Derivation of demand curve for foreign exchange

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Economics of International Finance
Econ. 315
Chapter 5:
The Price Adjustment Under
Flexible and Fixed Exchange Rates
I. Overview
Objectives:

Examining how a nation’s current account is affected by price
changes under fixed and flexible exchange rates.
Assumptions:

We assume no autonomous international private capital flows,
i.e., they take place as a response to temporary trade balances.

Current account is corrected only by exchange rate changes.

Since this approach is based on trade flows and the speed of
adjustment depends on how responsive (elastic) imports are to
price changes (exchange rate changes), it is also called trade or
elasticity approach.
II. Adjustment with Exchange Rates

Current account is corrected by a depreciation (a flexible
exchange rate) or a devaluation (a fixed or pegged exchange
rate).

Depreciation or devaluation operates on prices to bring about an
adjustment in the current account and BOP, i.e., affects the
relative prices of exports and imports.
Example :





Look at figure 1, where USA and EMU are assumed to be the only two
economies in the world. There are no international capital flows, such
that the US demand and supply for € reflects only trade in goods and
services.
At R = $1/ €1, the US demand for € is 12 bn, while supply is only €8
bn, i.e., a deficit € 4 bn.
If demand and supply for euros are D€ and S€, a 20% devaluation
would equilibrate BOP at €10 bn (point E).
If demand and supply for euros are less elastic D€’ and S€’ a 20%
devaluation would not equilibrate BOP at €10 bn. A 20% devaluation
would reduce the deficit to €3 bn, and 100% devaluation (R = $2/ €1)
would completely eliminate the deficit (point E’). Why?
The scale of depreciation depends on how elastic is the demand and
supply for foreign currency (imports and exports).
A deficit is corrected by
a 100% devaluation
The 20% devaluation would reduce
the deficit but not to correct for it
A deficit is corrected by a
20% devaluation
Figure 1 Balance-of-Payments Adjustments with Exchange Rate Changes.
III. Derivations and Term of Trade
- Derivation of demand curve for foreign exchange

Look at panel A of figure 2. the demand for imports is DM at
R=$1/€1 while the European supply of imports is SM. Suppose
that the euro price for a unit of imports is PM = €1, and the
quantity of imports = 12 bn units (this corresponds to point B’ in
figure 1 (i.e., 12 bn units × €1 = €12 bn).

If the dollar depreciates by 20% pushes the DM down to to DM’,
SM remains unchanged, Why?. For the US to continue to demand
12 bn units the euro price of US imports would have to fall to PM
= €0.8, i.e., by exactly the 20% depreciation of the dollar in order
to leave the dollar’s price of European imports almost unchanged
(point H on DM).
Panel A
A compromise price € .9 per unit
at which BOP is in eq.
If the $ depreciates by 20%, DM shifts down.
PM should go down to € .8 (by 20%)
for US to continue buying 12 bn. units
Figure 2 Derivation of the U.S. Demand and Supply Curves for Foreign Exchange

It is obvious that DM’ should not be parallel (compare points J-G
and H-B’)

With DM’ and SM the price of imports is PM = €0.9 and QM = 11
bn. the US will move to point E’ and demand of the € would be
(11 bn. × 0.9 = 9.9 bn) ≈ 10 bn.

So: at R=$1/€1 the demand was € 12 bn, (point B in figure 1)
and at R=$1.2/€1 the demand was 10 bn, (point E in figure 1).
Therefore, D€ is derived from the demand and supply of imports.
(If demand for imports is less elastic, the demand for euros
would be D€* in figure 1)

The less elastic is the demand for euros, the steeper is the
demand.
- Derivation of the supply curve for foreign exchange.

Look at panel B of figure 2. SX is the supply of US exports, and DX is the
European demand for US exports. If the US price in euros is € 2, the quantity
of exports would be 4 bn and supply of euros would be 2 × 4 = € 8 bn (point
A in figure 1).

With A devaluation of 20% of the dollar DX remains unchanged but SX would
shift down to SX’. The price of exports would be €1.6 for each unit, this will
encourage European to demand more and there will be a movement toward E’
on DX which is an increase in the quantity exported by US from 4 bn to 5.5
bn. (i.e., 5.5x1.8≈ €10 bn).

