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

Question 1

Assume that unemployment, u, is related to inflation, , according to the following Phillips curve:

u = u ( ^e ) ,

where u is the natural rate of unemployment and e is the expected rate of inflation. Assume

rational expectations and that t

Question 1 Consider a household living for two periods, t = 1,2. Let c and y 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) and C2 = (1 + r)s + yz. (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(c) = Inc. 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 c and c2 and interpret your results