Question

Consider an individual who only cares about the quantity of goods she consumes this year and the quantity of the same goods she consumes next year. Let C1 be the quantity consumed this year and C2 be the quantity consumed next year. Her preferences can be represented by the following utility function: ? = 2(√?1 + √?2) Suppose she earns $2,000 this year and nothing next year. Let the price index this year be 2 and the price index next year be 4. The interest rate is R. What is her total quantity consumed this year as a function of R? A. 1000 / (3+R) B. 3000 / (1+R) C. 1000(1+R) / (3+R) D. 2000 / (3+R) E. None of the above

Answer 1

Budget constraint is given by

2 x C1 + 4 x C2 / (1 + R) = 2000 + 0 / (1 + R)

2C1 + 4C2/(1 + R) = 2000

The slope of the budget constraint is -2 / 4/(1 + R) or -0.5(1 + R)

From utility function MRS = -MUC1/MUC2 = -2*0.5C1^-0.5/2*0.5C2^-0.5 or -C2^0.5/C1^0.5

At the optimum choice, MRS = slope of budget line

-C2^0.5/C1^0.5 = -0.5(1 + R)

C2/C1 = 0.25(1 + R)^2

C2 = 0.25C1(1 + R)^2

Use this in the budget equation

2C1 + 4*(0.25C1(1 + R)^2)/(1 + R) = 2000

2C1 + C1(1 + R) = 2000

C1(2 + 1 + R) = 2000

C1* = 2000/(3 + R)

Correct choice is D. 2000 / (3+R)