metadata: authors: 0: author: Lopeza, Ramon
count: World,India,China
docna: 0: docna: Trade and migration with renewable natural
            resources : out-of-steady-state dynamics
docty: Policy Research Working Paper
subtopic: Human Migrations & Resettlements,Construction Industry,Common Carriers Industry,Food & Beverage Industry,General Manufacturing,Pulp & Paper Industry,Plastics & Rubber Industry,Coastal and Marine Resources,International Trade and Trade Rules,Energy and Natural Resources,Business Cycles and Stabilization Policies,International Migration,Global Environment,Migration and Development
teratopic: Private Sector Development,Macroeconomics and Economic Growth,Health, Nutrition and Population,Finance and Financial Sector Development
abstracts: cdata!: Commodity price increases associated
            with the entry of China, India, and other countries into the
            world economy have led to increased pressure on
            common-property renewable natural resources. The problem is
            particularly worrisome for economies that obtain a large
            share of their income from the exploitation of natural
            resources in the production of an exportable commodity. This
            paper contributes to the analysis by examining the issue in
            the framework of a general equilibrium dynamic model and by
            solving for both the steady state and the transition
            dynamics. The authors show that i) a resource-rich,
            capital-poor economy is more likely to be subject to a
            "natural resource curse" and complete
            (irreversible) depletion of natural resources; ii) the
            latter's likelihood rises with the relative commodity
            price and labor inflow; iii) a labor inflow under internal
            equilibrium results in a higher steady-state capital-labor
            ratio and manufacturing output, and unchanged natural
            resources and commodity output; iv) import and export taxes
            result in larger steady-state natural resources and
            commodity output and smaller capital stock and manufacturing
            output, and may prevent complete depletion of natural
            resources; and v) the latter may also be prevented through
            capital inflows (foreign aid), labor outflow (
            liberalization of the North's immigration policy),
            improved regulation, technical change, and a production tax.
geo_reg_key: 517198,119225,517212,517191
repnme: repnme: Trade and migration with renewable natural
            resources : out-of-steady-state dynamics
display_title: Trade and migration with renewable
            natural resources : out-of-steady-state dynamics
listing_relative_url: /research/2010/05/12252610/trade-migration-renewable-natural-resources-out-of-steady-state-dynamics
topicv3: Natural Resources m1326446 1979,Manufacturing Sectors m1326521 1281,Trade m1326924 698,Environment, Natural Resources and Blue
            Economy m1327391 566,Immigration m1504162 2837
publishtoextweb_dt: 2010-07-01T00:00:00Z
historic_topic: Private Sector Development,Macroeconomics and Economic Growth,Health, Nutrition and Population,Finance and Financial Sector Development
no_of_pages: 30
model_extractions: WPS5310 Policy Research Working Paper 5310 Trade and Migration with Renewable Natural Resources Out-of-Steady-State Dynamics _Ramón Lópeza Maurice Schiff_ The World Bank Office of the Chief Economist Latin American and Caribbean Region May 2010
Policy Research Working Paper 5310

# **Abstract**

Commodity price increases associated with the entry of China, India, and other countries into the world economy have led to increased pressure on commonproperty renewable natural resources. The problem is particularly worrisome for economies that obtain a large share of their income from the exploitation of natural resources in the production of an exportable commodity. This paper contributes to the analysis by examining the issue in the framework of a general equilibrium dynamic model and by solving for both the steady state _and_ the transition dynamics. The authors show that i) a resourcerich, capital-poor economy is more likely to be subject to a “natural resource curse” and complete (irreversible) depletion of natural resources; ii) the latter’s likelihood rises with the relative commodity price and labor inflow; iii) a labor inflow under internal equilibrium results in a _higher_ steady-state capital-labor ratio and manufacturing output, and unchanged natural resources and commodity output; iv) import and export taxes result in larger steady-state natural resources and commodity output and smaller capital stock and manufacturing output, and may prevent complete depletion of natural resources; and v) the latter may also be prevented through capital inflows (foreign aid), labor outflow ( liberalization of the North’s immigration policy), improved regulation, technical change, and a production tax.

This paper—a product of the Office of the Chief Economist, Latin American and Caribbean Region—Office of the Chief Economist. Policy Research Working Papers are also posted on the Web at http://econ.worldbank.org. The author may be contacted at mschiff@worldbank.org.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
# **Trade and Migration with Renewable Natural Resources: Out-of-Steady-State Dynamics**<sup>*****</sup>

# **and Maurice Schiff**<sup>**b**</sup> **Ramón López**<sup>**a**</sup>

Keywords: renewable natural resources, depletion, transition dynamics, steady state, trade, migration, capital flows JEL Code: F22, O13, O15, Q17, Q27

* The views presented in this paper are those of the authors and do not necessarily reflect the views of the World Bank, its Executive Directors or the governments they represent.

a. University of Maryland at College Park

- b. World Bank, University of Chile, and IZA (Bonn)
# **I. Introduction**

Many developing countries obtain a large share of their income from the exploitation of common-property renewable natural resources, including fisheries, forests, grazing grounds, and water resources. Their degradation has typically been caused by activities such as logging, agriculture, commercial fishing, and others.<sup>1</sup> It has also been associated with the extraction of exhaustible resources. For instance, mining and oil extraction has led to the depletion of water supplies, water contamination, deforestation, and more.<sup>2</sup> As is well known, a lack of property rights for natural resources results in their excessive exploitation compared to the social optimum and thus in a higher rate of depletion and a smaller long-run (steady-state) stock. López (1998) estimates the losses from non-cooperative behavior on common-property lands and lack of internalization of the external costs of biomass use in land allocation decisions in Côte d’Ivoire to be as high as 14 percent of total village income. He finds that the degree of internalization of the negative externalities is less than 30 percent and declines with community size. López (1997) obtains similar estimates for the income loss in Ghana. These and other studies make it clear that the problem of imperfect property rights is of crucial importance for many countries and may even result in total depletion of the natural resource and disappearance of poor communities.

A large number of studies have examined communities that had been stable for long periods but then started a process of impoverishment that worsened over time (see the forthcoming paper by López for a review of such studies). These communities typically experienced important changes over time – such as an increase in population or in market size which resulted in increased pressure on the natural resource and a decline in the degree of internalization of the negative externalities – but failed to develop adequate institutions to deal with them.

