Practice problems 2 - answers 1. Answer: PPP states that the exchange rate between two countries’ currencies equals the ratio of the countries’ price levels. A fall in a currency’s domestic purchasing power (i.e. an increase in the domestic price level) will be associated with a proportional currency depreciation in the foreign exchange market and vice versa. E$/E = PUS/PE where P is the price of a reference commodity basket. Rearrange: PUS = (E$/E) x (PE) Thus, PPP asserts that all countries’ price levels are equal when measured in terms of the same currency. 2. Answer: PPP theory is a monetary approach to the exchange rate. It is a long-run theory because it does not allow for price rigidities. It assumes that prices can adjust right away to maintain full employment as well as PPP. 3. Answer: All else equal, a rise in a country’s expected inflation rate will eventually cause an equal rise in the interest rate that deposits of its currency offer. Similarly, a fall in the expected inflation rate will eventually cause a fall in the interest rate. Ex: If the expected U.S. inflation were to rise permanently from Π to (Π + ΔΠ), current dollar interest rates R$ would eventually catch up to the higher inflation, rising by a value ΔR$ = ΔΠ in accordance with the Monetary Approach that in the long run purely monetary developments should have no effect on an economy’s relative prices since the real rate of return on dollar assets would remain unchanged. 4. Answer: The real exchange rate between two countries is a broad summary measure of the prices of one country’s goods and services relative to the other’s. PPP predicts that the real exchange rate never permanently changes, which is different from nominal exchange rates that deal with the relative price of two currencies. 5. Answer: The chain of events leading to exchange rate determination: The spot exchange rate is equal to the real exchange rate times the ratio of U.S. to European price levels. Increase in U.S. money supply: The price level in the U.S. rises in proportion to the money supply; the real exchange rate remains the same. All dollar prices will rise (including the dollar price of the euro). Increase in growth rate of U.S. money supply: The inflation rate, dollar interest rate, price level in the U.S., and spot exchange rate rise in proportion to the increase in the price level in the U.S. Increase in world relative demand for U.S. products: E falls, and q does as well. Increase in relative U.S. output supply: The dollar depreciates, lowering the relative price of U.S. output. The real exchange rate rises; the effect on E is not clear since the real exchange rate and the price level in the U.S. work in opposite directions. 6. a) Nigeria suffers a depreciation of its real exchange rate as the price of non-traded goods in Nigeria falls with its fall in income. b) There will be no effect, at least in the long run, of this purely monetary change. In the short run, we would see a nominal and real depreciation. As prices adjust, the real exchange rate returns to its original level. 7. A rise in the expected future rate of the real dollar/euro depreciation causes the long-run exchange rate to depreciate. An increase in the expected rate of depreciation of the real exchange rate increases the domestic nominal interest rates, all else equal, as shown by the relationship between interest rate differences, expected inflation differences and the expected change in the real exchange rate. An increase in the domestic nominal interest rate causes excess money supply. The money market is brought back into equilibrium through an erosion of real balances due to an increase in the price level. By PPP, an increase in the price level causes a depreciation of the currency. 8. Answer: The figure below shows the phenomenon of overshooting. A permanent increase in the money supply starting from full employment equilibrium will shift the AA curve to the right from AA1 to AA2. Now, a steadily increasing price level shifts the AA and the DD schedules to the left until a new long-run equilibrium is reached. Note that point 3 is above point 1, because Ee is permanently higher after a permanent increase in the money supply. The expected exchange rate, Ee , has risen by the same percentage as Ms. Notice that along the adjustment path between the initial short-run equilibrium (point 2) and the long-run equilibrium (point 3) the domestic currency actually appreciates (from E2 to E3) following its initial sharp depreciation (from E1 to E2). This exchange rate behavior is an example of overshooting, in which the exchange rate’s initial response to some change is greater than its long-run response. 9. Answer: a) In this case the AA schedule is vertical and the DD schedule retains its former positive slope. b) A temporary increase in the money supply has a larger effect on the exchange rate and on output when we assume that the exchange rate always equals its long-run level. c) A temporary increase in the government spending has no effect on output, and a larger effect on the exchange rate when we assume that the future exchange rate always equal its long run level. 