Question

1. Cindy has $70 a month to spend on sport activities, and she can spend as much time as she likes playing golf and tennis. The price of an hour of golf is $20, and the price of an hour of tennis is $10. The table shows Cindy’s marginal utility from each sport.

Hours per month	Marginal Utility from Golf	Marginal Utility from Tennis
1	60	40
2	50	36
3	40	30
4	30	10
5	20	5
6	10	2
7	6	1

1. If Cindy spends all her money playing golf, how many hours of golf can she afford? What will be her total utility?
2. If Cindy spends all her money playing tennis, how many hours of tennis can she afford? What will be her total utility?
3. What are the marginal utilities per dollar from playing golf and tennis for the various hours per month played?
4. How many hours of golf and tennis should Cindy play to maximize her utility given her budget?
5. Explain why, if Cindy equalized the marginal utility per hour of golf and tennis, she would not maximize her utility?
6. Cindy’s tennis club raises its price of an hour of tennis from $10 to $15, other things remaining the same, how many hours does Cindy now spend playing golf and tennis that maximizes her utility? Are there any left over money?
7. Cindy loses her math tutoring job and the amount she has to spend on golf and tennis falls from $70 to $40 a month. With the price of an hour of golf at $20 and of tennis at $10, calculate the change in the hours she spends playing golf. For Cindy, is golf and tennis a normal good or an inferior good?

Answer 1

Cindy's income = $70; price of golf per hour = $20; price of tennis per hour = $10

a. If Cindy spends all her money on golf, she can play 3.5 hours of golf. (70/ 20 = 3.5)

b. If Cindy spends all her money on tennis, she can play 7 hours of tennis. (70/ 10 = 7)

c. The marginal utililty/ $ of tennis and golf:

Hrs/ m	MUg	MUt	MUg/$	MUt/$
1	60	40	3	4
2	50	36	2.5	3.6
3	40	30	2	3
4	30	10	1.5	1
5	20	5	1	0.5
6	10	2	0.5	0.2
7	6	1	0.3	0.1

d. Cindy can play the following combinations:

1 hour of golf and 5 hous of tennis,
2 hours of golf and 3 hours of tennis, or
3 hours of golf and 1 hour of tennis.

But her uility will not be maximized in any of these combinationsf.

e. If Cindy equalized her MU per hour of golf and tennis, she would not maximize her utility. This would be a combiantion of 3 hours of golf and 1 hour of tennis (MU per hour of golf = MU per hoour of tennis = 40 -- from the table).
But her MU/$ would not be equalized. MUg/$ for 3 hours = 2, but MUt/$ for 1 hour = 4.

Thus her utility is not maximized.

On the other hand, if she wants to equalize her MU/$, that too is not possible. In this case, (i) Her budget would be underspent, or (ii) she does not have the budget to maximize her utility.

For example, it is possible for her to equalize her MU with 1 hour of golf and 3 hours of tennis (MUg/$ = MUt/$ = 3). But she would be spending $50 only (1*20 + 3*10 = 20+30 = 50). She would be still left with $20.

On the other hand, she can also equalize her MU with 5 hours of golf and 4 hours of tennis. But for this, she would need $140 (5*20 + 4*10 = 100+40 = 140). She does not have that budget.

So, Cindy cannot maximize her utility.

f. Cindy's income = $70; price of golf per hour = $20; price of tennis per hour = $15

Cindy can play 2 hours of golf and 2 hours of tennis. It will cost her $70 (2*20 + 2*15 = 40 + 30 = 7).
No money will be left. But her utility is not equalized either. She gets 0.1 MU/$ more from golf at this combination.

The table with MU/$:

Hrs/ m	Mug	Mut	Mug/$	Mut/$
1	60	40	3	2.67
2	50	36	2.5	2.4
3	40	30	2	2
4	30	10	1.5	0.67
5	20	5	1	0.33
6	10	2	0.5	0.13
7	6	1	0.3	0.07

g. Cindy's income = $40; price of golf per hour = $20; price of tennis per hour = $10

Now Cindy can buy 1 hour of golf and 2 hours of tennis. This is the only combination possible with her budget. But her MU/$ is not equalized.

For CIndy, golf and tennis are normal goods. Because her consumption decreases when her income decreases. This is the property of normal goods.