answer sheet for the second homework assignment

Econ 434Professor IckesFall 2005Homework Assignment #2: Answer Sheet1. The US government wants the Chinese government to let its currency (yuan) be flexible (abandonits fixed exchange rate) so it can appreciate in value. Draw a demand-supply diagram forthe yuan under these current conditions (i.e., before it becomes flexible).brief answer See figure 1. The fixed exchange rate e is greater than the shadow exchangerate e. At e there is an excess supply of dollars.e =yuandollarSee~DdollarsFigure 1:(a) How can the fixed exchange rate be kept different from the market-clearing exchange rate?Explain. Can the Chinese government persist in this activity over time? Explain.brief answer The Central Bank of China (CBC) can purchase the extra dollars byselling yuan. This puts downward pressure on the value of the yuan. China can printas much yuan as it likes, it just has to build warehouses for the dollar. The onlyproblem is that this policy may be inflationary. China could try to sterilize the inflowof reserves. To do this they must sell bonds to soak up liquidity, offsetting the impactof the inflow of reserves. Given that China limits the investment opportunities of itscitizens the cost of this is less than it would be in a country with an open capitalaccount.(b) If there was a forward market for yuan what would be the likely relationship between theforward price and the current price of the yuan? Explain.1

ief answer The forward price of the yuan should be higher than the current price ifinvestors expect the yuan to appreciate. How much depends on the probability thatthe CBC will let the yuan appreciate during the period.(c) What if the yuan were overvalued instead of undervalued? What problems would theCentral Bank of China face if it tried to maintain the pegged rate?brief answer In this case e

TQ 0PC ~ P 0Figure 2:NXPNT3. Suppose that you are a US exporter expecting to receive a payment of 100 euros in 12 months.The one-year interest rate on euro deposits is 5% per annum, and the one-year interest rateon dollar deposits is 8%. The present spot exchange rate is $0.50 per euro.(a) What is the one-year forward exchange rate?1+ibrief answer Covered interest parity implies that F t = e t ,sowehaveF1+i ∗ t = .50 1.08 = 1.05.5142. The dollar is expected to depreciate, that is why domestic interest rates exceedeuro rates.(b) Assuming that you ultimately need dollars, describe at least two ways you can coveryourself from the exchange rate risk.brief answer You could purchase the dollars for delivery in one year with a forwardcontract. This would involve a contract with a commercial bank. At the end of theyear you deliver euros and get dollars at the price of the contract today. Alternatively,you could purchase a one year ahead futures contract. This is also a commitmentto buy foreign exchange at a given price, but it is traded on a centralized market infixed sizes. At the end of the year you are committed to trade euros for dollars atthe price you contracted for today. Notice that if the dollar ended up depreciatingby more than the 2.8% that was anticipated, the actual spot price next year will beeven higher than .5142. So had you not hedged you would be able to convert theeuros back into even more dollars. But you still hedged the risk. 1 But there is a thirdway to hedge the risk: purchasing a currency option. This gives you the right to selleuros for dollars at a fixed rate, but it is not an obligation. If the euro appreciatedmore than expected you could walk away from the option. If the dollar appreciated,on the other hand, the option would protect you from the currency risk. Notice thatyou have to pay something for this insurance. That is the price of the option. You1 If you drive to school and don’t have an accident it does not mean you wasted your money on car insurance.3

might also note that the greater the volatility of currencies the more valuable suchan option would be.(c) Now suppose your claim on euros is six months hence. The interest rate on 6 monthdollar deposits is 8% and on euros it is 4%. What is the six-month forward rate?brief answer F t = .50 1.08 = .51921.04(d) What do your answers to (a) and (c) imply about the ”market’s expectations” about thepath of the exchange rate over the next year? Explain.brief answer The dollar is expected to depreciate over the next six months by 3.8%and then appreciate over the following six months, by about 1%.4. Suppose that the price level in the home country is given by P = Pn α Pt1−α ,whereP t is theprice of traded goods, and α is the share of non-traded goods in the domestic price index, andsimilarly P ∗ = P ∗ αnfor the foreign country. Suppose that tradables have a common priceof 1 in both countries. Show how the ratio of home to foreign prices depends on the relativeprice of non-traded goods (e.g., derive a simple expression for this).P ∗ 1−αtbrief answer This part is trivial and is only to set up the rest. P =(1) 1−α Pn α = Pn α andlikewise P ∗ =(Pn) ∗ α for the foreign country. Henceà ! αPP = Pn(1)∗ Pn∗Thus in this model the real exchange rate depends only on the internal relative price ofnon-traded goods.(a) Let P b be the growth rate of the price level and let P b∗ bethegrowthrateoftheforeignprice level. If α is constant, when will P> b P b∗ ?brief answer Looking at (1) we can see that the only way the left-hand side can getbigger, given α>0 and constant, is if the price of non-traded goods rises faster athome than abroad; i.e., if P b n > P b n.∗(b) Let A b T be productivity growth in tradable goods in the home country and let A b N beproductivity growth in the non-traded goods sector (and A b∗ T , A b∗ N for the foreign country).Suppose that A b T − A b∗ T > A b N − A b∗ N. What would you expect to happen to P b − P b∗ ?Why?brief answer It should rise. If this condition holds, it follows that A b T −A b N > A b∗ T −A b∗ N.So we should expect wages to be rising faster domestically than in the foreign country.Higher productivity growth in traded goods raises wages in the entire economy.(c) Is the condition A b T − A b∗ T > A b N − A b∗ N more likely to hold in richer countries or poorercountries? What then would you expect to happen to a country’s real exchange rate as itgets richer?brief answer More likely in poorer countries that are developing. Catchup is whenproductivity growth in traded goods will be highest. Rich countries can only growat the rate of technological progress, but poorer countries catch up by accumulatingcapital, etc. Just as Japan after WW2. In these cases their real exchange ratedepreciates (for them recall that the rich country is the foreign country).4