Question

Problem Set 5 Consumer Demand -- Utility Analysis

1. Assume that the table below shows the marginal utilities that a consumer derives from food and clothing respectively.

Quantity Food MU FOOD   Quantity Clothing        MU CLOTHING  

1                            56                                   1                                    32

                 2                            48                                   2                                    28

                 3                            32                                   3                                     24

                 4                            24                                   4                                     20

                 5                            20                                   5                                     12

                 6                            16                                   6                                     10

                 7                            12                                   7                                       8

You are told that food costs $8 per unit and clothing costs $4 per unit.

a. If the consumer had $52 of income, how much food and clothing should he buy to maximize his satisfaction?

b. What if he only had $28?

Answer 1

For maximizing utility we want to stay on a condition that (MU of food/ price of food) = (MU of cloth/price of cloth)

So MU food/8 = MU cloth /4

i.e.

MU food/ MU cloth = 2/1

Means marginal utility of food must be double of marginal utility of cloth

for that combination we have 4 combination as

1) (2 food and 3 cloth) which costs 2*8+3*4 = 28

2) (4 food and 5 cloth) which costs 4*8+ 5*4 = 52

3) (5 food and 6 cloth) which costs 5*8+ 6*4 = 64

4) (6 food and 7 cloth) which costs 6*8+ 7*4 = 76

So when our income is 52 dollar then we choose combination 2nd of 4 food and 5 cloths in order to use our imcome and maximize our utility.

When our income is 28 then we choose 1st combination of 2 food and 3 cloth .

(Combination 3 and 4 are out of budget)