status preference (1949) or Weber’s capitalist spirit (1958). If people have adesire to be richer than others, they continue to save since others also accumulate wealthand hence they can never feel richer than others. Keynes (1972, p.326) states:
Now it is true that the needs of human beings may seem to be
insatiable. But they fall into two classes—those needs which are
absolute in the sense that we feel them whatever the situation of our
fellow human beings may be, and those which are relative in the sensethat we feel them only if their satisfaction lifts us above, makes us feelsuperior to, our fellows. Needs of the second class, those which satisfy
the desire for superiority, may indeed be insatiable; for the higher thegeneral level, the higher still they are.
If such status preference is directed toward a producible asset, such as real capital,
new employment is created and extra production is invested in capital, which would
generate permanent growth. However, if it is directed toward an unproducible asset,
such as money and land, new employment is not created. Then, a shortage of demand
would occur and deflation would last. Keynes (1936, p.235) also states:
Unemployment develops, that is to say, because people want themoon;– men cannot be employed when the object of desire (i.e.
money) is something which cannot be produced and the demand forwhich cannot be readily choked off.
Using a dynamic optimization model with status preference, this paper exhibits such a
sharp contrast between the status preference directed toward capital and that towardmoney or land.
Recently, the literature on status preference has been expanding. When analyzing
long-run growth in the presence of status preference, most of them, e.g., Cole, Mailathand Postlewaite (1992), Fershtman, Murphy and Weiss (1996), Corneo and Jeanne(1997, 1999), Rauscher (1997), Zou (1995, 1998), and Futagami and Shibata (1998),
assume constant returns to capital. Under this assumption long-run growth naturally
occurs regardless of status preference, as is widely known in the literature of1

endogenous growth. When decreasing returns to capital are assumed, long-run growthdoes not occur and thus the effect of status preference on the absolute level of capital in
the steady state is analyzed (Rauscher, 1997; Zou, 1998). However, Max Weber’s
original view is that the spirit of capitalism alone generates growth. In fact, Zou (1994)
and Corneo and Jeanne (1995) show that in the presence of status preference directed
toward real capital long-run growth can occur even under decreasing returns to capital.
This paper shows that in such an economy if people’s status preference is directed
toward an unproducible asset (viz. money) instead of real capital, deflation andstagnation occur as steady-state phenomena. Thus, whether status preference is directed
toward a producible asset or an unproducible one leads to a quite opposite performanceof an economy; namely, long-run growth or long-run stagnation.
The plan of this paper is as follows. Section 2 examines the dynamics of a nonmonetary economy where people’s status preference is directed toward real capital. It isshown that there is a case where capital eternally grows on the unique equilibrium patheven under decreasing returns to capital. This endogenous growth is purely supported bypeople’s desire to climb up the ladder of social status.
Section 3 considers a monetary economy where people’s status preference isdirected toward money. It finds that an economy with weak status preference is mostprobably located in a state with persistent deflation. It also shows that no dynamic
equilibrium path is supported if status preference is strong. In such a case, if nominal
wage adjustment is sluggish, deflation and unemployment would occur. Section 4
examines this property and shows that unemployment caused by a demand shortage
persistently occurs on the unique dynamic equilibrium path. Finally, section 5summarizes the implication of this paper.

2. An Economy with Capital Accumulation
As a benchmark I first examine an economy in which status preference directed
toward real capital creates long-run growth, such as presented by Corneo and Jeanne(1995). In a one-commodity economy firms are assumed to input labor l and capital k to
produce y using the following linear homogeneous production function:2y = F(l, k) = f(n)k, where n = l/k,f′(n) > 0,f″(n) < 0,f(0) = 0, f(∞) = ∞,f′(0) = ∞,f′(∞) = 0.

(1)

Without adjustment costs of investment, the optimal conditions areω = f′(n), r = f(n) − f′(n)n,(2)

where ω is the real wage. Needless to say, the maximized firm value is k in this setting.
A representative household holds wealth a and earns interest ra and wage ω,
where his (or her) labor endowment is normalized to unity. The flow budget equation isa& = ra + ω − c.

(3)

The household’s utility is assumed to depend on consumption c and relative social
status a − a* where a* is the social average of wealth holding.1 Let ρ the subjective
discount rate, the utility is given by∞U = ∫ (u (c) + w(a − a*))exp(−ρt )dt ,0u′(.) > 0,u″(.) < 0,u′(0) = ∞;w′(.) > 0,w″(.) < 0.