10. a) By interest parity logic, raising the interest rate should bring money back into country causing the exchange rate to appreciate, or at least counterbalance the attack. b) The act of raising the interest rate may make some investors feel the cost of policies necessary to maintain a fixed exchange rate are too high and that the government will be unable to maintain them. These costs could be due to high government debt that becomes more expensive when rates go up, or due to high unemployment which may get worse due to monetary tightening. These costs may lead some domestic constituencies to call for a devaluation, further raising investors’ concerns. c) Yes. Even if the fixed rate was originally sensible, if the costs of defending the attack weakens the government to the point that it no longer looks able to maintain the current exchange rate, then investors who originally thought the rate was sensible may now feel that a change in the exchange rate is necessary. For example, the costs of high interest payments during the time of the attack may take the government more likely to raise the money supply growth rate and thus make more investors inclined to attack the currency even if they would not have done so before the initial attack. 11. A contraction of the German money supply shifts the interest parity curve out. British monetary authorities would be forced to contract their money supply in response to maintain the fixed Pound/DM exchange rate. 12. For example, we may find the following (only the direction of change, not the actual amounts, can be inferred from the question). The Fed decreases its holdings of dollar assets and increases its euro holdings thus increasing the public’s supply of dollar assets and decreasing its holdings of euro assets. Balance Sheet of the ECB Balance Sheet of the ECB Before intervention After intervention Assets Liabilities Assets Liabilities Domestic 2000 bill. 2800 bill. Domestic 2300 bill. 2800 bill. Foreign 800 bill. Foreign 500 bill. 13. Answer: •Sterilized foreign exchange intervention – policy by which central banks carry out equal foreign and domestic asset transactions in opposite directions to nullify the impact of foreign exchange operations on domestic money supply. •Example: Bank of Pecunia sells $100 in foreign assets, receives $100 check from PecuniaCorp. Central foreign assets and liabilities decline simultaneously by $100; fall in money supply. •To negate effect on money supply, central bank buys $100 of domestic assets. This increases its domestic assets and its liabilities by $100, offsetting the money supply effect of sale of foreign assets. 14. Answer: Under floating, by purchasing domestic assets the central bank causes an initial excess supply of domestic money that simultaneously pushed the domestic interest rate downward and weakens the currency. However, under fixed exchange rate the central bank will resist any tendency of the currency to depreciate by selling foreign assets for domestic money and so removing the initial excess supply of money its policy move has caused. 15. Answer: 1. Allow the government to fight domestic unemployment despite the lack of effective monetary policy. 2. Improve the current account. 3. Increase foreign reserves held by the central bank. 16. Answer: The fixed exchange rate DD – AA model requires the assumption that E = E0 . This shows that the economy’s short-run equilibrium is at point 1 when the central bank fixes the exchange rate at the level C. Output equals Y1 at point 1 and the money supply is at the level where a domestic interest rate equal to the foreign rate (R*) clears the domestic market. To Increase Output: Hoping to increase output to Y2, the central bank increases the money supply through the purchase of domestic assets and shifting AA1 to AA2. Because the exchange rate is fixed, the central bank must maintain E0, it has to sell foreign assets for domestic currency, thereby decreasing the money supply immediately and returning AA2 back to AA1. Output is unchanged as the initial equilibrium is maintained. 17. Answer: An expansionary fiscal policy shifts the DD curve to the right. Under flexible exchange rate, point 2 in the figure is the equilibrium, e decreases (appreciates) and Y goes up. The picture is more complicated under fixed exchange rate, however, since E cannot change. Output is going up as a result of the fiscal expansion, and thus the demand for domestic money increases. To prevent the increased money demand from increase domestic interest rate above R*, and with the appreciation of the currency, the central bank must buy foreign assets with domestic money and thereby increase the money supply. The AA shifts to the right until E is restored to the initial fixed exchange rate, E0, at point 3 in the figure. So under fixed exchanger rate, Y will increase by more than under a flexible exchange rate regime. Unlike monetary policy, fiscal policy can be used to affect output under a fixed exchange rate. A central bank is forced to expand the money supply through foreign exchange purchases.
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