THE ACCOUNTING PRICE OF FOREIGN EXCHANGE
3.5 The Accounting Price of Foreign Exchange When Exports Are Taken into Account
In previous sections, it was assumed that the supply of foreign exchange (exports) was completely inelastic with respect to (small) variations in the exchange rate. However, this was only for the sake of simplification. In general, the supply of exports will be an increasing function of the exchange rate (Figure 3.3), reflecting the price elasticity of both domestic supply and demand of the goods exported.
Let us consider first the case in which only consumer goods are exported.
The project under consideration will increase the supply of foreign exchange
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ACCOUNTING PRICE OF FOREIGN EXCHANGE
Figure 3.3. The Effects of an Increase in the Supply of Foreign Exchange
by d\ — ds, of which only d\ — do will be additional net availability, whereas d0 — ds will replace the supply of other producers who will reduce their sales abroad because of the reduction in the exchange rate from EER0 to EER\. The additional net supply d\ — d0 will allow for additional imports of the same magnitude to be made and the sum of CVs per additional unit of foreign exchange can be calculated, for example, as
bearing in mind that the weights <PI have to be calculated with respect to the project's additional supply of foreign exchange. In algebraic form, the weights will be
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that is, the GIF value of the additional imports of good / as a proportion of the additional foreign exchange produced by the project.
To arrive at the sum of the CVs of foreign exchange d0 - ds, it is necessary to turn to the markets of the only two export (and domestic consumption) goods e and h. Let us suppose that e is the good whose production increases, and that the firm will export all its additional production. Figure 3.4(a) and (b) show the long-term equilibrium positions in the markets of e and h. In Figure 3.4(a) it can be seen that additional production e, - e\ will increase the net supply of the exports of e by
since due to the effect on the exchange rate, it will replace other sources by ef> - e\ and increase domestic consumption (reduce the exports of other producers) by ef - e$. If the domestic prices of the resources released by the reduction es$ - e\ are acceptable approximations of their efficiency prices (in the consumption numeraire), the sum of the CVs in the market of e will be the willingness to pay for additional consumption
[3.17]
plus the value at efficiency prices of the resources released
[3.18]
In the market of h, Figure 3.4(b), the reduction in the equilibrium exchange rate will reduce the domestic price, increasing consumption by a total value of [3.19]
and, on the assumption that the domestic market price of the good exported is equal to its long-run marginal cost at efficiency prices,8 it will release re-sources by
[3.20]
Consequently, the foreign exchange produced by the project will be
8. If the assumption were not acceptable, the APRFE could be calculated by using input-output techniques through a process similar to that described in Chapter 13. See Londero (1994).
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ACCOUNTING PRICE OF FOREIGN EXCHANGE
Figure 3.4. The Effects of the Reduction in the Exchange Rate on the Market for Exported Goods
in which FOBe is the f.o.b. price expressed in foreign exchange. This is partially compensated by the reduction in exports from other producers for a total of
FOBe [(4 - <?|) + (el - 4)] + FOBh ((hs0 - h\) + (hd{ - hd0)]
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and the difference between both quantities of foreign exchange is used to increase imports, i.e.
I To summarize, from [3.17] and [3.18] we can see that the value of additional consumption in the market of e will be
[3.21]
and, from [3.19] and [3.20], that in the market of h will be
[3.22]
Following the same procedure as in the case of imports, and assuming again that the domestic transport and trade margins are nil, we can express the domestic prices of the two exported consumer goods as
[3.23]
[3.24]
in which FOBi and tt (i = e, h) are the FOB prices in foreign exchange and the export tax rates, respectively.9 Substituting [3.23] and [3.24] in [3.21] and [3.22] we get
[3.25]
Since for small changes in the supply of foreign exchange
9. Export incentives, such as drawbacks or credits at interest rates lower than the discount rate, will be treated as "negative" taxes.
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ACCOUNTING PRICE OF FOREIGN EXCHANGE
expressions [3.25] can be written as
[3.26]
As a result, the value of the additional consumption made possible by the increase in the supply of foreign exchange d\ — ds would be equal to:
(a) that resulting from additional imports for an amount in foreign exchange equal to d} — d0, whose value, according to the example in Section 3.2, will be
(b) that resulting from the increase in the domestic consumption of exported goods, the value of which, according to expressions [3.26], will be
(c) the value of the resources made available for the additional production of other goods, because of the reduction in the production of export goods
The increase in the supply of foreign exchange produced by the project being analyzed will consist of:
(a) the net addition to foreign exchange availability (d\ - d0), which is used entirely for additional imports; and
(b) the reduction in exports from other producers due to the increase in the domestic quantity demanded (&ed and Ahd) and the reduction in domestic production (Ae5 and Ahs)
Consequently, since the APFE has been defined as the sum of the CVs of the additional supply of foreign exchange per unit thereof, and in keeping with
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the assumptions already mentioned, this sum of CVs will be equal to total willingness to pay plus the value of the resources released, expression [3.6]
can be redefined as
and calculated in accordance with expressions [3.9] and [3.26]. Defining CIFi Am, as the increase in the value of the imports of good i per additional unit of foreign exchange d\ — ds produced by the project and FOBj AJC,- as the reduction in the value of the exports of goody per unit of d\ — ds, the APFE will be
[3.27]
Finally, since the accounting price ratio of foreign exchange has been defined as
defining
[3.28]
[3.29]
and substituting [3.28] and [3.29] in [3.27], the APRFE can be presented as
[3.30]
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ACCOUNTING PRICE OF FOREIGN EXCHANGE
In other words, the APRFE is a weighted average of one plus ad valorem foreign trade taxes rates (or its equivalent for other types of restrictions or incentives) in which the weights represent the share of the change in the value of the imports or exports of each good, in the supply change generated.
If imports and exports were also subject to domestic taxes ft and tj, respec-tively, the equivalent of [3.30] would be
If the change in exports includes intermediate or capital goods, expressions [3.30] and [3.31] will continue to be valid if:
(a) we can assume that domestic demand for such goods is a good approxi-mation of the value of their marginal product (in consumption units) as shown in expression [3.14] for the case of imports; or
(b) the domestic prices of the inputs used in the production of consumer goods are regarded as good approximations of their efficiency prices (in the consumption numeraire), which would result in the same as shown in expression [3.15] for imported intermediate goods.
The calculation of the weights <p requires that the price elasticity of the supply of exported goods and of the domestic demand for imported goods be known, information which in practice is not available. As a result, the APRFE is frequently calculated on the assumption that the weights <p are equal to the average share of each product in total imports and exports. Thus, for example, in the case of imports, the weights are calculated as
Substituting [3.32] and its equivalent for exports in [3.27], and dividing by the EER we obtain
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in which
The same expression has been presented in various texts as the formula for calculating the "standard conversion factor", which is used to convert values expressed in the consumption numeraire to the foreign exchange numeraire.10
3.6 The Accounting Price of Foreign Exchange When There Is Domestic