> 1 The classic case of natural resource depletion is that of fisheries which has affected a large number of countries over the years and was the focus of early natural resource depletion studies (e.g., Gordon 1954, Scott 1955). An example is that of Peruvian anchovies whose world price increased dramatically in the late 1970s and early 1980s. This raised the incentive to invest in fishing boats, an investment subsidized by the government when a tax would have been optimal. The higher prices and subsidies led to a dramatic increase in the fishing fleet and the stock of anchovies disappeared for several years, leading to a decline in the use of these boats and thus in fishing. This enabled the anchovy stock to replenish over time. 2 It is estimated that nearly one third of all active mines and exploration sites are located within areas of ecosystems with high conservation value (Miranda et. al., 2003).

2
Often located in tropical areas, land quality in such communities has typically been of poor quality, with natural resource depletion impeding regeneration of soil fertility and leading to further decline in their quality by hampering nutrients deeper in the soil to rise to the surface. The ensuing deforestation has, in extreme cases, led to the disappearance of entire communities. A well-known such case is that of Easter Island where excessive logging led to the disappearance of its population. A more recent one is the deforestation in low-lying areas in the Philippines, with some four million people moving from low-lying to high-lying areas in recent years to (Washington Post, February 23, 2009, pp. 1-2). Similarly, excessive pressure on natural resources has led to the advance of the Sahara and Gobi deserts.

This paper examines the welfare consequences of commodity production under a lack of property rights for natural resources. Unlike most previous studies that are based on static and partial equilibrium analysis, we focus on the dynamics of the economy’s adjustment to changing conditions and policies, and explicitly account for general equilibrium interactions. We consider a two-sector economy where one of the productive sectors, the primary commodity-producing sector, is directly dependent on renewable natural resources. The economy uses three factors, labor, capital and natural resources. The first two are allocated competitively across the two sectors while the natural resource stock is exclusively used in the commodity-producing sector. The economy can save and invest its savings in expanding the stock of capital. The natural resource and capital stocks are determined endogenously and in turn determine the evolution of the economy.

An issue that has become a matter of increasing concern in recent years is the link between trade and the environment.<sup>3</sup> A common argument is that international trade has resulted in greater environmental degradation in developing countries. Existing studies have focused on long-run equilibrium effects but have not examined the adjustment dynamics to changes in the trade regime. This is likely to be a significant problem, particularly since shocks typically occur frequently and the economy rarely has time to reach its long-run equilibrium but rather tends to adjust to the various shocks while being in a disequilibrium situation. Moreover, introducing this type of analysis is critical as it allows for alternative long-run equilibria – such as the total depletion of natural resources

> 3 For a good review and analysis of trade’s environmental impact, see Copeland and Gulati (2004).

3
– that are not generated by models that focus exclusively on static or steady-state analysis.

This paper is a first effort to fill this important gap in the literature. We examine out-of-steady-state adjustments to changes in policy and other conditions, as well as their impact on the steady state. Policies considered include those affecting the international movement of goods and factors – including in- and out-migration and foreign aid – as well as regulation of natural resource use and technology designed to reduce the naturalresource intensity of commodity production. Changes in terms of trade are analyzed as well.

This issue is particularly relevant in the context of China, India and other countries’ recent integration into the world market and the resulting boom in commodity prices and increased pressure on natural resources. The importance of this boom is illustrated by the fact that it affected a larger share of important commodities for the Latin America and Caribbean region than ever recorded in the past (World Bank, forthcoming). This phenomenon is expected to continue in the future due, first, to these countries’ high expected growth rates and, second, to the associated massive internal (rural-urban) migration in a part of the world where over a third of the world’s population resides together with the fact that per-capita commodity demand is substantially higher in urban than in rural areas.<sup>4</sup> An analysis that emphasizes conditions outside long-run equilibrium in a context of two state variables (physical capital and natural resource) in a general equilibrium framework can be exceedingly complex. In order to keep the problem tractable, we provide a basic dynamic model with sufficient complexity needed to yield important insights on the behavior of the economy when subjected to a variety of shocks.

The remainder of the paper is organized as follows. Part II presents the benchmark model, Part III examines the transition path of a resource-rich, capital-poor economy, and Part IV examines the impact of trade policy, factor movement policy and other ones. Part V looks at the situation of environmental collapse and Part VI concludes.

> 4 Higher commodity demand implies higher derived demand for both renewable natural resources (for consumption, e.g., agricultural and fish products, and for production, e.g., wood and cellulose) and exhaustible resources (for production, housing, infrastructure, etc).

4
# **II. The benchmark model**

The small open economy consists of two sectors, a resource-dependent commodity sector _C_ and a manufacturing sector _S_ that does not depend on the natural resource as an input. Each sector uses labor ( _l_ ) and capital ( _k_ ). The commodity sector also uses a renewable natural resource input, _n_ , in addition to capital and labor. The production functions are:  1  (1) _ys_  _Aks ls_ (2) where<sup>_y_</sup> _s_<sup>and</sup><sup>_y_</sup> _c_<sup>are the output levels of the manufacturing and commodity goods,</sup> respectively (0<  1, 0    1) and _A_ and _D_ are fixed parameters. The natural resource enters the production of the commodity (equation (2)) in the way it is conventionally done in the literature (Gordon 1954, Schaefer 1957, Copeland and Taylor 1994, and many others).

The manufacturing (commodity) sector represents the modern urban (traditional rural) sector. We assume the modern sector is more capital intensive than the traditional one, i.e., we assume    . The dynamics of the natural resource stock is given by (3) The term _g_  _n_ is the intrinsic growth function of the renewable natural resource. The second term represents the reduction of the natural resource stock due to production of the commodity good _C_ . The parameter 0  1 measures the intensity of the environmental demands per unit of _C_ . We follow the literature and assume that the intrinsic growth of the natural resource takes the quadratic form (4) _g_ ( _n_ )   _n_ (1  ( _n_ / _~~n~~_ ) , 5 where _~~n~~_ is the maximum carrying capacity and   _yc_ / _n_ is a parameter.

The aggregate stock of physical capital grows according to: (5)

> 5 The condition   _yc_ / _n_ ensures a positive value for _n_ in steady state, i.e., _n_<sup>_*_</sup> > 0.