(4)

The household maximizes U subject to (3), and then the optimal conditions areu′(c) = λ,(5)

λ& /λ = ρ − r − w′(a − a*),(6)

where λ is the co-state variable of k. The transversality condition islim λtatexp(− ρt) = 0.
t →∞

(7)

Since social average wealth a* always equals individual wealth holding a, at any
point in timew′(a − a*) = w′(0) > 0.
This implies the statement of Keynes shown at the outset of the introduction: the needs
which satisfy the desire for superiority are insatiable since the social average wealth andeach household’s wealth increase in parallel. Therefore, from (5) and (6), c& 
η(c)  = r + w′(0)/u′(c) − ρ,
c

(8)

where η(c) = − u″(c)c/u′(c).

1

See also the first model of Clark and Oswald (1998) and model 3 of Bakshi and Chen (1996) for this setting of statuspreference.

3

The market equilibrium conditions are
the commodity market:

f(n)k = c + k& ,(9)

the labor market:

nk (= l) = 1,(10)

the asset market:

a = k.

(11)

 c& 
η( c )  = f(1/k) − f′(1/k)(1/k) + w′(0)/u′(c) − ρ,
 c

(12)

k& = f(1/k)k − c,(13)

Using (2), (8), (9) and (10),which formulate an autonomous dynamic system with respect to c and k. Figure 1
illustrates the boundary curves of (12) and (13) in the case where the two curvesintersect whereas figure 2 does so in the case where they do not.
As shown in figure 1, there are two intersection points k1 and k2 if the two curvesintersect. They satisfy
ρ = f(1/k) − f′(1/k)(1/k) + w′(0)/u′(c),c = f(1/k)k.

(14)

If the initial level of k is smaller than k2, the economy approaches A and hence keventually becomes k1 on the dynamic equilibrium path.
Without status preference, the steady state level of k is k0 that satisfies
ρ = f(1/k0) − f′(1/k0)(1/k0),(15)instead of (14). This is the steady-state level of k in the standard neoclassical growthmodel. In figure 1 k0 is given by the intersection point of the c& = 0 curve and the k axis.
Note that k1 is higher than k0 –i.e., status preference raises the steady state level of k.
If the initial level of k is higher than k2, the path along BD is the uniqueequilibrium path.2 Note that on BD k diverges to infinity and yet the transversality
condition is satisfied. In fact, from (13), along BD
lim k& /k = lim f(1/k) − c/k = 0,
k →∞

k →∞

and λ (= u′(c)) is finite since c stays to be finite:c = u′−1(w′(0)/ρ).

2

As proven in the appendix all the other paths cannot be dynamic equilibrium paths.

4

Therefore, from (11) transversality condition (7) is valid.
When status preference w′(0) is large enough, the two boundary curves do notintersect. This case is illustrated in figure 2. Along the dynamic equilibrium path k
always diverges to infinity while c increasingly approaches u′−1(w′(0)/ρ), regardless of
the initial capital level. The transversality condition is proven to be valid in the same
way as above.

3. A Monetary Economy
In the capitalist-spirit economy capital eternally grows although consumption
stays below a finite level. Extra commodity production is all invested in capital.
People’s demand for capital does not disappear since the social average of wealth rises
together with the representative household’s wealth and hence the representative
household is never satiated with capital accumulation. This is quite in conformity withthe spirit of capitalism à la Max Weber (1958).
Whether capital is accumulated in order to receive its returns or to satisfy statuspreference, commodity demand (for the purpose of investment) is created and hencelabor demand also is. However, if status preference is directed toward an unproducible
asset, such as money and land, the commodity demand decreases. Therefore deflation ora shortage of demand, causing persistent unemployment, may occur.
This section considers a pure monetary economy in which people accumulatemoney to satisfy status preference, and explores the possibility of persistent deflation. It
also applies the same argument to the case where status preference is directed towardland. In the latter case persistent land-price inflation obtains. The possibility of apersistent shortage of demand is examined in the next section.
In the present monetary economy firms are assumed to produce output y by using
only labor l with a constant-returns-to-scale technology:y = θl,(16)

where input-output ratio θ is constant. Therefore, given real wage ω, the firm sector’s
demand for labor l satisfies

5l = 0 if ω > θ,
0 < l < ∞ if ω = θ,(17)l = ∞ if ω < θ.
Because of technology (16) the firm value is zero and thus money is a sole asset inthis economy. The representative household’s labor endowment is again assumed to be
1, but in order to take into account the possibility of unemployment its actual labor
supply is denoted x, wherex = min(1, l).

