answer sheet for the second homework assignment

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