 # D now let the world interest rate be 5 the coin flip

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(d) Now, let the world interest rate be 5%. The coin flip has determined that the home country hasthe low output level in period 0. People in each country can achieve constant consumption usingborrowing and lending. Work out how much is borrowed/lent and repaid in each period, and solvefor the consumption levels for each country over time. Explain why your answer here differs fromthe answer with the zero interest rate. Hint: Consider the PV of each country’s output stream.
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Let’s see what is going on with the foreign country. Foreign is lending out the amount B inperiod 1 and getting back (1+r)B in period 2. Foreign’s consumption in periods 1 and 2 are:C*1= 200-48.78 = 151.22C*2= 100 + (1.05*B) = 151.22Why is the level of consumption higher in the foreign country? The foreign country has the”high” level of output in period 0 and the PV of output is higher in the foreign country. Unlessthe question were reworded and explicitly asked you to compute the PV of output for eachcountry you would not have to do that. It is clear from inspection that the PV is higher forthe foreign country.If you did want to compute the PV of output in each country, you would proceed as follows.The PV of output for the home country can be more easily calculated by separating the lowoutput periods from the high output periods.The low output periods form an infinite sumthat are discounted back two periods at a time using the discount factor (1+r)ˆ2.A similarcalculation is done on the high output periods. Then the home PV of output isPV= 200 + 200/(1.05)2+ 200/(1.05)4...+ 100/(1.05) + 100/(1.05)3+ 100/(1.05)5+...= 200/(1-(1.05)2) + 100/((1.05)(1-(1.05)2))= 200 + 200/0.1025 + 100/((1.05)*(0.1025))= 1075.61 + 1,858.38= 2933.99(1)The PV of output for the foreign country is computed similarly:PVforeign= 100 + 100/(1.05)2+ 100/(1.05)4...+ 200/(1.05) + 200/(1.05)3+ 200/(1.05)5+...= 100 + 100/((1.05)2) + 100/()(1.05)2)2...+ (1/1.05)*[200 + 200/(1.05)2+ 200/((1.05)2)2+...= 100 + 100/((1.05)2-1) + 200/((1.05)((1.05)2)-1)= 100 + 100/0.1025 + 200/((1.05)*(0.1025))= 200 + 1951.21 + 929.15= 3080.37(2)Check: PV of world output = 300 + 300/0.05 = 6000.

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Term
Spring
Professor
Srdjan Divac
Tags
Foreign exchange market, United States dollar
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