Production and Market-Clearing Conditions

Since employment is assumed constant, output can be expressed exclusively in terms of the commodity input. The production functions for countries A and B are given by

Since the commodity is nonstorable and there is no capital, profit maximization is done on a period-by-period basis. Demand for the commodity input derived from setting marginal product equal to marginal cost leads to

and

Given the functional forms assumed, world demand for the commodity is characterized by a rectangular hyperbola.

Closing the system requires specifying the behavior of the public sector. To focus on the reallocative effects of government spending, the government is assumed to run a balanced budget and the lump-sum tax levied on the households of the home country, $T_t^A$, is assumed to be directed entirely to the purchase of the home good, as in Metzler (1949).⁴ These purchases are denoted by $g_{1t}^A$. All markets clear continuously; the equilibrium conditions for the commodity, good 1, and good 2, respectively, are given by

and

Clearing of the asset market requires that all debt be held:

Solution and Properties of the Model

Relative prices are solved for by imposing market clearing in three of the four markets and invoking Walras’ law. The appropriate substitutions in equation (11) yield an expression for the domestic real commodity price, (q/p¹), in terms of the real exchange rate and the exogenously determined supply of commodities:

This market-clearing condition lies at the heart of the inverse correlation between real commodity prices (in U.S. dollars) and the U.S. real exchange rate found in the data by Dornbusch (1985), Morrison and Wattleworth (1988), and Gilbert (1989). This theoretical model suggests that this sensitivity of commodity prices to the real exchange rate should depend on the relative elasticities of industrial country output with respect to commodity prices, and so would he between 0 and -1. There is far less agreement in the empirical literature about the magnitude of this coefficient, but many of the studies cited estimate it to be higher (see Gilbert (1989)).

Substituting equations (6a)-(6c) into the market-clearing condition for good 1 (equation (12)) and using the results from equation (15) yields a reduced-form expression for the real exchange rate;

where

As equations (15) and (16) show, relative prices depend on the exogenously given commodity endowment and government spending. Note that the numerator of the government multiplier, (1 – a), measures the difference between public and private preferences for good 1. The assumption, thus far, has been that the government only consumes the domestically produced good—its propensity to consume good 1 out of tax receipts is unity—while the private sector consumes a.

Since preferences are identical across countries, relative prices do not depend on the international distribution of wealth. However, because consumption in countries A and B (equations (6a) and (6b)) depends on the distribution of the internationally traded asset, $B_t^A$, the solution to the system requires that the path of the interest rate on the bond $r_t^A$, be established. Following Guidotti and Vegh (1988), I subsequently show that in this system the interest rate will equal the subjective rate of time preference, 5, for all t. The continuous equality between the rate of time preference and the world interest rate has the implication that asset distribution at any point in time will equal the initial endowment, (B^A_t, = B^A₀, for all t), and adjustment to disturbances occurs instantaneously.

To establish this, consider the market-clearing condition for good 1, Since the market clears at each point in time, and as equations (15) and (16) show, relative prices and output adjust instantaneously, changes in demand over any period of time must sum to zero; that is

The first two terms on the right-hand side are given by the Euler conditions, while the last follows from differentiating equation (6c) with respect to time. ⁵ Making these substitutions leads to

Since consumption in the industrial countries moves together (sign of ${Dc}_{1t}^A$= sign of ${Dc}_{1t}^B$, market clearing requires that consumption in country C move in the opposite direction. ⁶ This, as equation (17) illustrates, requires that follow an unstable dynamic equation when linearized around the steady state. Under the assumption of rationality, or more precisely, perfect foresight, agents would rule out explosive paths and choose the interest associated with the stable dynamics—that is, an interest rate equal to the constant subjective rate of time preference. Thus, stability rules out intrinsic dynamics, and the system is characterized by instantaneous adjustment from one steady state to another.

The reduced forms for consumption in each country are given by

and output in countries A and B is given by

Increase in Government Spending

In this simple trade model, the government of country A finances its purchases of the home good by levying a lump-sum tax on households.

