Harvey Habit has a utility function U(c₁, c₂)= min{c₁, c₂}, where c₁ and c₂ are his consumption in periods 1 and 2 respectively.Harvey earns $147 in period 1 and he will earn $63 in period 2.Harvey can borrow or lend at an interest rate of 10%.There is no inflation. A)Harvey will save $102. B)Harvey will borrow $40. C)Harvey will neither borrow nor lend. D)Harvey will save $40. E)None of the above.

Question

Quizplus · Accepted Answer

To maximize his utility, Harvey needs to allocate his consumption between the two periods in a way that maximizes his overall satisfaction. We can solve for his optimal consumption using the following equation: MRS = (MU1/MU2) = (1+r) MU1 = U1, MU2 = U2 Taking the partial derivative of U with respect to c1 and c2, we can derive the following conditions for Harvey's optimal consumption: MU1/MU2 = (1+r) MU1/P1 = MU2/P2 Plugging in the values for U, P1, P2, and r, we get: (c₁/2) / (c₂/2) = 1.1 (c₁/2) / 147 = (c₂/2) / 63 Solving for c1 and c2, we get: c₁ = 90 c₂ = 210 Harvey's total consumption over the two periods will be 300. Given that he earns $147 in period 1 and will earn $63 in period 2, he will have a total income of $210. Therefore, he will save $40 to finance his consumption in period 2, as his optimal consumption for period 1 exceeds his income in that period. Option D is the correct answer.

Harvey Habit Has a Utility Function U(c1, C2)= Min{c1, C2}

Harvey Habit Has a Utility Function U(c₁, C₂)= Min{c₁, C₂}