Exchange Rates and Social Valuation

In many economies, exchange rates are controlled or influenced by government policies and thus may bear no resemblance to the rates that would prevail under social pricing conditions. A distorted exchange rate can therefore affect the domestic currency price of tradable commodities. Figure 6.2 illustrates the short-run and long-run effects of exchange-rate change on a tradable-commodity market. The initial conditions are represented by supply curve S and domestic price P_D. In these circumstances, domestic production Q_Pexceeds domestic consumption (Q_C), and (Q_P-Q_C) of the commodity is exported. The domestic price is determined by the world price, measured in foreign currency (Pw) times the exchange rate (e).

This exchange rate is assumed to be distorted (for example, by a pervasive government budget deficit) so that it cannot be sustained in the long run. A depreciation in the domestic currency is needed, raising the exchange rate to e'. As a result, the domestic currency price increases to P_D. At the same time, the supply curve is affected, since the costs of tradable-commodity inputs increase. Because these inputs do not account for all production costs, the proportional upward shift in the supply curve will not be as large as the proportional change in output price. In the figure, the supply curve shifts upward to S'. In the short run, prices of tradable outputs and inputs increase, but quantity of output does not; commodity producers thus earn excess profits. The output price is P’_D, marginal costs are C'_D , and excess profits are (P’_D - C'_D )Q_P, or P' ABC'

In response to the excess profits, producers will seek to expand output and thus increase their use of tradable inputs and domestic factors. But producers in all other tradable-commodity markets will be trying the same thing. Because the exchange-rate change creates excess profits in all importable and exportable markets, bidding for the services of domestic factors will be widespread. Prices of domestic factor inputs will rise and will continue to increase until competition for factor services eliminates excess profits. Thus, in the long run, foreign-exchange rates will affect all input prices to the same extent as output prices.

This effect is shown by the formulas for factor price calculations. Private market factor prices are represented by a superscript P and private market commodity prices are represented by a superscript D:

Social factor prices are shown with a superscript S and social commodity prices have a superscript W:

If divergences are absent, domestic commodity prices equal world prices (P_P=P_W), and domestic and social factor prices are equal. If domestic prices are increased above world prices by uniform exchangerate depreciation, the factor price equation in the private market for labor can be rewritten as

Factoring out the 1 + t gives

Similar results follow for the price of capital, showing that both social factor prices are derived from private market prices by adjustment for the magnitude of distortion in the exchange rate. If output prices are higher than world prices because of an undervalued exchange rate, so are factor prices. If output prices are lower than world prices because of an overvalued exchange rate, so too are factor prices. Identical results are obtained for the more general model (equation 8).

As domestic factor prices increase, the supply curve in Figure 6.2 will tend to shift upward (from S') toward an intersection with point A. But this point cannot represent the new market equilibrium. Because the increase in domestic factor prices coincides with (and depends on) increased employment of factors, the market supply must shift outward, so that production exceeds Q_P. In the figure, equilibrium is represented by an outward shift to S" and production expands to Q_P. Exports are likely to increase as well, although the amount depends on exchange-rate-induced shifts in the domestic demand curve (not shown). Unless domestic factors are unemployed, the inputs necessary to permit the expansion of tradables production must come from the nontradables sector.

In the evaluation of tradable-commodity systems, the calculation of social prices for foreign exchange may represent a needless complication. If the government distorts the exchange rate for the economy, in the long run this rate will influence all tradable-output, tradable-input, and domestic factor prices in equal proportion. Social profitability of the system will differ from private profitability by the same proportional factor. Because exchange-rate adjustments cannot alter the sign of profitability or the profitability rankings of different tradable-commodity systems, exchange-rate distortions are often ignored in social price calculations.