5
where _p_ is the commodity market price (the manufacturing good price is normalized to 1),  is the rate of capital depreciation, and _c_  _cs_  _pcc_ is the total real consumption expenditures measured in units of the manufacturing good. The sum of the first two terms on the right-hand-side of equation (5) is the total real income of the economy, _y_ , measured in units of the manufacturing good, with gross capital accumulation equal to savings _y - c_ .<sup>6</sup> Labor and capital markets are assumed perfectly competitive so that at any moment in time, the economy is in full employment and the stock of physical capital is fully utilized. We assume the total labor force _L_ is fixed: As is well known, the behavior of a competitive economy can be replicated by a constrained optimum for the economy that maximizes the present value of welfare, subject to the parameters and institutional constraints. Among the institutional constraints, we assume that property rights on the natural resource are non-existent. That is, condition (3) above does not enter directly into the inter-temporal optimization process. However, it does show the evolution of the natural resource stock, an evolution which itself plays a central role in the dynamics and steady state of the economy.

We assume that the economy’s indirect utility function is, (8) _u_  _u_ ( _c_ / _e_ (1, _p_ )) , where _e_ (1, _p_ ) is the unit expenditure function. The indirect utility function in (8) implies that the underlying direct utility function is homothetic. Also, _u_ is assumed to be increasing and strictly concave in _c_ . The indirect utility function implies that the consumer has already solved the static consumer problem by picking the optimal combination of<sup>_c_</sup> _s_<sup>and</sup><sup>_c_</sup> _c_<sup>conditional on the price,</sup><sup>_p_, and on a level of total consumption</sup>

> 6 Equation (5) also represents the budget constraint of the economy. It reflects, in the context of an open economy, the trade balance equilibrium or, equivalently, the situation where the total value of domestic output is equal to the value of expenditures in consumption of the two goods plus investment, with differences between commodity (manufacturing) production and consumption exported (imported) at a fixed price.

6
expenditure, _c_<sup>7</sup> . The optimal level of _c_ (and hence of capital accumulation) is determined by the inter-temporal optimization.

A competitive economy behaves “as if” it maximizes the present discounted value  of the utility function, _u_ ( _c_ / _e_ (1, _p_ )){exp  _t_ } _dt_ (  is the time discount rate), subject to  0 the relevant economic and institutional constraints. It does so by choosing the levels  of _c_ , _lc_ , _ls_ , _kc_ , _ks_ and investment _I_  _K_   _K_ at each point in time subject to equations (5), (6) and (7), and subject to the given initial conditions _K_ (0)  _K_ 0 and _n_ (0)  _n_ 0 . As a consequence of the institutional failure, the economy ignores the impact of its choices on the environmental dynamic represented by (3). However, the above choices do impinge upon the dynamics of the natural resource according to equation (3), which in turn carries implications for future choices. Thus, despite the assumption of competitive markets the existence of the institutional constraint associated with imperfect property rights on the natural resource implies that the solution to the optimization problem should be interpreted as the best path possible _given_ the institutional imperfection.

This problem can be solved by maximizing the current value Hamiltonian (9) _H_  _u_  _c_ / _e_ (1, _p_ )    _Aks_  _ls_ 1   _pnDkc_  _lc_ 1    _K_  _c_  where  is the co-state variable of the capital stock. Assuming interior solutions, the first order conditions are: where _w_ and _r_ are the market wage rate (in units of the manufacturing good) and the rental price of capital or interest rate, respectively<sup>8</sup> . Equations (11) and (12) indicate that

> 7 In fact, by Roy’s identity, one can retrieve the optimal conditional consumption bundle from the indirect utility function.

7
factor returns in competitive markets are equal to their respective marginal value products and, given factor mobility, such returns are equalized across the sectors. Equation (10) shows the equalization between the marginal utility of current consumption and the shadow price of capital (or the present value of the utility derived from an extra unit of capital created by reducing current consumption). Equation (13) is the classical noarbitrage condition reflecting temporary competitive equilibrium in the asset market. It states that the expected returns to holding one unit of capital (the interest rate, _r_ , plus the expected capital gain,  / ) must be equal to the marginal cost of holding one unit of capital (the capital depreciation rate,  , plus the opportunity cost,  ).

Dividing (11) by (12), we obtain: Given the assumption that    , it follows that  1. Substituting equation (15) in equation (12), we can obtain an expression for the capital/labor ratio in the commodity sector as a function of the stock of natural resources and various parameters, i.e.: Thus, equations (15) and (16) solve for the capital-labor ratios in each industry as a function of the relative commodity price, fixed parameters, and the natural resource stock, _n_ . The fact that the two capital-labor ratios are functions of _n_ ( _t_ ) determines their evolution over time. The capital-labor ratios are increasing in _n_ , the commodity price _p_ and total factor productivity (TFP) in the commodity sector ( _D_ ), and decreasing in TFP in the manufacturing sector ( _A_ ). Note that these ratios depend on the product _pn_ , i.e., they are invariant to changes in _p_ and _n_ that keep _pn_ unchanged.

The reason the capital-labor ratios are increasing in _n_ is as follows. An increase in the natural resource stock raises the economy’s demand for labor more than for capital

> 8 An optimal path with perfect property rights on the natural resource would require that the selection of the control variables incorporate their effect on the changes of the natural resource stock (valued at its shadow price) in the optimization problem. An unrestricted optimum would thus need to consider an additional term,  _n_  (where  is the optimal shadow value of the stock of natural resources), in (9). Lack of property rights on the resource means that the economy behaves myopically with respect to the natural resource stock, i.e., as if  = 0.

8
because the commodity sector is labor-intensive relative to the manufacturing sector (    ). This causes the wage rate to increase relative to the rental rate of capital and leads producers to select more capital-intensive techniques.<sup>9</sup> With the definitions of factor prices _w_ and _r_ given in equations (11) and (12), and using equations (15) and (16), we obtain explicit expressions for the factor prices: More succinctly, we can write the factor prices as (19) (i) _w_  _w_ ( _Dpn_ , _A_ ) , (ii) _r_  _r_ ( _Dpn_ , _A_ ) , with _w_ 1<sup>(</sup> _Dpn_ , _A_ ) > 0, _w_ 2 < 0 and _r_ 1<sup>(</sup> _Dpn_ , _A_ )  0 , _r_ 2  0<sup>(where subscripts denote first</sup> derivatives). Factor prices also follow a dynamic path over time as they are functions of the evolution of the _NR_ stock. Thus, since    , it follows that the wage rate (interest rate) is increasing (decreasing) in _n_ ( _t_ ), _p_ and _D_ , and decreasing (increasing) in _A_ .

