Reference no: EM133295053
Assignment:
Consider the following utility function: u(C) = C1-θ / 1-θ , θ > 0
(a) Show that it satisfies the Inada conditions.
(b) Write down the lifetime utility function assuming discount factor β and an infinitely lived consumer.
Assume now that the consumer receives exogenous labour income of Yt in each of the infinite periods for which she is alive. Assume that the consumer can save, in order to smooth consumption intertemporally. Assume assets follow a law of motion as follows: At+1 = (1 + r)(At - Ct + Yt), where r is the interest rate.
(c) Derive the intertemporal budget constraint, by substituting the law of motion for At+1 forwards in time.
(d) Formulate the constrained optimisation problem of the consumer, using the Lagrangean method. for k=0 and k=1.
(e) Derive the Euler equation.
(f) Find the ratio Ct+1/Ct . How does the size of the parameter θ influence the intertemporal substitution of consumption?