So at R = $2/ €1, the supply of euros is €8 bn (point A in figure 1), at R =
$2.4/ €1, The supply of euros is 10 (point E in figure 1). The supply of euros
is driven from the supply and demand for US exports.

If demand for exports is less elastic there could be a movement form point A
to point C instead of E in figure 1.
Panel B
the price of exports € 1.8 per unit
at which BOP is in eq.
If the $ depreciates by 20%, SX shifts
and PX should go down to € 1.6 (by 20%)
This encourages demand for US exports
that pushes the price up to 1.8 euros
Figure 2 Derivation of the U.S. Demand and Supply Curves for Foreign Exchange
- Effect of Exchange Rate on Domestic Prices & Terms of Trade
1.
Depreciation or devaluation stimulates the production of import substitutes and
exports leading to a rise in prices, i.e., depreciation is inflationary. The greater
the depreciation or devaluation, the greater is the inflationary impact, and the
less flexible is the increase in exchange rates as a method of correcting deficit
in BOP.
2.
A depreciation or devaluation is also likely to affect the nations terms of trade
TOT (the ratio between export prices and import prices), since TOT are either
measured in domestic prices or in foreign currency, a depreciation or
devaluation will cause TOT to increase, fall, or remain unchanged.

Look at figure 2, before depreciation, the price of exports PX = €2 (point A’ in
the right panel) and PM = €1 (point B’ in panel A). Hence TOT (PX / PM =2/1 =
2 or 200%). After a 20% depreciation PX = €1.8 (point E’ in panel B) and PM =
€ 0.9 (point E’ in panel A), so TOT = 1.8/0.9 = 2 or 200%. TOT remain
unchanged. But in general we expect TOT to change in case of depreciation.

The Dutch Disease
When an industrial nation begins to exploit a domestic
natural resource previously imported, the nation’s
exchange rate might appreciate to cause the nation’s
loss of international competitiveness in its traditional
industrial sector, and even face deindustrialization.
IV. The Stability of Foreign Exchange Markets:
1.
Stable Foreign Exchange Market: when disturbances from the
equilibrium exchange rate give rise to automatic forces that push
exchange rate back to the equilibrium level.
2.
Unstable Foreign Exchange Market: when disturbances from the
equilibrium exchange rate push the exchange rate further away
from the equilibrium level.
Note: A foreign exchange market is stable when the supply curve of
foreign exchange is positively slopped or if it is less elastic
(steeper) than the demand curve for foreign exchange.

When foreign exchange market is unstable, a flexible exchange
rate system increases, rather than reduces, BOP deficit. The
revaluation or appreciation not depreciation is required to
eliminate the BOP deficit, while devaluation is required to
correct for BOP surplus.

Determining whether the foreign exchange market is stable is
important. If the foreign exchange market is stable, elasticity of
the demand for foreign exchange and supply of foreign exchange
become important.
The Marshall-Learner Condition

The condition that tells us whether the foreign exchange market is
stable or unstable is the Marshall-Learner condition (M.L.C).
The simplified version of the M.L.C is that if supply curve of
imports and exports are infinitely elastic.

the M.L.C indicates that a stable foreign exchange market occurs
if the sum of price elasticities of demand for Dx and Dm of
foreign exchange in absolute terms is greater than one.

If the sum of elasticities of demand for Dx and Dm of foreign
exchange is less than one 1, the foreign exchange market is
unstable.

If the sum of elasticities of demand for Dx and Dm of foreign
exchange is one, the BOP will remain unchanged.
V. Elasticities in the Real World.
A. Elasticities Estimates

M.L.C postulates a stable foreign exchange market if the sum of price
elasticities of DM and DX exceeds one in real absolute terms. However, the
sum of elasticities of DM and DX should be substantially greater than one to
make depreciation feasible as a method of correcting a deficit in BOP.

Before world war II Marshall argued that price elasticities in international
trade are high (stable foreign exchange markets). This was not based on
empirical support (prewar optimism).

Econometric estimates, after the WWII however, show that the sum of price
elasticities of DM and DX is either less than 1 or barely exceed 1. prewar
optimism was replaced by post war pessimism.
B. The J curve and revised elasticity estimates

The BOP may worsen soon after the depreciation before improving later on.
This is due to the tendency of the domestic currency price of imports to rise
faster than export prices with quantities initially not changing very much.

