Question

Please show work.

Ms. Laura Mussel’s preferences between golf and tennis are represented by U(g, t) = gt, where g is the number of rounds of golf and t is the number of tennis matches she plays per week. She has $24 per week to spend on these sports. A round of golf and a tennis match each cost $4. She used to maximize her utility subject to this budget. She decided to limit the time she spends on these sports to 16 hours a week. A round of golf takes 4 hours. A tennis match takes 2 hours. As a result of this additional constraint on her choice,

a. she plays 1 less round of golf and 1 more tennis match each week.

b. she plays more golf and less tennis, but can’t say how much.

c. her choices and her utility are unchanged.

d. she plays 2 less rounds of golf and 3 more rounds of tennis per week.

e. There is too little information to tell about her choices.

Answer 1

She has $24 per week to spend on these sports. A round of golf and a tennis match each cost $4.

i.e. 4g + 4t = 24

g + t = 6

Since, utility is Cobb-Douglas, thus she will spend a fix amount of her income in each sport.

i.e. g = t = 3

Now if She decided to limit the time she spends on these sports to 16 hours a week. A round of golf takes 4 hours. A tennis match takes 2 hours.

i.e. 4g + 2t = 16

2g + t = 8

from above, g + t = 6

Solving these two equations, we get : g = 2, t = 4

So. she plays 1 less round of golf and 1 more tennis match each week.

Option a