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

Keeva Mahoney · Accepted Answer

Final Answer : C, Explanation :  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 c 1 , we get:MU1 = 0.8/(c 1 )^1.8Taking the first partial derivative of the utility function with respect to c 2 , we get:MU2 = 0.2/(c 2 )^0.8Substituting these expressions for MU1 and MU2 in the Euler equation and rearranging, we get:c 2  = 5c 1 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 = c 1  + (1/1.25)c 2 500 = (1+0.25/1.25)c 2 Solving for c 1  and c 2 , we get:c 1  = 269.22c 2  = 805.56If Mandy wins the lottery, her budget constraint in period 2 becomes:1000 = c 1  + (1+0.25/1.25)c 2 Solving for c 1 , we get:c 1  = 429.63This represents an increase in consumption of $160.41 in period 1 ($429.63 - $269.22).

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