Question

Utility Problem Set

1. Suppose that the price of good X is $5 per unit and the price of good Y is $2 per unit. In addition, suppose that your income is $25

If you spend all your money on good X, how many units can you buy?

2. The table below shows total utility for two products. Suppose that the price for product X is $5 and the price for product B is $2.

Number of product X	Total Utility for X	Number of product Y	Total Utility for Y
0	0	0	0
1	300	1	100
2	450	2	180
3	500	3	250
4	520	4	300
5	530	5	320

Given this data, complete the table below:

Quantity of X	Marginal Utility for X	Marginal Utility for X per dollar	Quantity of Y	Marginal Utility for Y	Marginal Utility for Y per dollar
0			0
1			1
2			2
3			3
4			4
5			5

Use the information above to answer questions 3 and 4:

The table below shows total utility for two products. Suppose that the price for product X is $5 and the price for product Y is $2.

3. Suppose that a person has $25.

How many units of each good should she buy to maximize her happiness given her budget constraint? Why?

4. Suppose income falls to $18. How many units of each good should she buy to maximize her happiness given her budget constraint? Why?

Answer 1

1. If I spend all my money in purchasing good X, so with the given amount of income that I have i.e $25, and the given price of X, i.e $5 per unit, I will be able to buy a maximum of 5 units of good X. As 5 units * $5 = $25, which is the available income.

2. Marginal unit is the change in total utility due to increase in units of consumption of a good. It can be calculated as (TUn - TUn-1)

Units of X	MU x	MU x per dollar	Units of Y	MU y	MU y per dollar
0	0	0	0	0	0
1	300	300/5 = 60	1	100	100/2 = 50
2	150	150/5 = 30	2	80	80/2 = 40
3	50	50/5 = 10	3	70	70/2 = 35
4	20	20/5 = 4	4	50	50/2 = 25
5	10	10/5 = 2	5	20	20/2 = 10

3. According to the law of equi marginal utility, a consumer tends to distribute his/ her consumption in such a way that the marginal utility obtained per dollar, for all the goods are equal. In the question above, we see that the consumer gets equal MU per dollar when he/ she purchases 3 units of X and 5 units of Y. The total cost of purchasing 3 units of X will be $15 and the total cost of purchasing 5 units of good Y will be $10. The total combined cost for both the goods will be $25. Given he/she has $25 income, this combination of good X and Y is within his/her budget limit. Hence he/she will tend to purchase 3 units of X and 5 units of Y, to attain maximum satisfaction.

4. At Budget = $18, he/ she will not be able to afford the combination of good X and Y which provided him/ her equal level of satisfaction per unit of dollar. So he/ she can either use the entire $18 in purchasing good X or purchasing good Y. So he can either purchase 9 units of Y, as purchasing of 9 units of Y at $2 per unit will be equal to his//her income, i.e $18 or he /she can purchase, 3.6 units of X, as 3.6 units of X at the rate of $5 per unit will be exactly equal to his/ her budget of $18.