As is well known, the total level of income in the economy (in units of the manufacturing output) can be expressed in terms of the value of output ( _y = ys_  _pyc_ ) or, equivalently, of the total factor returns. Thus, using (19), it follows that total economy’s income ( _y_ ) is (20) ( _y pn_ , _K_ ; _L_ ) = _w_ ( _Dpn_ , _A_ ) _L_ + _r_ ( _Dpn_ , _A_ ) _K_ where the income or (dual) revenue function _y_ is increasing in _K_ and _L_ . Moreover, the dual revenue function must be increasing and convex in _p_ , and the first derivative of the income function with respect to _p_ is equal to the commodity output level, by the socalled Hotelling’s lemma (Diewert, 1981); that is,  _y_ /  _p y_ 1( _pn_ , _K_ : _L_ ) _n_  _yc_ . This means that the net effect of _p_ on national income must be positive, which in turn also

> 9 Despite unchanged quantities of labor and capital (in the short run), capital-labor intensities can increase in both sectors due to a change in output composition, with competitive forces leading to the contraction of the capitalintensive manufacturing sector and the expansion of the labor-intensive commodity sector.

9
means that the national income function is increasing in _n_ (that is, the positive wage effect associated with a higher level of _n_ dominates the negative capital price effect). Moreover, the convexity of the national income function in the commodity price means that <sup>_y_</sup> _c_ /  _p_ 0 , i.e., commodity output increases in its price. This also means that<sup>_y_</sup> _c_<sup>is</sup> increasing in _n_ . Specifically, we can write<sup>_y_</sup> _c_<sup>as the first derivative of (20) with respect</sup> to _p_ , i.e.:

> (21)<sup>_y_</sup> _c_ ( _p_ , _n_ , _K_ ; _L_ )  _w_ 1( _Dpn_ , _A_ ) _DnL_  _r_ 1( _Dpn_ , _A_ ) _DnK_ . Since _w_ 1  0<sup>and</sup> _r_ 1  0 , it follows that<sup>_y_</sup> _c_<sup>_increases_in</sup><sup>_L_and</sup><sup>_decreases_in</sup><sup>_K_.</sup>

The following lemma summarizes these results.

**_Lemma 1._** _Assume the manufacturing sector is more capital intensive than the commodity sector. Then: (i) the economy’s wage rate increases in the stock of natural resources and in the commodity price while the interest rate  falls in the same variables, and (ii) production of primary commodities (manufacturing) is increasing (decreasing) in the resource stock and in the labor force and decreasing (increasing) in the stock of capital._ Since both capital and resource stocks change endogenously over time, it follows that

both factor prices and the level and composition of national income must also adjust over time. Before analyzing the dynamics of the system, it is convenient to consider its long run equilibrium or steady state.

# **1. Steady State**

Let’s re-write equation (13) using (19.ii), and the equation of motion of the natural resource, equation (4) as, We define the steady state using these two conditions: the interest rate ( _r_ ) must be equal to the opportunity cost of capital (   ) and the stock of natural resources must be   constant, i.e.,  _n_  0 . The first equality means that * (22) _r_ ( _Dpn_ , _A_ )    10
* That is, there is a unique level of the natural resource stock, _n_ , for which the rate of  return on capital is equal to its opportunity cost. Setting _n_  0 , we can solve equation (4’) for the steady state level of capital, _K_ * : * * * (23)<sup>_y_</sup> _c_ ( _p_ , _n_ , _K_ ; _L_ )  _g_ ( _n_ ) / 

Equations (22) and (23) uniquely determine the steady-state levels of capital and natural resources _K_ * and _n_ * . It is clear that there is no net investment in steady state since, by (22), the rate of interest is just equal to the opportunity cost of capital, and by (23) the consumption of natural resources is just equal to its natural renewal.

* Substituting (18) in (22), we can derive an explicit solution for _n_ , namely:

* **_Lemma 2_** _. The steady state level of the stock of natural resources n under internal equilibrium is decreasing in the commodity price p, the discount rate_  _, the depreciation rate of capital δ and the commodity sector TFP, and is increasing in the manufacturing sector TFP. Interestingly, it is not affected by the size of the labor force L._

Substituting (24) into (17), we obtain an explicit solution for the steady state level of the wage rate: Thus, the steady state level of the wage rate is increasing in the manufacturing sector TFP and decreasing in the discount and depreciation rates but is unaffected by the commodity * sector TFP. The reason for the latter is that _r_    is given in steady state, and since _p_ is given as well, _w*_ is fully determined by the implicit zero profit condition of the manufacturing sector (needed for that sector to have a positive production level) and must therefore be independent of _D_ . However, when _A_ increases, since _r_ = _r_ * is given, _w*_ must increase.

11
## **2. Dynamics**

Rewriting equations (3), (5) and (13), and using some of the results in Lemma 1, we have: We thus have two possible out-of-steady state conditions for the initial stock of natural resources _n_ :

* (i) If _n_  _n_ , it follows from (22) and (28) that _r_    , which implies that the economy  has no incentive to invest in capital and hence _K_  _K_  0 . And since there is no investment and therefore no savings, it follows that _c_  _Y_ ( _pn_ , _K_ , _L_ ) . The rate of growth   of consumption is: _c_ / _c_  (1/ _a_ )  /  (1/ _a_ )[ _r_ ( _Dpn_ , _A_ )  (   )]  0 , where _a_  _cucc_ / _uc_  0 is the elasticity of marginal utility, which is assumed constant; *  (ii) If _n_  _n_  _r_     _K_  0 . In addition, the rate of growth of consumption in this case is positive.

# **III. Transition path of a resource-rich, capital-poor economy**

We now turn to the case of a prototype developing economy that is rich in natural resources and poor in capital, and examine the transition dynamics outside the steady state. The importance of the out-of-steady-state situation depends on the length of time an economy finds itself in such a situation – which is a function of the size and frequency of shocks to which the economy is subjected and on its speed of adjustment – as well as on the likelihood that the economy converges to a permanently inferior equilibrium.

