Vanessa's utility function is U(c¹, c²)= c^1/2₁ + 0.83c^1/2₂, where c₁ is her consumption in period 1 and c₂ is her consumption in period 2.In period 2, her income is 4 times as large as her income in period 1.At what interest rate will she choose to consume the same amount in period 2 as in period 1? (Choose the closest answer.) A)0.10 B)0 C)0.30 D)0.80 E)0.20

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Quizplus · Accepted Answer

Vanessa's utility function can be rewritten as: U(c¹, c²) = F1F1F1S1 + F1F1F10 + 0.83*[c^1/2*(1+r) + c^1/2]*4/(1+r) where (1+r) is the interest rate. Her optimization problem is to maximize U subject to the budget constraint: c¹*(1+r) + c² = y¹*(1+r) + y², where y¹ and y² are her incomes in period 1 and period 2 respectively. Taking the partial derivative of U with respect to c², we get: 0.83*(4/(1+r)) = 1 Solving for (1+r), we get: (1+r) = 4.82 Therefore, the closest answer is 0.20, choice (E).

Vanessa's Utility Function Is U(c1, C2)= C1/21 + 0

Vanessa's Utility Function Is U(c¹, C²)= C^1/2₁ + 0