Mandy has an income of $800 in period 1 and will have an income of $500 in period 2.Her utility function is U(c₁, c₂)=c^0.80₁c^0.20₂, where c₁ is her consumption in period 1 and c₂ is her consumption in period 2.The interest rate is .25.If she unexpectedly won a lottery which pays its prize in period 2 so that her income in period 2 would be $1,000 and her income in period 1 would remain $800, then her consumption in period 1 would A)stay constant. B)double. C)increase by $320. D)increase by $400. E)increase by $320

Question

Quizplus · Accepted Answer

To determine the optimal consumption pattern, we use the Euler equation: MU1/MU2 = (1+r) where MU1 and MU2 are the marginal utilities of consumption in periods 1 and 2, and r is the interest rate. Taking the first partial derivative of the utility function with respect to c₁, we get: MU1 = 0.8/(c₁)^1.8 Taking the first partial derivative of the utility function with respect to c₂, we get: MU2 = 0.2/(c₂)^0.8 Substituting these expressions for MU1 and MU2 in the Euler equation and rearranging, we get: c₂ = 5c₁ This means that the optimal consumption pattern is to consume 5 times as much in period 2 as in period 1. Using the budget constraint, we can solve for the initial levels of consumption: 800 = c₁ + (1/1.25)c₂ 500 = (1+0.25/1.25)c₂ Solving for c₁ and c₂, we get: c₁ = 269.22 c₂ = 805.56 If Mandy wins the lottery, her budget constraint in period 2 becomes: 1000 = c₁ + (1+0.25/1.25)c₂ Solving for c₁, we get: c₁ = 429.63 This represents an increase in consumption of $160.41 in period 1 ($429.63 - $269.22).

Mandy Has an Income of $800 in Period 1 and Will