The top panel of Figure 1 depicts the relationship between the rate of return on capital (or interest rate) _r_ and the stock of natural resources _n_ . The second panel in Figure 1 is a phase diagram depicting the dynamics of the system in the { _K_ , _n_ } space. The third panel shows the dynamics of the adjustment in the {<sup>_y_</sup> _c_ ,<sup>_n_} space.</sup> 12
Consider the case of an economy that is initially rich in natural resources * * ( _n_ (0)  _n_ ) and poor in capital ( _K_ (0)  _K_ ) **,** as illustrated by point M in the three panels * of Figure 1. Since _n_ (0)  _n_ , it follows that (0) _r_    (equation 18). This implies that initially there is no investment in capital and _K_   0 . Initial commodity output<sup>_y_</sup> _c_ (0)<sup>must</sup> * * be above its steady-state level because _K_ (0)  _K_ and _n_ (0)  _n_ , as shown by point M in the bottom panel.<sup>10</sup> The adjustment process goes through the following phases:

# **Phase I: The “Resource Curse”**

The economy disinvests in capital (which falls at the rate of depreciation) and allows the natural resource endowment to degrade (see panel 2 in Figure 1). Hence, both output and consumption – which, in the absence of investment, is equal to output – fall. How long the economy will remain in such a situation will depend on the speed with which it adjusts when it is not in steady-state equilibrium.

# **Phase II: Economic Growth with Resource Degradation**

The natural resource continues to degrade and the capital stock starts increasing. In this phase, <sup></sup> is negative which, by (10), implies that consumption starts growing from a low initial level. As the economy is poor in capital, accumulation may be very slow and the  adjustment path may be so flat that it never crosses the _n_  0 schedule. In this case, the economy follows a non-sustainable path that eventually leads to a total (and irreversible) depletion of the natural resource stock.

 The likelihood of this outcome is enhanced if the _n_  0 schedule, the commodity price and the discount rate are higher, and if the economy is initially poorer (i.e., its level of capital is lower). These points are summarized in the following proposition:

**_Proposition 1_** _. An economy is more likely to fall into a total and irreversible resource depletion trap the higher the commodity’s environmental impact (_  _), the discount rate and the relative commodity price (p), and the lower its capital stock and the intrinsic growth rate parameter_ (  ) _of the natural resource._

> 10 Recall that<sup>.</sup>

> <sup>_y_</sup> _c_<sup>is increasing in</sup><sup>_n_, and decreasing in</sup><sup>_K_</sup>

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 **_Proof:_** From (26), it follows that for a given level of _n_ , the _n_  0 schedule requires a larger capital stock _K_ – i.e., it is higher in Figure 1 – if  and _p_ are higher (because<sup>increases with</sup><sup>_p_and decreases with</sup><sup>_K_). Also, the likelihood of reaching the resource</sup><sup>_y_</sup> _c_ depletion trap falls with the size of the initial capital stock. There are two reasons for this: first, the economy is more likely to be in or close to Phase III (see Figure 1) and, second, the adjustment path in Phase II is flatter for higher values of _p_ and  (the proof is available from the authors).  An important implication of Proposition 1 is that an economy in Phase II runs the risk of total and irreversible resource depletion. While this risk depends on initial conditions _n_ (0) and _K_ (0) and on technical conditions (i.e., on  and  ) that are difficult to affect in the short run, it depends as well on conditions (e.g., the relative commodity price, _p_ ) that policy can impact directly. This is examined in Parts IV and V below.

## **Phase III: Economic Growth with Resource Recovery**

Phase III in Figure 1 is characterized by growth of both the capital and natural resource stock, with consumption also growing in this phase. The capital stock is sufficiently large and commodity output is sufficiently small for the natural resource stock to start recovering. The system may converge directly to the steady state equilibrium; however, as shown in Figure 1, the capital stock and the natural resource stock may overshoot before convergence to the steady state is achieved.

# **IV. Trade and migration**

We now proceed to examine the impact of a number of trade and factor movement policies on the economy’s transition dynamics and steady state. Section 1 looks at the impact of an outflow of labor from the country under analysis to another developing country and Section 2 examines changes in trade policy.

## **1. South-South migration**

Assume two small developing neighbors that are open to trade and are identical, except for TFP in the manufacturing sector ( _A_ ) which is higher in the home (H) than in the 14
foreign (F) country. Assume an internal equilibrium (the case of total depletion of the natural resource is examined below). Then, as shown by (24) and (25), the steady-state natural resource stock and wage rate are higher in H than in F, providing an incentive to emigrate from F to H. Suppose now that H opens its door to a fixed number of immigrants.

# _<u>Long run effects</u>_

Neither the wage rate nor the natural resource stock is affected by immigration in the long run (see (24) and (25)) under an internal solution (an alternative solution is * examined below). Since the steady-state level of the natural resource, _n_ , is identical to the level prior to the inflow of immigrants, it follows that commodity output is the same * as well since there is a unique level of output that can be supported by _n_ .<sup>11</sup> Rewriting (23) and evaluating it at the steady state, we have:

* * * * * (23’)<sup>_y_</sup> _c_ ( _p_ , _n_ , _K_ ; _L_ )  _L_ [ _w_ 1( _Dpn_ , _A_ ) _Dn_  _r_ 1( _Dpn_ , _A_ ) _Dn_ ( _K_ / _L_ )] As immigration causes an increase in the labor force _L_ , the long-run level of commodity output can only remain constant if the capital-labor ratio of the economy increases. Since _w_ 1<sup>(</sup> _Dpn_ *, _A_ ) **>** 0, an increase in _L_ raises the level of _yc_ and, given that _r_ 1<sup>(</sup> _Dpn_ *, _A_ ) < 0, _K/L_ must increase to restore _yc_ to its original level, i.e., the economy must invest sufficient resources along the adjustment path to raise the long-run level of capital proportionately more than labor.<sup>12</sup>

Using (20), the total level of per capita income is

* * * (20’) _y_ ( _pn_ , _K_ ; _L_ )/ _L_ = _w_ ( _Dpn_ , _A_ ) + _r_ ( _Dpn_ , _A_ )( _K_ / _L_ ) . Since immigration raises the _K/L_ ratio, it follows from (20’) that it raises per capita income in the long run.

According to the Rybczynski Theorem, the labor-(capital-) intensive commodity sector expands (contracts) as the labor force increases. The reason we obtain different results is that the commodity sector uses a third factor of production, the natural resource,

> 11 A lower (higher) level of output implies a positive (negative) natural resource growth rate.

> 12 If _K_ increases in the same proportion as _L_ , so do _yc_ and _ys_ . From Rybczynski’s Theorem, an increase in _K_ lowers _yc_ and raises _ys_ . Thus, _K_ must increase by a greater proportion than _L_ ( _K/_ L must increase) in order to keep _yc_ unchanged.

