Determining the lifetime utility function

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Reference no: EM133295053

Assignment:

Consider the following utility function: u(C) = C^1-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 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 θ influence the intertemporal substitution of consumption?

Reference no: EM133295053

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