International Macro & Policy

Problem Set $2$

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Consider a two$-$period endowment economy. There are two countries, France and Morocco.

Consumers in France have log preferences:

ln C$1+$ ln C$2$

where C$1$ and C$2$ refer to French consumption in period $1$ and in period $2.($The same expression

holds for Morocco, just write C$$

$1$ and C$$

$2$ instead.$)$ Endowments in France are Y$1$ and Y$2,$ whereas

endowments in Morocco are Y $$

$1$ and Y $$

$2.$

$1.$ Find expressions of C$1,$ C$2$ and B$2$ in France. All these expressions should be functions of

Y$1,$ Y$2$ and r$.$ Hint: this is IDENTICAL to the problem we solved in class.

$2.$ Find expressions of C$$

$1,$ C$$

$2$ and B$$

$2$ in Morocco. All these expressions should be functions

of Y $$

$1,$ Y $$

$2$ and r$.$ Hint: this is identical to $1,$ except that all variables have an asterisk.

The expressions in $1.$ and $2.$ above will be very useful for the subsequent questions. Now assume

that Y$1=10,$ Y$2=11,$ Y $$

$1=8$ and Y $$

$2=10.$

$3.$ Compute the autarky $($closed economy$)$ interest in France, rA$,$ and the autarky $($closed

economy$)$ interest rate in Morocco, rA$.$ Give numbers. Hint: recall that under autarky,

no one borrows and no one lends, so that C$1=$ Y$1$ and C$$

$1=$ Y $$

$1.$ This is the same as

assuming that B$2=0$ and B$$

$2=0.$

$4.$ Compute the utility level in both countries under autarky. Give numbers. Hint: substitute

C$1$ and C$2$ into the log utility function. Do the same with C$$

$1$ and C$$

$2.$

$5.$ Compute the free trade interest rate. Give a number. Hint: since in free trade the borrowing

of one country should be equal to the lending of the other, you can determine the free trade

interest rate rF T by imposing the condition B$2=$B$$

$2$ and solving out for the interest rate.

$6.$ Determine the trade balances in period $1$ and period $2$ in both France and Morocco. Give

numbers. Hint: the trade balance in France is Y$1$ C$1$ in period $1$ and Y$2$ C$2$ in period $2.$

$7.$ Compute the utility level in both countries under free trade, and compare them to the

autarky utility levels. Hint: follow the same procedure as in question $4.$

$1$