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which imposes a long-run constraint on the level of output of the commodity sector but not the manufacturing sector.

The following proposition summarizes immigration’s long run effects.

**_Proposition 2._** _The long-run effects of allowing entry by a limited number of workers into a small open economy under an internal solution are: (i) the stock of natural resources, the labor-intensive commodity sector output and the wage rate are unaffected; (ii) the capital/labor ratio, per-capita income and the capital-intensive manufacturing sector output increase._

The economy may also converge to another long-run equilibrium. This is examined in (ii) below.

# _<u>The adjustment process</u>_

The economy may follow one of two divergent paths in response to the labor inflow: (i) convergence to a new steady state with a positive stock of natural resources, or (ii) destruction of the natural resource. The transitional dynamics caused by the one-time influx of immigrants are depicted in Figures 2 and 3.

(i) _Internal steady-state equilibrium_ : The economy is at a point such as _M_ in Figure 2. Immigration raises commodity output<sup>_y_</sup> _c_<sup>and reduces per capita output</sup><sup>_y/L_(see (20’)),</sup>  and shifts the _n_  0<sup>schedule upwards. The natural resource stock falls, causing the rate</sup> of return to capital _r_ to rise above its opportunity cost (   ) and stimulating capital accumulation. Thus, the system moves up and to the left of _M_ (Figure 2). The capital stock continues to grow,<sup>_y_</sup> _c_<sup>starts declining (both because of the increase in</sup><sup>_K_and</sup> decline in _n_ ) from the high level caused by immigration, and _n_ continues to decline until the new _n_  '  0 schedule is reached. At that point, the higher capital stock has lowered<sup>_y_</sup> _c_ to the point where _n_ starts recovering. At the new steady state (point _N_ ), the capital stock * is equal to _K_ 1 and, since _r =_   , there is no further incentive to increase it.  (ii) _Natural resource depletion trap_ : The fact that the _n_  0 schedule shifts upwards means that migration raises the likelihood of an irreversible collapse of the natural resource (see Proposition 1). Thus, an economy in Phase II and on a sustainable path such as MN in Figure 3 may shift to an unsustainable path such as MF following the inflow of immigrants. Thus, analysis of the out-of-steady-state adjustment dynamics reveals a 16
potential for bifurcation: depending on initial conditions, immigration will lead to different long-run equilibria, one of which is characterized by an irreversible depletion of the natural resource and no long-run commodity output.

These results are collected in the following proposition.

**_Proposition 3_** _. The effect of a one-time increase in the number of immigrants induces the economy to take one of two alternative adjustment paths, depending on initial conditions at the time migration takes place:(i) convergence to a new steady state characterized by a greater stock of capital and an unchanged natural resource stock (as in Proposition 2); or (ii) convergence towards a steady state characterized by an irreversible resource depletion if the capital stock is sufficiently small. Note that immigration reduces per capita output in the short-run but raises it in the long run._

# **2. Trade policy**

Assume the type of trade policy observed in many resource-rich low-income countries: protection for the import-competing manufacturing sector and/or export taxes on the primary or commodity sector.<sup>13</sup> A decrease in import tariffs or export taxes causes the relative commodity price _p_ to increase, which, from (17) and (18), reduces the interest rate and raises the wage rate. Manufacturing output falls and commodity output increases, causing the natural resource stock to decline. As the interest rate is below capital’s opportunity cost, investment is nil and the capital stock falls. That is, the increase in _p_ moves the economy to Phase I, with smaller _K_ and _n_ values. As shown in Figure 4, the  increase in _p_ shifts the = 0 schedule to the left of and the _n_  0 schedule up. Thus, the steady-state level of the capital stock increases to _K**_ and the natural resource stock falls to _n**_ (see equation (22)).

Since both productive assets fall in Phase I, so does total output. As _n_ declines, _r_ increases and the gap _r - (ρ_ + _δ)_ declines, eventually reaching zero. At that point, _K_ stops declining and as _n_ continues to fall, _r_ rises above _ρ + δ_ and the economy starts investing. That is, the economy reaches Phase II where _K_ increases and _n_ continues to decline, with potential bifurcation: the larger the increase in _p_ , the greater the upward shift of the   _n_  0 schedule and the leftward shift of the _K_  0 schedule.

> 13 Trade tax revenues are redistributed in a lump-sum fashion.

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Thus, the greater the liberalization of trade, the greater the price increase, the lower the capital and natural resource stocks at the onset of Phase II and, as discussed in Section III, the greater the likelihood of a total resource depletion trap. This finding is supported by several case studies reported by Larson and Nash (2010) who state: “The studies provide examples of how new export-tied demands can arise along with incentives to rapidly diminish important environmental resources, sometimes in irreversible ways.”<sup>14</sup> Under internal equilibrium, the economy reaches _n_ ** and _K_ ** , and the long-run interest rate and wage rate return to their pre-trade reform levels.

The findings are collected in the following proposition:

**_Proposition 4._** _Trade policy reform that raises the relative commodity price has one of two sets of long-run effects. If the price increase is below a critical level, not too large, the economy may converge to a long-run equilibrium where (a) the stock of natural resources is smaller but still positive; (b) the stock of capital is larger; (c) the wage rate and the rate of interest return to their pre-reform levels; and (d) the level of output of the capital-intensive sector increases and that of the labor-intensive commodity sector declines. On the other hand, if the price increase is sufficiently large, the economy may diverge into a steady state where the natural resource is irreversibly destroyed._

# **V. Preventing environmental collapse**

Various interventions designed to prevent a potential environmental collapse associated with commodity production are examined in this section.

## **1. The issue**

At was shown in Part III, the natural resource stock falls in Phase II and only starts to increase once Phase III is reached. However, the economy may follow a less favorable path, with its natural resource stock totally depleted before it ever reaches Phase III.

This outcome is more likely when the negative impact of commodity production on the stock of natural resources is large and the exogenous regeneration rate of the natural resource is low, i.e., for a high value of parameter  (equation (3)) and a low value of parameter γ (equation (4)). This outcome can be represented in the middle panel

> 14 They add, however, that the result is also likely to depend on location-specific conditions.

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of Figure 1 by a point on the vertical axis, for instance by _K_ (0). At that point, continues to be negative and the stock of natural resources cannot regenerate.

