Question

Richard is trying to decide what combination of gum and mints to buy. Gum costs half as much as mints. If no mints are purchased, he can buy 6 pieces of gum. If no gum is purchased, he can buy 3 mints. What is the total utility if Richard buys 2 mints and 4 pieces of gum?

Mints Utility Gum Utility

1 29 1 15

2   56 2 29

3   81 3 42

4 --- 4 54

5 --- 5 65

6 --- 6 75

Answer 1

Utility maximizing condition:

(i) Marginal Utility of Gum / Price of Gum = Marginal Utility of Mint / Price of Mint

(ii) He should spend all its income.

Marginal utility of 4 units of gum = Total utility of 4 gum - Total utility of 3 gum

= 54 - 42 = 12

Marginal utility of 2 units of Mint = Total utility of 2 mint - Total utility of 1 mint

= 56 - 29 = 27

Let Price of mint be 2P thus Price of Gum = P

=> Marginal Utility of Gum / Price of Gum when quantity of gum is 4 = 12/P

Marginal Utility of Mint / Price of Mint when quantity of Mint = 2 is 27/(2P)

Thus Marginal Utility of Mint / Price of Mint is almost equal to Marginal Utility of Gum / Price of Gum when quantity of gum = 4 and quantity of mint = 2. Also They he have spent all its resources. Thus, It is a profit maximizing combination.

Hence, Profit maximizing combination is 2 Mint and 4 piece of gum.

We can sew from above table that when he buys 2 mints, his utility = 56 and when he buys 4 Gum his utility = 54

Thus, Total Utility when he buys 2 Mint and 4 piece of Gum = 56 + 54 = 110