Question

A consumer purchases two goods, food (F) and clothing (C). Her utility function is given by U(F,C)=FC+F. The marginal utilities are MUF=C+1 and MUC=F. The price of food is PF, the price of clothing is PC, and the consumer’s income is W. Suppose W=10, PF=4, PC=6. What is the optimal bundle?

Group of answer choices

(F,C)=(1/3,1)

(F,C)=(2,1)

(F,C)=(2,1/3)

(F,C)=(1,3)

Answer 1

ANSWER : 3. (F,C) = (2, 1/3)

A consumer purchases two goods, food (F) and clothing (C). Her utility function is given by;

U(F,C)=FC+F

The marginal utilities;

MUF = C + 1

MUC=F

The price of food, P_F = 4
The price of clothing, P_C = 6

Consumer's income, W = 10

The marginal rate of substitution is;

MRS = MUF / MUC
MRS = C+1 / F

At optimal level;

MRS = P_F / P_C
C+1 / F = 4/6
C+1 / F = 2/3
3C + 3 = 2F
3C = 2F - 3
C = 2F/3 - 1

Putting this in budget constraint;

P_F F + P_C C = W
4F + 6C = 10
2F + 3C = 5
2F + 3(2F/3 - 1) = 5
2F + 2F - 3 = 5
4F = 8
F = 2

C = 2(2)/3 - 1
= 4/3 - 1
C = 1/3