Question: Consider the following utility function: u(C) = C 1 / 1 , > 0 (a) Show that it satisfies the Inada conditions. (b) Write down

Consider the following utility function: u(C) = C¹ / 1 , > 0

(a) Show that it satisfies the Inada conditions.

(b) Write down the lifetime utility function assuming discount factor and an infinitely lived consumer.

Assume now that the consumer receives exogenous labour income of Y_t 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: A_t+1 = (1 + r)(A_t C_t + Y_t), where r is the interest rate.

(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 C_t+1/C_t. How does the size of the parameter influence the intertemporal substitution of consumption?

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