(18)

Since full employment is assumed to hold in this section, x equals 1.
Subject to the flow budget equation:
m& = ωx − c − πm,

where π is the inflation rate of nominal commodity price P, the household maximizes its
utility:∞U = ∫ (u (c) + w(a − a*) + v(m) )exp(−ρt )dt ,0v′(m) > 0,v″(m) < 0,v′(0) = ∞,v′(∞) = 0,

lim v′(m)m > 0,

m→∞

(19)

where m represents real money balances and v(m) is liquidity preference for thetransaction motive.3 Status preference is represented by w(a − a*), as in the previous
model. In the present setting individual total wealth a equals real balance m.
a=m

(20)

People hold money for both the status and transaction motives.
The optimal conditions of this problem areu′(c) = λ,λ& /λ = ρ + π − [w′(a − a*) + v′(m)].

(21)

Since a* always equals a, as mentioned in the capitalist-spirit model, these conditionsyield
 c& 
ρ + η( c )  + π = [w′(0) + v′(m)]/u′(c).
 c
3

(22)

Feenstra (1986) proves that a cash-in-advance model can equivalently be replaced by a money-in-utility model. The
last property in (19) is imposed so that a hyper-inflation path is avoided. See Blanchard and Fischer (1989, p.241) for
this property.

6

The transversality condition is the same as (7).
Market equilibrium conditions are
the money market:

M/P = m,(23)

the commodity market:

θx = c,(24)

the labor market:

l = 1,(25)

where M is the nominal money stock. From (18), (24) and (25),c = θ.

(26)

m& / m (= − π) = ρ − [w′(0) + v′(m)]/u′(θ).

(27)

From (22) and (26), m satisfies

Figure 3 illustrates this dynamics in the case where status preference w′(0) or production
capacity θ is so low thatρ > w′(0)/u′(θ).

(28)

In this case the path along which P jumps to the level that makes m equal m*, where m*satisfies[w′(0) + v′(m*)]/u′(θ) = ρ,(29)

and thereafter stays is an equilibrium path.
This path is essentially the same as in the standard money-in-utility model.4 In thepresence of status preference w′(0), however, this is not the sole equilibrium path. All
the hyper-deflationary paths along AB in figure 3 are also equilibrium paths. In fact,from (19), (20) and (27), on these paths
lim a& / a = lim m& / m = ρ − w′(0)/u′(θ) < ρ,
t →∞

t →∞

which implies the validity of transversality condition (7). Thus, this economy is mostprobably located in a state with persistent deflation.
In the case where status preference w′(0) or production capacity θ is so high that
ρ < w′(0)/u′(θ)(30)

instead of (28), m& / m given by (27) is always negative. It is well known that these pathsof m are all infeasible under the last property of (19) since m becomes negative within afinite time.5 Therefore, there is no equilibrium path under (30).
4See e.g. Blanchard and Fischer (1989, pp.239-245) for this model.

5

See Blanchard and Fischer (1989, p.241-242) for the proof of this property.

7Note that the same argument applies to the case where land is the object of statuspreference if nominal commodity price P is taken as the relative commodity pricecompared to the land price and money supply M as land endowment. In this economy
people prefer not the land size but the land value for the purpose of achieving social
status. Since the land price is given by 1/P in this case, the hyper-deflationary paths aretaken as those on which the land price keeps expanding while consumption remains to
be constant. As the status preference directed toward land increases, any price pathcannot be an equilibrium path.
The discussion of the present section may remind us of the Japanese land-pricehyperinflation and crash. In the late 1980s Japanese land prices were pushed up by
people’s status preference, and eventually they attained the level equivalent to the priceof the whole U.S. territory or even double. As the status preference escalated more, theequilibrium path was lost and eventually land prices crashed in the early 1990s. Then,the object of people’s status preference converted to money, and thereafter long-run
deflation has been occurring.

