Question

The following table shows​ Madison's utility from consuming popcorn and Coke. Suppose that Madison has income of ​$10.50​,

the price of popcorn is ​$3.00, and the price of Coke is ​$2.25.

If Madison wants to maximize her​ utility, how much popcorn and Coke should she​ buy?

	Popcorn	Coke
Quantity	Marginal Utility	Marginal Utility
1	192	144
2	144	108
3	96	72
4	48	36
5	24	18
6	12	9

Madison should buy (blank) boxes of popcorn and (blank) cans of Coke. ​(Enter your responses as​ integers.)

Enter your answer in each of the answer boxes.

Answer 1

There are two goods, Popcorn and Coke

Price of Popcorn = $3

Price of Coke = $2.25

From the given table of MU of popcorn and coke, calculate MU per dollar.

MU per dollar = MU ÷ Price

Quantity	Popcorn	Coke
Marginal Utility	MU/Price of Popcorn	Marginal Utility	MU/Price of Coke
1	192	64	144	64
2	144	48	108	48
3	96	32	72	32
4	48	16	36	16
5	24	8	18	8
6	12	4	9	4

The equilibrium condition is

(MU of Popcorn ÷ Price of Popcorn) = (MU of Coke ÷ Price of Coke)

However, the equilibrium will be at that combination where the total expenditure equals to the income of the consumer.

Income of the consumer given is $10.50

In the table at all the combinations the (MU of Popcorn ÷ Price of Popcorn) = (MU of Coke ÷ Price of Coke)

The expenditure at each combination will be

Combination	Popcorn	Price	Expenditure	Coke	Price	Expenditure	Total Expenditure
A	1	3	3	1	2.25	2.25	5.25
B	2	3	6	2	2.25	4.5	10.5
C	3	3	9	3	2.25	6.75	15.75
D	4	3	12	4	2.25	9	21
E	5	3	15	5	2.25	11.25	26.25
F	6	3	18	6	2.25	13.5	31.5

It can be seen at the combination B, the total expenditure is equal to the given income of 10.50

Therefore, Madison should buy 2 boxes of popcorn and 2 cans of Coke.