Question

Marisol has income and consumes for two periods. Period 1 income is A1 and period 2 income is A2. We normalize the price of period 1 consumption to 1. There is inflation. Marisol is trying to figure out how much to save or borrow.

a) Write the budget constraint with period 1 and 2 prices and the nominal interest rate.

b) If the inflation rate is i, what is the relationship between prices in periods 1 and 2?

c) Rewrite the budget constraint the the real interest rate, the inflation rate and the period 1 price.

Answer 1

(a) Suppose the nominal rate of interest is r. The budget constraint of first period will be or , as price is 1 in that period, for c1 be the consumption and s be the savings/borrowings. The second period budget constraint is . As or , we have or or , which is the lifetime budget constraint.

(b) If inflation is i, then prices in period 1 and 2 would have the relation as , and as p1 was one, hence . In that case, the budget constraint would be written as .

(c) Taking the real interest rate as n, the nominal interest rate would be as r=n+i (supposing the inflation is equal to the expected inflation). Hence, the budget constraint would be .

Note: When solving for the lifetime utility max subjected to this constraint, we would assume that n,i,r,A1 and A2 are given, and the solution would only be of c1 and c2, and thereby for s.