1 Intertemporal Choice There are N = 1000 countries in the world, and in each country there is a...

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1 Intertemporal Choice There are N = 1000 countries in the world, and in each country there is a representative consumer with Cobb-Douglas preferences that lives for two periods, 0 and 1. In country i (i = 1, . . . , N ), the representative consumer has (exogenous) income of Y i 0 in period 0, and Y i 1 in period 1. Consumer i discounts the future at rate ßi . In country i, the representative consumer solves: max Ci 0 ,Ci 1 {log(C i 0 ) + ßi log(C i 1 )} (1) subject to : C i 0 + C i 1 1 + r = Y i 0 + Y i 1 1 + r (2) Where C i 0 is consumption of country i in period 0, C i 1 is consumption of country i in period 1, and r is the interest rate. The maximization problem has solutions: C i 0 = 1 1 + ßi (Y i 0 + Y i 1 1 + r ) (3) C i 1 = ßi 1 + ßi [(1 + r)Y i 0 + Y i 1 ] (4) a) Write savings of country i (S i 0 = Y i 0 - C i 0 ) as a function of i, Y i 0 , Y i 1 and r. How do savings respond to the interest rate? How do they respond to income in each period? What is the intuition? Suppose that ßi = 0.9524 for any i, and that Y i 0 = Y i 1 = 10 for any i. Find the equilibrium interest rate in the world. Do the countries trade with each other? Explain. b) Suppose that ßi = 0.9524 but that the income levels have uniform distribution with bounds 0 and 20. Use sequences of random numbers to simulate the economy. You can do this using the numbers from problem set 2 that you got using the code generator.R. That code generates numbers between 0 and 1

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Problem Set 4, International Economics, NYU, Summer 2012 Gilberto Noronha Due 08/10/2012 1 Intertemporal Choice There are N = 1000 countries in the world, and in each country there is a rep- resentative consumer with Cobb-Douglas preferences that lives for two periods, 0 and 1. In country i (i = 1; : : : ;N ), the representative consumer has (exoge- nous) income of Y i 0 in period 0, and Y i 1 in period 1. Consumer i discounts the future at rate i. In country i, the representative consumer solves: max Ci0;Ci1 flog(Ci0) + ilog(Ci1)g (1) subject to : Ci0+ Ci1 1 + r = Y i 0 + Y i 1 1 + r (2) Where Ci0is consumption of country i in period 0, Ci1is consumption of country i in period 1, and r is the interest rate. The maximization problem has solutions: Ci0= 1 1 + i (Y i 0 + Y i 1 1 + r ) (3) Ci1= i 1 + i [(1 + r)Y i 0 + Y i 1 ] (4) a) Write savings of country i (Si0= Y i 0 ?? Ci0) as a function of i, Y i 0 , Y i 1 and r. How do savings respond to the interest rate? How do they respond to income in each period? What is the intuition? Suppose that i = 0:9524 for any i, and that Y i 0 = Y i 1 = 10 for any i. Find the equilibrium interest rate in the world. Do the countries trade with each other? Explain. b) Suppose that i = 0:9524 but that the income levels have uniform dis- tribution with bounds 0 and 20. Use sequences of random numbers to simulate the economy. You can do this using the numbers from problem set 2 that you got using the code generator.R. That code generates numbers between 0 and 1 1so you need to adapt your procedure (since you want numbers between 0 and 20). It should be easy but if you have trouble a Google search may solve your problem. Compute the equilibrium interest rate in the simulated economy. How does it compare to the one in a)? What is the intuition? c) Compute the current account balances of each country. Do they add up to zero? How many countries are net exporters? Do you think your results are reasonable? Explain. d) Now suppose that all...

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David · Accepted Answer

Answer to 4: 
a) [Suppose fixed exchange rate regime] 
Due to fiscal expansion, IS curve would shift rightward (IS1 to IS2) and due to 
monetary contraction, LM curve would shift leftward (LM1 to LM2). As a result, rate 
of interest increases (from r1 to r2) whereas the effect on output (Y) would be 
unclear (refer the figure1 below). Higher interest rate increase the foreign capital 
inflow, creates BP surplus and upward pressure on currency. In order to keep 
exchange rate fixed, central bank would start buying foreign currency from the 
market and thereby increasing money supply in the economy. As a result LM curve 
would now start shifts rightward (from LM2 to LM1), Y increases (from Y1 to Y2) 
and r decreases (from r2 to r*). [Refer figure1 below] 
Figure1:
(b) Foreign investors expect a depreciation of the domestic currency: If domestic 
currency depreciates, domestic exports become cheaper whereas imports become 
costly. So exports will increase whereas imports will fall, causing net exports to 
increase and thereby rightward shift in IS curve. The rightward shift in IS curve will 
cause domestic interest rate to increase.

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1 Intertemporal Choice There are N = 1000 countries in the world, and in each country there is a representative consumer with Cobb-Douglas preferences that lives for two periods, 0 and 1. In country i...

Answer To: 1 Intertemporal Choice There are N = 1000 countries in the world, and in each country there is a...

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