4. A Monetary Economy with Nominal Wage Sluggishness
In the previous section it is shown that there is no equilibrium path under (30) –i.e., the case where status preference w′(0) is so high that if consumption c takes the full
employment level θ, a wealth-holding desire exceeds a desire for consumption, the latterof which is ρ when P stays constant. Thus, P has to keep moving so that an equilibrium
path would be realized. As shown in the previous section, however, any price movement
cannot realize an equilibrium path. In such a case a shortage of effective demand andunemployment may naturally occur as steady-state phenomena once nominal wage
adjustment is sluggish.6 This section is devoted to proving this property.
It may be noteworthy that in a standard money-in-utility model without statuspreference full employment is eventually reached even under nominal wage

6

If perfect nominal wage adjustment is assumed, any labor demand shortage at any point in time is ‘by definition’
avoided.

8

sluggishness. In the presence of status preference, however, full employment is neverreached, as shown below. Unemployment occurs as a steady-state phenomenon.
To represent sluggish adjustment of nominal wage W, a new Keynesian Phillips
curve with the following functional form:7
W& /W = α(l − 1),(31)

is assumed, where the full employment level is normalized to unity. The commodity andmoney markets are assumed to adjust perfectly, as in (23) and (24). From (17), if W/P >θ, labor demand l is zero and therefore commodity supply is zero, which immediately
makes P jump upward so that W/P = θ. If W/P < θ, then from (17) l is ∞ and hence evenunder the sluggish money wage adjustment given by (31) W instantaneously rises to θP.
Thus, it is always satisfied that
W/P = ω = θ,

(32)

W& /W = π.

(33)from which

Since (32) is valid, from (17) l can take any value. Then, l is determined byeffective demand x (= c/θ from (24)).
l = c/θFrom this property, (31) and (33), the dynamics of P is
π = α(c/θ − 1),(34)which implies that P and W move in parallel in accordance with the gap between
production capacity θ and effective demand c.8 From (22), (23) and (34),m& / m (= − π) = − α(c/θ − 1),(35) c& 
η( c )  = [w′(0) + v′(m)]/u′(c) − α(c/θ − 1) − ρ.
 c

(36)

(35) and (36) formulate an autonomous dynamic system with respect to m and c.9

7

See Roberts (1995) for discussions on various models of such sluggish price/wage adjustment, called new KeynesianPhillips curves.

8

Note that this equation is valid only when c/θ ≤ 1. If c/θ > 1, demand exceeds supply in the commodity market since
the maximum commodity supply is θ, and because of the instantaneous adjustment of the commodity market P
immediately jumps upward so that c/θ = 1. Thus, the following dynamics is valid only in the case where c/θ ≤ 1.

9This dynamics is similar to that in Ono (1994, 2001). In the present model status preference w(a − a*) and nominal
wage sluggishness cause persistent unemployment while in Ono insatiable liquidity preference (v′(∞) > 0) and9As long as full employment eventually obtains, the steady state is essentially thesame as that in the standard money-in-utility model. In fact, from (35) and (36), thesteady-state levels of c and m are the same as those in (26) and (29), viz. those under
perfect nominal wage adjustment. However, in the previous section it has already beenshown that this state does not exist under (30).
In this case a shortage of effective demand occurs (c < θ), and thus from (35) m
diverges to infinity, causing v′(m) to be zero. In this state, from (36), c satisfies
w′(0)/u′(c) = ρ + α(c/θ − 1).

(37)

In figure 4, the l and π curves respectively stand for the left- and right-hand sides of (37)and cu is the level that satisfies (37). Under (30) the l curve is located above the π curvewhen c = θ. Thus, in order for cu to be positive the π curve must be located above the lcurve when c = 0. This condition is valid when nominal wage adjustment speed α must
be sluggish enough to satisfy
ρ > α.

(38)

Figure 5 illustrates the dynamics of (35) and (36) under conditions (30) and (38).
There is a unique equilibrium path represented by AB. Along this path m diverges toinfinity, causing v′(m) to be zero, and from (36) c asymptotically approaches cu thatsatisfies (37). Thus, c remains to be smaller than θ, causing unemployment to lastforever. In this state P continues to decline and m (= a from (20)) expands to infinity,and yet the transversality condition is valid. In fact, from (35) and (36), along this path
lim a& / a = ρ − w′(0)/u′(cu) < ρ,t →∞which implies the validity of transversality condition (7). Any other path is either
infeasible or inconsistent with the transversality condition, as proven in the same way asin the case of figure 2.
It may be interesting to compare figure 5 with figure 2. They have quite similar
structures to each other, and yet their implications are quite opposite. The statuspreference toward real capital leads to persistent growth while that toward money resultsin persistent stagnation.

nominal price sluggishness lead to persistent excess supply.

