International Macro & Policy Problem Set $2$ Please upload a single PDF file of your problem set onto Canvas. Please don't send your problem set by email, don't upload formats that are not PDF$,$ and don't upload multiple files. You will lose half of your grade if you don't follow these instructions. Thank you. Consider a two$-$period endowment economy. There are two countries, France and Morocco. Consumers in France have log preferences: In C$1+$ In 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 $1=10,$Y$2=11,$Y $*1=8$ and Y$*2=10\mathrm{.}3$ 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 t~C$1=$Y$1$~i 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