ECONOMICS DEPARTMENT

(Cost of a Market Basket of Goods and Services at Foreign Prices)

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(Cost of the Same Market Basket of Goods and Services at U.S. Prices)

If the exchange rate is at PPP at time 0 and the foreign country experiences
a rate of inflation of (1+^{F}) while the U.S.
experiences a rate of inflation of ^{$} then the
cost of the market basket in foreign currency will increase in one year by a factor
of (1+^{F}) while the cost of the market basket in
dollars will increase by a factor of (1+^{$}).
Thus the exchange rate at time 1 year, E_{1} will equal to:

= [(1+

or

g = (

If we consider the direct form of the exchange rate, dollars per unit of foreign currency the growth rate g' would be:

Strictly speaking, the projection of the future exchange rate considered
above should be based upon the current PPP exchange rate. This would give
the expected future PPP exchange rate that would be a reasonable estimate
of the market exchange rate will be. Let __E__ stand for the PPP exchange
as opposed to E for the market exchange rate. Then the theory is given
by the followiing equations:

The expected rate of return for a dollar investment, RET^{$},
is just i^{$}. The expected rate of return in dollar terms for
an investment in France, RET^{FF}, is given by computing the
number of francs a dollar amount will be equivalent to, determineing
the number of francs that will be received after one year, and finding
the number of dollars those future francs can be expected to be
converted to on the basis of the expected exchange rate at
t+1, E^{e}_{t+1} ; i.e.,

(E

= 1/(E

This means that:

i

= 0.80 - 0.75 = 0.05

(1/e

= e

Thus

RET

= (e

which is not as good as the U.S. rate. Under these circumstances no American investor would want to invest in the Canadian financial market. It is intuitive that Canadians would under these circumstances prefer to invest in the American market, but we should check the numbers. If the direct quote exchange rate from the American perspective went from $1.00/C$ to $0.95/C$ (the 5 percent depreciation mentioned above) then the direct quote (units of domestic currency per unit of foreign currency) exchange rate from the Canadian perspective went from C$1.00/$ to C$1.05263/$, an appreciation of the dollar of 5.263 percent. Thus for the Canadian investor the rate of return from an investment in the U.S. market is:

Let e_{t} be the spot exchange rate (direct form)
at time t and let f_{t,t+1} be the forward rate at time
t for conversions at time t+1. Then the rate of return RET on
an investment in the foreign financial market is:

(1/e

This means that if there is equilibrium between the two markets so that

= i

= i

It is clear that when a country has a higher real rate of interest than other countries do, as was the case with the U.S. in the early 1980's, there is an increase in the value of its currency with respect to the value of other countries' currencies. However it is also clear that financial markets do not adjust instantaneously to achieve an equilibrium. The difference in the real interest rates between the U.S. and other countries persisted for years despite the substantial net inflows of capital to the U.S.

Let us consider the particular case of the Deutsche Mark/Dollar exchange
rate. There are various components of demand for DM. One componenet stems from
the demand for the importation of German goods and services. Let q(P_{$})
be the demand function for a German product, say sport cars, as a function of
the dollar price of these cars. If E_{$/DM} is the exchange rate
for the DM, then the dollar price for the cars to American buyers is
P_{DM}E_{$/DM}, where . But the demand function is in terms of physical
units. The DM expenditure on German sports cars is then
P_{DM}q(P_{DM}E_{$/DM}). It should always be remembered
that although the demand function q() is downward sloping, the expenditure
function pq(p) can have any slope. However in this case if the German price
of the cars is independent of the exchange rate the relationship between the
quantity of DM demanded and the exchange rate will the same as the relationship
betweeen physical demand function and the price of the product.

Likewise the supply of DM from Germans who want to buy American goods
and services. Suppose the demand function of Germans for some American product,
say wheat, is h(P_{DM}). The DM price for the wheat is then
P_{$}/E_{$/DM} so the supply of DM is
(Pa
_{$}/E_{$/DM})h(P_{$}/E_{$/DM}). The
dependence of the quantity of DM supplied to the American currency market
from this source is a little more complicated than the case of the
demand for DM. Generally we expected that the supply of DM will be a
positive function of the exchange rate.

The supply of DM through capital market flows depends upon the expected rate of return in the U.S. capital market compared to the rate of return in the German capital market. Interestingly enough this does not depend directly upon the rates of inflation in the U.S. and Germany. It depends upon the nominal interest rates in the two countries and the expected rate of change of the exchange rate, as was shown in the previous section; i.e.,