Question

Question 1. (Consumption-Saving Problem): Suppose that a consumer lives for two periods. The utility function of the consumer is given by 1-1 1-1 with μ > 0

Answer 1

Suppose that a consumer lives for two periods. The utility function of the consumer is given by v(c_1, c_2) = c_1^1 - mu/1 - mu + c_2^1 - mu/1 - mu with mu > 0 where c_1 and c_2 are consumption. Given that: The utility function of the consumer is given by v(c_1, c_2) = c_1^1 - mu/1 - mu + c_2^1 - mu/1 - mu with mu > 0 where c_1 and c_2 are consumption. 0 < a < 1 in period 2. To calculate The inter - temporal budget constraint. The consumer optimization problem. The first order condition. Optimal capital investment, k. Now, The intertemporal budget constraint. C_1 = y - s (1) C_2 = RS (2) adding (1) and (2) c_1 + c_2 = y - s + Rs The consumptions in time 2 is \r\n divide by R to get discounted value. therefore c_1 + c_2/R = y - s + Rs/R c_1 + C_2/R = y - Rs + Rs c_1 + c_2/R = y. C_1 and C_2 are consumptions in time (1)