ECON6002 Tutorial 5 (RBC Model)
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ECON6002
Tutorial 5 (RBC Model)
1. Consider an RBC model without capital such that the production function is Yt = AtLt and the resource constraint is Yt = Ct + Gt . Assume firms are profit maximizing and face a competitive labour market. Assume households maximize expected “lifetime” utility with discount rate ρ and felicity ut = lnct + bln(1 − yt), b > 0.
(a) Write out the analytical expressions for the equilibrium wage in the labour market and the first-order condition for yt .
(b) Solve for the steady state values of wages, output, and consumption given = 0.2, = 1, = 0, and b = 4.
2. Consider the special case of the RBC model of Section 5.5 of the Romer textbook. Suppose, however, that the instantaneous utility function is given by
(1 − yt)1 −y
(a) Write out the analytical expressions for the equilibrium wage in the labour market, the Euler equation, and the first-order condition for yt .
(b) With this change in the model, is the saving rate still constant? If yes, solve for . If not, explain why.
(c) Is leisure per person (1 − y) still constant? If yes, solve for it. If not, explain why.
2022-11-09