Three types of policies to prevent this outcome are examined: trade policy, factor movement policy, and policies tackling the source of the externality directly. The first one is controlled by the country at risk and the second one by developed countries and international organizations. Recent commodity price increases associated with China and other Asian countries’ entry into the world market have raised the pressure on natural resources and have thus increased the urgency of implementing such policies.

# **2. Trade and factor movement policies**

This section examines the impact of goods and factor movement policies.

## _<u>Trade policy</u>_

First, as described in Part IV, Section 2, the home country can impose an import tariff or, equivalently, an export tax. These trade taxes reduce commodity production and raise the stock of natural resources or slow down its decline. In terms of the middle panel of Figure 1, these programs result in a decline in the schedule. Thus, an economy that finds itself in Phase II would either be closer to reaching Phase III or would find itself in Phase III right away. This would depend on the size of the tariff or export tax that the country would impose.

Developing countries have typically favored the urban sector and have discriminated against the rural sector. This has been achieved through commodity export taxes as well as through tariffs or other barriers on manufacturing imports, thus turning the internal terms of trade against the output ‘exported’ by the rural to the urban sector.<sup>15</sup> In addition to being viewed as harmful from the distributional viewpoint, these trade policies have been thought to result in an inefficient allocation of resources. However,

> 15 See Schiff and Valdés (1992) and Anderson (2006) for the impact of trade policy on relative prices in agriculture from 1960 forward.

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under a lack of property rights, such policies might actually improve efficiency. Whether or not they do depends on the level at which the trade taxes are set.<sup>16</sup>

# _<u>Factor movement policy</u>_

Policies regarding the movement of factors can also help prevent environmental collapse. Two policies are examined in this section, namely immigration policy and transfer of capital (foreign aid). These policies are under the control of the developed countries and the development community rather than under the control of the country at risk.

# i. _<u>Foreign aid</u>_

By providing capital in the form of foreign aid to the country at risk, developed countries and international donor organizations can help raise manufacturing sector output, reduce commodity output and reduce natural resource depletion. Thus, foreign aid can move an economy in Phase II closer to Phase III – with a slowdown in natural resource depletion – or to Phase III right away under a sufficiently large inflow of capital and reverse the depletion. This analysis contributes to the ongoing debate as to whether foreign aid benefits or hurts developing countries by showing that it has a positive impact that had so far been ignored, an impact that is particularly important for poor countries that are highly dependent on natural resources.

# ii. _<u>Developed country immigration policy</u>_

The second factor-movement policy examined consists of immigration policy liberalization by the developed destination countries. This also raises output in the manufacturing sector and reduces it in the commodity sector, thereby slowing down the depletion of natural resources or even reversing it under a sufficiently large outflow of labor, and reduces the likelihood of total natural resource depletion.

Moreover, the fact that South-North migrants send remittances to their country of origin means that migration results in a reduction in the labor force as well as in an

> 16 For instance, any tax below the optimal one raises welfare above its level in the absence of the tax, while a tax above the optimum has an ambiguous welfare impact. A tax above the optimum exists where welfare is equal to that obtained in absence of the tax, and any tax below (above) it raises (lowers) welfare relative to its level in the absence of the tax.

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increase in the stock of capital in the country of origin. In other words, the liberalization of immigration policy by the North has two beneficial effects on the country at risk since both the reduction in the labor force and the increase in the remittances-related stock of capital lead to a reduction in output in the commodity sector. Hence, one advantage for the North of liberalizing its immigration policy is that it generates a transfer of capital that is paid by the immigrants rather than by the North’s taxpayers. The capital stock and the capital-labor ratio in the new steady state are smaller than in the initial steady state and thus so is per-capita income.

# **3. Attacking the negative externality at the source**

A number of additional policies are likely to help reduce the depletion of the natural resource. Three policy measures are examined under this type of intervention, the first one depending at least in part on the international community and the others under the control of the country facing the problem. The first measure consists in using technology designed to reduce the environmental impact of commodity production, i.e., to reduce the value of parameter  in equation (3). Donor countries as well as regional and multilateral institutions have been actively involved in knowledge development and knowledge diffusion programs designed to help developing countries reduce the destruction of renewable natural resources associated with the production of agricultural and other types of commodities, and have also been involved with the second policy measure, namely establishment of (better) regulations to deal with the negative externalities of commodity production.<sup>17</sup> The reduction in the environmental demands of commodity production results in an increase in (equation (3’)), i.e., in a smaller decline or increase in the natural resource stock, thus raising the likelihood of reaching Phase III or of moving to Phase III

> 17 For instance, Chile, Peru and Ecuador possess large fisheries and aquaculture but lack adequate regulatory systems. Overfishing in Peru caused a decline in the anchovy stock (exacerbated by the El Niño cycle) which took years to recover. And though the optimal policy would have been a production tax (or improved regulation), the problem was exacerbated by the subsidies given to the fleets. In Chile, the salmon production, which grew very rapidly in recent years, fell by at least 50 percent in 2009 due to the closely-located fish farms and high salmon density which led to the propagation of diseases, a situation which stands in stark contrast with Norway’s strictly regulated industry. An example of involvement by international organizations is the World Bank support for the introduction of a vessel quota system in Peru’s fishery, resulting in improved control of anchovy stocks and in increasing economic returns.

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 right away. As with trade policy, this lowers the _n_  0 schedule (see middle panel of Figure 1) since the steady-state natural resource stock is now sustainable at a higher level of commodity production, i.e., with a lower stock of capital. Whether an economy that is in Phase II would be closer to reaching Phase III or move to Phase III right away would  depend on the extent of the decline in the _n_  0 schedule. This would obviously depend on the extent of reduction of parameter  .

An economy that finds itself above the _g_ ( _n_ ) schedule and with a stock of natural resources below _n*_ (see lower panel of Figure 1) is shown to have a transition path that ends up either with a steady-state natural resource stock _n*_ or with the disappearance of the natural resource stock. The reduction in parameter  implies a reduction of <sup>_y_</sup> _c_ in the economy’s position in the ( <sup>_y_</sup> _c_ , _n_ ) space, with a greater likelihood that the transition path will lead to _n*_ . These results are collected in Proposition 5 below.

Third, the externality can also be resolved with an optimal production tax, which is preferable to optimal trade taxes since it does not distort the consumption choice. However, implementation of such a production tax is unfeasible in many developing countries, particularly where the sector consists of a large number of small producers.

The results are summarized in the following proposition.

