APPENDIX Optimal Relationship Between Taxes and Subsidies on Capital Flows
Let there be only two countries, A and B.
U, UA, and UB ≡ utility in general, in A, and in B
qx ≡ amount of securities (capital account items) exported from A to B
qm ≡ amount of securities imported from B to A
PxA and PxB ≡ price of A’s securities in A and B
PmA and PmB ≡ price of S’s securities in A and B
t ≡ proportionate tax in A on import of securities from B
s ≡ proportionate subsidy in A on export of securities to B
ϵ ≡ elasticity of net supply of B-securities to A
μ ≡ (negative) elasticity of net demand for A-securities in B
UA and UB ≡ marginal utility of money in A and in B.
Then U = UA (qm, qx, …) + UB (qm, qx, …)
Mr. Fleming, Deputy Director in the Research Department, is a graduate of Edinburgh University. He was formerly a member of the League of Nations Secretariat, Deputy Director of the Economic Section of the U.K. Cabinet Offices, U.K. representative on the Economic and Employment Commission of the United Nations, and visiting Professor of Economics at Columbia University. He is the author of Essays in International Economics and numerous articles in economic journals.
J. Marcus Fleming, “Dual Exchange Rates for Current and Capital Trans actions: A Theoretical Examination,” in Essays in International Economics (Har vard University Press, 1971), pp. 296–325. See also Vittorio Barattieri and Giorgie Ragazzi, “An Analysis of the Two-Tier Foreign Exchange Market,” Banca Nazion ale del Lavoro, Quarterly Review, No. 99 (December 1971); Pascal Salin, “Ui double marché des changes est-il justifié?” Revue d’Economie Politique, No. (November-December 1971), pp. 959-74; and Anthony M. Lanyi, “Separat Exchange Markets for Capital and Current Transactions” (unpublished, Intei national Monetary Fund, 1973).
Fleming, op. cit., pp. 298 ff.
If the system is to make its maximum contribution to buffering external influences on the domestic monetary system, a slightly different criterion must be followed—that of buying or selling as much domestic currency on the capital market as is sold or bought on the official market. This involves some reserve changes, corresponding to net profits or losses.
Compare Barattieri and Ragazzi, op. cit.
Herman C. Verwilst (doctoral candidate, The Johns Hopkins University) has drawn my attention to a third possible mechanism whereby movements in the “capital” rate might affect capital flows, namely, through a change in the degree of uncertainty of investors regarding the future level of that rate. A rise in uncertainty such as might occur when the “capital” rate diverged from its normal relation to the “current” rate would presumably discourage capital flows, both inward and outward, and also reduce the net capital flow corresponding to any given level of the capital rate.
Lanyi, op. cit.
The reason why maintenance of the original rate discrepancy does not maintain precisely the original payments balance is that the evaders make profits—in reserves or in domestic currencies—at the expense of the authorities. Maintenance of the original payments balance in the face of evasion thus calls for some widening of the original rate discrepancy when the domestic currency is at a discount in the “capital” exchange market, but is compatible with some narrowing of the discrepancy when the domestic currency is at a premium in that market.
See, however, John H. Williamson, The Crawling Peg, Essays in International Finance, No. 50 (Princeton University Press, December 1965).
ϵ = elasticity of net supply of B securities to A
μ = elasticity of net demand for A securities in B
UA, UB = marginal utility of money in A, B
t = the tax in A on the import of securities from B as a proportion of the price in B
s = the subsidy in A on the export of securities to B as a proportion of the price in B.
This formula will permit equality between t and s, that is, a uniform capital exchange rate only if either
(a) the elasticity of net demand for A’s securities in B and the elasticity of net supply of B’s securities to A are both infinite
(b) the marginal utility of money in A relative to that in B happens to be precisely equal to the exchange rate for B’s currency in terms of A’s currency for capital transactions. In this case both numerator and denominator on the right-hand side of the equation would be zero.
The foregoing argument calls for some qualification to take account of the possibility that, given the uncertainty of the future “capital” rates in any dual exchange market system, such a system may create greater uncertainty regarding the profitability of capital flows both inward and outward than would a system of administrative restraints on such flows (compare footnote 4). To the extent that this is the case, there is a possibility that the dual exchange market system may unduly restrict gross capital flows in a way that the system of administrative restraints would not, though the effect on net flows might be welcome.
Apart from the unevenness, inseparable quantitative controls and licensing arrangements, countries are often loath to apply such restrictions to the outflow of nonresident funds or the inflow of national funds held abroad. Inhibitions about applying the “capital” rate to such transactions may be less marked.
This is true whether the variation in investment demand that has to be compensated for is due to a change in interest rates undertaken for balance of payments reasons or to a change in the incentive to invest to which monetary policy, for balance of payments reasons, fails to respond.
Both flexible unitary rates and dual markets are open to objection because of the unduly discouraging effect which their uncertainty may exercise on gross capital flows, especially in the medium term, and because of their tendency to discourage net capital flows whether or not this is called for in the interests of short-term equilibrium. Neither appears to have a differential advantage over the other in this respect.
The use of the dual exchange market as an instrument to limit the range of variation of a unified floating rate is discussed below.
Some of the features of this arrangement are approximated in Italy’s present dual float.
It is vital to the operation of such a system that official intervention on the two exchange markets follow rules (3) and (4) above. Any attempt to operate the system without official intervention could be saved from disaster only by leakages from one market to the other, since a completely segregated current exchange market would be highly unstable as the impact effect of exchange rate changes on the current account would naturally be perverse.