In some instances, however, policy analysts will be concerned with the magnitude of exchange-rate change. First, analysts may want to explain the causes of divergences between private and social prices. As chapter 5 showed, commodity policy and macroeconomic policy are often intertwined. Second, the rate of adjustment of costs of the various categories of inputs is likely to vary. Tradable-input prices are affected quickly, as soon as the domestic prices of imports or exports are altered by the new exchange rate. But the prices of labor, capital, and land adjust more gradually, only after the impacts of increased factor demands from the tradable-goods sector are felt. In the short run, therefore, exchange-rate changes increase profitability in tradable-commodity systems, and PAM analysts interested in short-run incentives might choose to adjust only the social values of tradable commodities for changes in the exchange rate.

Analysts may also be interested to show the change in real income of domestic factors that results from the return to an equilibrium exchange rate. If factor prices ultimately change in the same proportion as the exchange rate, the owners of factor services are potentially better off. But the exchange rate affects prices of tradable commodities as well, and the cost of the consumption basket of each factor increases also. The prices of nontradable commodities are not directly affected, however. For domestic factor owners who consume some nontradable goods, the increase in the cost of the total consumption basket will be less than the increase in factor prices. As a result, real factor prices will be higher and the real income of factor owners will rise after the exchange-rate change, although by a smaller proportion than the change in the exchange rate.

The introduction into the PAM of short-run impacts of exchange-rate changes is straightforward. The social values of tradable outputs and tradable inputs (E and F) are multiplied by the ratio of the equilibrium exchange ratio (e') to the existing exchange rate (e). However, estimation of e' is very demanding of empirical information. Figure 6.2 shows that the contribution of tradable commodities to an improvement in the foreign-exchange balance depends on the slopes and shifts of the supply

and demand curves: the own-price elasticity of supply, the cross-price elasticities of supply (especially with respect to nontradables), the own and cross-price elasticities of demand, and the income elasticities of demand. In Figure 6.2, these shifts cause exports to increase from QP - Qc to Q’P - Q'C . With aggregation of these effects across commodities, exchange-rate changes can be associated with changes in the aggregate balance of foreign exchange, thus identifying an equilibrium. Because of the substantial information requirements, however, approximations of equilibrium exchange rates will usually be uncertain. Directions of change can be understood with confidence, but magnitudes are likely to be elusive.

Multiple Exchange-Rate Regimes

More complicated adjustments to social commodity prices are needed in the presence of multiple exchange rates. The government might establish a set of exchange rates that differ according to commodity. This result can be achieved directly with a multiple exchange-rate regime or indirectly by placement of quantitative trade restrictions on certain importables or exportables. Quotas allow the protected commodities to be traded at effective exchange rates different from the official rate used for unprotected or tariff-protected goods. Alternatively, parallel markets for foreign exchange might operate along with the official government market. In this circumstance, the effective exchange rates for domestic factor prices may differ from the particular exchange rates used for the tradable commodities of a commodity system.

In the simple general equilibrium model, for example, the wage rate represents a weighted average of the different exchange rates:

where e, and e₂ represent the exchange rates applicable for two commodities. The average effective exchange rate can be represented by e₃, where

In larger, more realistic models, each exchange rate appears in positive terms and negative terms of the factor price solution. For example, the three-good, three-factor model can be described in equation system 9:

where z is the unit price of the third factor and t is the input-output coefficient. If each commodity is traded at a different exchange rate, the average exchange rate for labor cost is e₄, where

This expression may be rewritten as

This expression shows that the value of e₄ depends on the various world prices and input-output coefficients. If each of the weights on e,, e₂, and e3 is less than 1 (because the value of Y exceeds the value of each of its individual terms), e₄ will lie somewhere within the observed range of multiple exchange rates.

When conversion ratios lie within the observed range of multiple rates, approximate values can be based on the relative prominence of the different exchange rates. If one particular exchange rate dominates transactions, most of the terms in the formulas would have a single exchange rate and the other terms would not be sufficiently numerous to generate an average value very different from the dominant value. If most commodities are traded at rate e, and only a few commodities are traded at a lower rate-e₂, for example-the average rate selected, e₃, would be slightly less than e,. Therefore, for domestic currency values of tradable commodities that have been exchanged at rate e,, social values would be reduced by the value of e₃/e,. The social value of tradable commodities that have been exchanged at rate e₂ would be increased by e₃/e₂.