The impact of government spending on relative prices, output, and consumption comes entirely from its role in the reallocation of demand, as in Metzler (1949). A permanent increase in government spending tilts demand in favor of the home good and drives up its relative price. The real exchange rate, appreciates, and real commodity prices, (q/p₁)_t, fall. The decline in real commodity prices increases the home country’s demand for the commodity input, and output in country A expands. At the same time, commodity costs for country B, (q/p₁)_t R_t rise with the fiscal expansion, leading to a decline in its output. Thus, the international transmission of a fiscal expansion in country A is negative.

Household consumption in the industrial countries declines. In the home country output is higher, but the higher taxes that finance the increase in spending reduce household disposable income. In the second industrial country, B, disposable income falls, owing to tower production and a deterioration in the terms of trade. The commodity exporting country also faces a deterioration in its terms of trade that reduces the value of its output, or alternatively expressed, that increases the burden of debt servicing.⁷ Households in country C would like to maintain their level of consumption and, in the absence of a liquidity constraint, would have been able to do so by borrowing from country A or (country B). Instead, their inability to borrow forces the entire adjustment on consumption, which also falls. In effect, the liquidity constraint has a shadow price that functions as an interest rate, so that when it is binding, the consumer behaves as if he or she faced a higher interest rate.

All of these results obtain if the government’s propensity to consume the home good exceeds that of the representative household. If, for instance, the government consumes both goods in the same proportion as households, then the numerator of the government multiplier in equation (16) would be (α - α), and relative prices would remain unchanged, since private consumption of good 1 in country A falls by -αT^A_t, while public consumption increases by the same amount (recall that the government maintains a balanced budget).⁸ As a result, world spending on both goods remains unchanged.

This simple model can describe the observed direction of movement in relative prices and even the differential economic performance of the early 1980s (see Tables 1 and 2).⁹ However, the model, which imposes balanced current accounts, falls well short of explaining the marked swings in the current accounts of industrial and developing countries that also characterized the past decade. Most likely, the absence of debt-financed public expenditure, as well as a monetary sector, accounts for this lack in the analysis.

Table 2.

Commodity Supply and Related Data

(Percent change)

Sources: International Monetary Fund (1990a, 1990b)

Table 2.

Commodity Supply and Related Data

(Percent change)

Price and Quantity Indicators	1975-80	1981-85
Terms of trade of non-oil, primary commodity exporting countries	-2.2	-15.0
	1977-82	1983-87
Commodity supply index	5.3	20.0
Export volme of 15 heavily indebted countries	17.9	25.3

Sources: International Monetary Fund (1990a, 1990b)

View Table

Table 2.

Commodity Supply and Related Data

(Percent change)

Price and Quantity Indicators	1975-80	1981-85
Terms of trade of non-oil, primary commodity exporting countries	-2.2	-15.0
	1977-82	1983-87
Commodity supply index	5.3	20.0
Export volme of 15 heavily indebted countries	17.9	25.3

Sources: International Monetary Fund (1990a, 1990b)

Expansion in World Commodity Supply

During the 1980s the terms of trade of developing commodity suppliers deteriorated markedly while their real debt-servicing costs rose.¹⁰ This unfavorable combination led many developing countries to try to increase the volume of their exports, so as to make up for the shortfall in revenues. However, since many commodity exporters responded similarly, the outcome was an expansion in world commodity supplies, which further aggravated the decline in their relative price. As Morrison and Wattle-worth (1988) note, this supply expansion played a significant role in explaining the observed weakness in relative commodity prices in 1984-86, despite the rapidly recovering demand for commodities in industrial countries.

In the basic model, the impact of a permanent expansion in world commodity supply, y^C follows intuition. As with the fiscal shock, the adjustment is instantaneous. The expansion in commodity exports reduces the real price of the commodity, (q/p₁)_t, (equation (15)), while the impact of the real exchange rate is ambiguous, since it depends on tastes and technology. As the numerator of the multiplier of the commodity stock (equation (16)) makes clear, if good 1 is consumed in a higher proportion than good 2 (that is, a > (1 — a)), other things equal, then the increase in world output increases world demand for good 1 by more than it increases demand for good 2, driving its relative price higher. If production of good 2 uses the commodity input more intensively than good 1 (that is, e > r), other things equal, then the production of good 2 rises relative to the output of good 1, and its relative price declines (that is, R goes up). In either case, the cost of the commodity input declines, thereby increasing output in the industrial countries A and B.¹¹ The higher levels of output, assuming they are not taxed away, increase disposable income and boost consumption in the commodity importing countries (equations (18a) and (18b)).

