Question

The consumer’s income in period 1 is 40 and in period 2 is 60.

She maximises her utility, given by the following function: $\dpi{120} \small U=lnC1+0,6*lnC2$

A) Assume r=0. Calculate C1 and C2

B) Assume now that the consumer is liquidity constrained and r=0. Calculate C1 and C2. What happens to Her utility?

C) Calculate C1 and C2 if r=0,2. What happens to U and why?

Answer 1

The consumer�s income in period 1 = 40 in parallel 2 = 60 U = ln C_1 + 0.6 * ln C_2 (A) Assume r = 0, calculate C_1 and C_2 ? rightdoublearrow U(C_1, C_2) = ln (C_1) + 0.6 ln (C_2) m_1 = 40, m_2 = 60, r = 0 max_c_1, c_2 [U (C_1, C_2)] subject to budget constraint (1 + r) C_1 + C_2 = (1 + r) m_1 + m_2 (1 + 0) C_1 + C_2 = (1 + 0) 40 + 60 C_1 + C_2 = 40 + 60 C_1 + C_2 = 100 C_2 = 100 - C_1 optimisation problem max_c_1 [ln (C_1) + 0.6 * ln (100 - C_1)] optimal consumption Ratio of (P_1/P_2) = 1/1 + r which is equal to ratio of marginal utilities \r\n U(C_1, C_2) = ln (C_1) + 0.6 ln (C_2) M V_C_1 = dU/dC_1 = 1/C_1 MUC_2 = dU/dC_2 = 0.6/C_2