10

Note that conventional Keynesian models need either nominal or real wage
rigidity when explaining persistent unemployment whereas neither of them is necessary
in the present status-preference model. In fact, in the steady state P and W continue toadjust and realize full-employment real wage θ, and yet consumption c stays below cu,
causing persistent unemployment to occur.
The steady state obtained above has Keynesian features. For example, an increasein fiscal spending raises consumption. Specifically, in the presence of fiscal spending g,
the commodity market equilibrium condition (24) is replaced byθx = c + g,
and then (37) is revised tow′(0)/u′(c) = ρ + α((c + g)/θ − 1).

(39)

Thus, an increase in g shifts the π curve upward in figure 4, causing intersection point A
to move rightward on the l curve and hence cu to increase.
Also, from the right-hand side of (39), a rise in nominal wage adjustment speed αturns the π curve counterclockwise around B with the l curve unaffected. Consequently,intersection point A moves leftward on the l curve and hence cu declines. This result isquite opposite to the conventional view shared by both neoclassical and Keynesian
economics –i.e., the more rapidly prices and wages adjust, the sooner an effective
demand shortage disappears. It is consistent with Keynes’s own view (1936, Ch.19) –i.e.,
a rise in the wage adjustment speed reduces effective demand.

5. Conclusion
In the presence of status preference people attempt to accumulate more wealththan others. As the economy grows, each individual accumulates wealth, but the social
average also rises and hence his (or her) desire for wealth accumulation remains to havethe same magnitude.
If such status preference is directed toward an asset that can be produced (viz. realcapital), it keeps generating new employment and expanding production, but
consumption does not increase. Extra products are all invested in capital formation in

11

order to satisfy status preference, and therefore the economy eternally grows. This isquite in conformity with Max Weber’s capitalist-spirit economy.
If the status preference is directed toward an asset that cannot be produced, suchas money and land, however, it does not create any commodity demand. People attempt
to accumulate money or land by restricting consumption. In the case where land is theobject of status preference, the commodity price compared to the land price continues todecline, that is, land-price inflation occurs. In the case where money is the object,commodity-price deflation occurs. In any case a decline in the relative commodity priceenables people to increase the real value of wealth.
As this status preference increases, an equilibrium price path disappears. In thiscase, if nominal wage adjustment is sluggish, as given by a new Keynesian Phillips
curve, a shortage of effective demand naturally occurs. There is a unique dynamic
equilibrium path along which unemployment persistently occurs.
It is contrasting to the standard money-in-utility model without status preference.
Without status preference full employment is eventually reached even under nominal
wage sluggishness. In the presence of status preference, however, full employment isnever reached although wages continue to adjust. The steady state is characterized by aKeynesian shortage of demand.
To summarize, whether status preference is directed toward a producible asset oran unproducible one leads to a completely opposite performance of an economy. If it isdirected toward a producible asset (viz. real capital), an economy eternally grows. If it is
toward an unproducible one (viz. money), an economy suffers persistent unemployment
and deflation.

Appendix
From (5), (12) and (13),λ& / λ + k& / k = − c/k + f′(1/k)(1/k) − w′(0)/u′(c) + ρ,

(A1)

From (1), (4) and (A1), on any path along which c converges to zero and k diverges toinfinity,

12lim λ& / λ + k& / k = ρ,t →∞which implies the invalidity of transversality condition (7).
On any path along which c increases and k decreases, k& given by (13) is strictly
negative when k is zero. Since k cannot be negative, this path is infeasible.

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14

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15

ck& = 0

u′−1(

w′(0)
)
ρ

D
c& = 0

B

A

O

k0

k2

k1

Figure 1kck& = 0

u′−1(

w′(0)
)
ρ

D
c& = 0Okk0

Figure 2

m&

B

A
O

m*

D

Figure 3mRlw′(0)/u′(θ)

π
ρ

B
A

ρ−α

O

cu

Figure 4θccm& = 0θcu

Bc& = 0Am

O

Figure 5