For the commodity supplier, the value of its output may increase or decrease, depending on the ambiguous real exchange rate response. World demand for the commodity input is characterized by a rectangular hyperbola; if no other relative prices change, country C’s revenues remain unchanged, since the output increase is exactly offset by a price decline (equation (15)). If the real exchange appreciates, world commodity demand declines, since the decline in country B’s commodity costs is smaller. In such a scenario, the decline in commodity prices (in terms of good 1) more than offsets the increase in output, and the value of country C’s output declines. With debt-servicing costs constant, a fall in consumption absorbs the shock. In this case, the gap between the value of output of the developed countries and the developing country widens.

Change in Rate of Time Preference in the Basic Model

As with the other shocks considered, a permanent change in the rate of time preference results in an instantaneous adjustment. For households in country C, this increased preference for consuming today cannot be translated into an increase in consumption, since a binding liquidity constraint prevents its residents from engaging in consumption smoothing. In the developed countries, households would not be willing to hold the existing stock of debt at an interest rate that is below their, now higher, subjective discount factor. Accordingly, asset market clearing will require that the real interest rate increase sufficiently, so as to insure that all debt is willingly held. This rise in the interest rate increases interest income for residents of A and B and finances a higher level of consumption.

For the debt-constrained citizens of country C, consumption adjusts according to Dc^C = —αB^CDr^A. Therefore, in order to meet the higher level of interest payments (for a given level of output), households must reduce their consumption. In the new steady state, the commodity supplier will have a larger merchandise trade surplus offsetting the deficit in the capital account.

A Variant of the Basic Model with Fixed-Rate Debt

The assumption that alt debt yields an instantaneously adjusted variable interest rate produces the starkly negative implications for consumption and welfare of the debtor country when the discount factor, which anchors the world interest rate, rises. Despite rapid increases in recent years in the share of developing country debt that is variable rate, as of 1987 nearly 50 percent of the stock of debt of the 15 most heavily indebted countries was still at fixed rates (Table 3). An alternative scenario is considered here, which although less descriptive of the stylized facts of developing country debt, provides a benchmark against which the previous results can be compared.

Consider the polar case: the development bond, B^C, is a consol promising fixed-stream coupon payments (in terms of good 1) to its holders. In this case, country C’s budget constraint is given by

where k represents the fixed coupon payment in terms of good 1, and B^C now represents the number of bonds outstanding. As equation (20) illustrates, the fixed coupon payments insulate the debtor’s consumption from fluctuations in the rate of interest, which now has two components— coupon payments and capital gains or losses. Defining v_t as the price of the bond (in terms of good 1), the instantaneous rate of interest is given by

where Dv/v represents the changes in the price of the bond—capital gains or losses. The budget constraints for the creditor countries are¹⁴

As equation (22) indicates, a permanent increase in the common discount rate would leave consumption in the debtor country unchanged, since neither output nor its debt-servicing payments have changed. In the new steady state we know that (1) the interest rate equals the now higher rate of time preference; and (2) the value of the bond will be stationary, Dv/v = 0. These situations imply that when the rate of time preference rises, the price of the bond, v_t, instantaneously declines. Households in countries A and B would like to reduce their holding of country C’s debt to consume more. This provides no incentive to trade and, instead, after the change in tastes, the value of debt, v_t $B_t^A$, falls, while the yield, k/v_t, rises by the same proportion. Consequently, the consumption of the debt holders also remains unchanged. In the case where the debtor country faces a liquidity constraint, the existence of fixed-rate debt helps insulate the consumer against fluctuations in interest rates.