Question

Suppose an economy with two individuals: Mrs. A and Mr. B. They each seek to smooth their consumption over two periods: the present (t -1) and the future (t -2).They each have an income of $100 per period and no initial wealth.The present consumer price, c1, is p1=1, while the nominal interest rate, i, and the rate of inflation , are both 5%.

a) Write down the intertemporal budget constraint of these two individuals and represent it graphically, taking care to specify the staffing point, the slope, as well as the intersections with the axes.

b) Mrs A's intertemporal preferences are such that her marginal substitution rate (MRS) between present and future consumption is c2/2c1, while Mr B's MRS is 2c2/c1. Find their optimal consumption choices. Are they lenders or borrowers at this interest rate?

c) Suppose that in this economy, there is no way to save at a rate i without finding someone to lend to (i.e. a borrower). Based on your answer in b), describe what should happen for the credit market to balance. Out of balance, would it be possible for both Mrs A and Mr B to lend (save)? Or that they both want to borrow? Detail your reasoning.