**_Proposition 5._** _Interventions by the countries at risk or by the international community that could help countries avoid a potential environmental collapse are: i) a tariff on imports or, equivalently, a tax on exports; ii) liberalization of the North’s immigration policy with respect to the countries at risk; iii) increase in capital flows provided by donor countries and/or regional and multilateral organizations; iv) institutional reform regarding the regulation of commodity production; and iv) transfer and help with the use of technology designed to reduce the intensity of use and destruction of environmental inputs in production. A potential advantage of the liberalization of immigration policy by the North is that, in addition to reducing the labor force in the countries at risk, it would also result in a transfer of capital to them in the form of migrants’ remittances._

# **VI. Conclusion**

This paper provided an analysis of the transition path and steady state outcome in response to various policies and exogenous shocks for a small open economy that obtains a large share of its income from the exploitation of a common-property renewable natural 22
resource. An important contribution is the examination of the various issues in a general equilibrium small-open-economy model, as well as the complete characterization of the steady state and the out-of-steady-state dynamics. The importance of such a framework is revealed by the fact that it enabled the identification of path bifurcation and state dependence as likely prominent features. It was shown that dynamic forces might lead the economy to dramatically different steady states, one of which being characterized by a complete and irreversible depletion of the natural resource.

We examined variables that raise the likelihood that this outcome prevails, as well as policies designed to reduce the chances that it will, with the following results. An economy with a small endowment of capital is more likely to be subject to a “natural resource curse” and to complete natural resource depletion. The latter is also more likely under a higher relative commodity price and under an inflow of labor. A labor inflow results either in a _higher_ steady-state capital-labor ratio and manufacturing output, and unchanged natural resource stock and commodity output, or in a total depletion of natural resources.

An import tariff or export tax results in a larger natural resource stock and steadystate commodity output, a smaller capital stock and manufacturing output, and reduces the likelihood of complete natural resource depletion. This may also be prevented through capital inflows (foreign aid), liberalization of immigration policies in developed countries, a production tax, development and diffusion of techniques that lower the natural-resource-intensity of production, and improved regulation.

The trade policy results yield a fundamental policy implication of the paper. Overemphasis on trade liberalization in poor countries with imperfect property rights with respect to natural resources is likely to be much riskier than for developed countries because of the latter’s benefit from capital abundance, superior natural-resource-saving technology and better property rights. While increasing trade openness in developed countries may only cause a marginal reduction in the long-run state of natural resources, doing so in a poor natural-resource-dependent country may trigger a qualitative shift in the economy, with a devastating and irreversible impact on its natural resources, an outcome made more likely by the recent increases in commodity prices. Thus, the donor community should beware of automatically providing highly resource-dependent 23
developing countries the type of advice that is valid for developed countries; rather, policymakers should be made aware of the risks associated with trade liberalization and incorporate them in their assessment of any trade reform under consideration.

# **References**

Anderson, K., Martin W., Valenzuela, E., 2006. “The Relative Importance of Global Agricultural Subsidies and Market Access,” _World Trade Review_ 5 (3): 357-76 Copeland, Brian and S. Gulati. 2006. “Trade and the Environment in Developing Countries.” In R. López and M. Toman (eds.) _Economic Development and Environmental Sustainability: New Policy Options,_ Initiative for Policy Dialogue Series, Oxford University Press, New York.

Copeland, B.R. and M.S. Taylor. 1994. “North-South Trade and the Environment.” _Quarterly Journal of Economics_ , 109(3): 755-787.

Diewert, W.E. 1981. “The elasticity of derived net supply function and a generalized Le Chatelier principle,” _Review of economic Studies_ XLVIII, 63-80.

Gordon, H.S., 1954. “The economic theory of a common property resource: the fishery.” _Journal of Political Economy_ 62, 124–142.

Larson, D. F. and J. Nash. 2010. “Resource Management and the Effects of Trade on Vulnerable Places and People: Lessons from Six Case Studies,” Policy Research Working Paper 5258, World Bank (March).

López, R. 1997. “Environmental externalities in traditional agriculture and the impact of trade liberalization: The case of Ghana”. _Journal of Development Economics_ 53 (1), 17–39.

______. 1998. “The tragedy of the commons in Cote d’Ivoire agriculture: empirical evidence and implications for evaluating trade policies.” _The World Bank Economic Review_ 12(1):105-31.

______. Forthcoming. “A Review Essay on the Economics of Forest Resources,” _Journal of Economic Literature_ .

Miranda M., P . Burris P and J.-F. Bingcang. 2003. _Mining and Critical Ecosystems: Mapping the Risks_ . Washington, DC: World Resources Institute.

Schaefer, M.B., 1957. “Some considerations of population dynamics and economics in relation to the management of marine fisheries,” _Journal of the Fisheries Research Board of Canada_ 14: 635–47.

Scott, A. D. (1955). “The Fishery: The Objectives of Sole Ownership”. _Journal of Political Economy_ 63:116-124.

Schiff, M. and A. Valdés. 1992. _The Political Economy of Agricultural Pricing Policy. A Synthesis of the Economics in Developing Countries_ (Vol. 4), Baltimore: Johns Hopkins Univ. Press.

Washington Post, 2009 (February 23, pp. 1-2).

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<!-- Start of picture text --> r<br>r<br> <br>k  0 k  0<br>ρ+δ<br>r0<br>  r<br>k  0 k  0<br>0 n* n0<br>n n<br>k <br>k  0<br> Phase<br>n  0 III<br>k*<br>k(0) M<br>Phase Phase<br>II I<br>n* n(0)<br>n<br> y c<br> y c (0) M<br>g(n)<br>0<br>n* n(0) n<br><!-- End of picture text -->

**Figure 1: Adjustment towards equilibrium by a resource-rich, capital-poor economy.**

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<!-- Start of picture text --> K<br>I<br>n  0<br>F<br>n = 0<br>N<br>M<br>0<br>n* n<br><!-- End of picture text -->

**Figure 3: The possible impact of immigration in Phase II**

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<!-- Start of picture text -->  <br>r ( p 0 n )<br>r ( p n 1 )<br>n ** n *<br>n<br> 1 <br>K  0 K  0<br>K<br> I<br>n  0<br><br>n  0<br>** B<br>K<br>N<br>*<br>K<br>** *<br>n n n<br><!-- End of picture text -->

**Figure 4: Adjustment following a commodity price increase**

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