Seminar 3: Microfoundations, the AS-AD model and inflation

Question 1

Consider a household living for two periods, t = 1,2. Let ct and yt denote consumption and income in period t. s denotes saving in period 1, r is the real interest rate and ? the weight the household places on future utility. The following must be true about the household's consump- tion in the two periods:

c1 = y1 ? s (2)

c2 = (1+r)s+y2. (3)

1. Derive the household's intertemporal budget constraint.
2. Assume that the preferences of the household can be represented by a log utility function so that u(ct) = lnct. Formulate the household's maximisation problem and derive the Euler equation.
3. Suppose that the real interest rate increases. How will this affect the household's con- sumption decision?
4. Suppose that ? = 1 and r = 0. Solve for c1 and c2 and interpret your results.

Seminar 3: Microfoundations, the AS-AD model and inflation Question 1 Consider a household living for two periods, t = 1,2. Let ct and y denote consumption and income in period t. s denotes saving in period 1, r is the real interest rate and B the weight the household places on future utility. The following must be true about the household's consumption in the two periods: C1 = y1 - s (2) C2 = (1+r)s+y2. (3) a. Derive the household's intertemporal budget constraint. b. Assume that the preferences of the household can be represented by a log utility function so that u(ct) = Inct. Formulate the household's maximisation problem and derive the Euler equation. c. Suppose that the real interest rate increases. How will this affect the household's con- sumption decision? d. Suppose that B = 1 and r = 0. Solve for c1 and c2 and interpret your results