Over time QX rises and QM falls so that the initial deterioration of the BOP is
halted and then reversed. This is known as the J curve effect because the
response of the trade balance to a depreciation looks like the curve of a J.

Empirical studies confirmed the existence of the J curve effect and came up
with high long term elasticities, i.e., real world elasticities are high enough to
ensure stability of the foreign exchange market in the short run and a fairly
elastic demand for and supply of foreign exchange in the long run.
FIGURE 4 The J-Curve.
BOP improves
Immediate deterioration of BOP
BOP deterioration halts
Deterioration lowers over time
C. Currency pass through

The increase in the domestic price of imported commodity may be smaller
than the amount of depreciation even after lags, i.e., the pass through from
depreciation to the domestic prices may be less than complete, e.g., a 10%
depreciation may result in a less than 10% increase in domestic currency
prices of the imported commodity. Why?

Exporters often having established a large share in domestic market may be
willing to absorb at least some of the price increase they could charge out of
their profits. A foreign company may increase the price of exports by 6% and
accept a 4% reduction in the price of its exports when the nation’s currency
depreciates by 10% to avoid the risk of losing foreign markets by large
increases in the price of their exports. This is known as the beachhead effect.
VI. Adjustment under the gold standard
A. The Gold standard

Operated from about 1880 to the outbreak of the WW I. After the war, there
was an attempt to reestablish the gold standard but this failed in 1931. It is
also unlikely that it will be reestablished in the future. But it is important to
understand its advantages and disadvantages.

Under the gold standard each country defines the gold content of its currency
and stands ready to buy or sell any amount of gold at that price. Based on that
exchange rates are determined.

For example, the £ contains 113 grains of gold while the $ contains 23.2
grains. The dollar price of the £ is 113/23.2 = 4.87. this is called the mint
parity.

Since shipping currencies between New York and London cost gold (about 3
cents), the exchange rate between the $ and £ could never fluctuate by more
than 3 cents above or below the mint parity.
FIGURE 5 Gold Points and Gold Flows.
An increase in the
demand for imports
 deficit and a
depreciation of $
sell gold abroad
Gold sold in US, exported to London
to buy £ at $ 4.90 Instead of buying
£ in US at $ 4.94
An increase in the
demand for exports
 Appreciation of $
Gold is imported from London
buy gold from abroad
due to selling the surplus of
£ there at 4.84 instead of 4.80 in US

None would pay more than $ 4.90 for £1 since he/she could purchase $
4.87 of gold in the US, ship it to London at 3 cents and exchange it for
£1 at the bank of England (central bank). Thus the US supply of £
becomes infinitely elastic at the rate of $ 4.90 for £1. This was the gold
export point of the US

On the other hand, the $/£ rate can’t fall below $ 4.84 because no one
would accept less than 4.84 for the £. He could always purchase £
worth of gold in London and ship it to New York at a cost of 3 cents
and exchange it for $ 4.87 (i.e. 4.84 net) as a result the demand curve
becomes infinitely elastic (horizontal) at the rate of $ 4.84 / £1. This is
the gold import point of the US. Exchange rate is prevented from
moving outside the gold points by US gold sales or purchases.
B. The price-specie-flow mechanism
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The automatic adjustment mechanism under the gold standard. The pricespecie-flow mechanism is working as follows
Under the gold standard money supply would fall in the deficit nation and rise
in the surplus nation causing prices to fall in the deficit and rise in the surplus
nation. Exports of the deficit nation would be encouraged and imports would
be discouraged until deficit is eliminated. This is based on the quantity theory
of money:
M.V=P.Q
As the deficit nation lost gold, M falls. A reduced M by 10% encourages
exports and discourages imports. The opposite would take place in the surplus
nation (due to gold inflow) internal prices increases and discourage exports,
and encourage imports until deficit and surplus are eliminated.
Note that while adjustment under the flexible exchange rate system relies on
high price elasticities of exports and imports, in the deficit surplus nation,
adjustment under the gold standard relies on changing internal prices of each
nation. The adjustment under the gold standard relies also on high price
elasticities of exports and imports in the deficit and surplus nation, so that the
volume of exports and imports respond readily and significantly to price
changes.
The price-specie-flow mechanism
M.V = P.Q
Deficit nation  M↓ P
↓  imports ↓
and exports ↑  bop equilibrium
Surplus nation  M ↑ P
↑  imports ↑
and exports ↓  bop equilibrium
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