Evan is an avid football and baseball fan but has decided he needs to limit his

Question

Evan is an avid football and baseball fan but has decided he needs to limit his time spent at games and the money he spends on tickets. To this end, he decides to limit the time he spends on attending games to 24 hours per month and limit his spending on tickets to $120 per month. Suppose the time Evan spends per baseball game is 4 hours and the time spent per football game is 5 hours. Suppose that baseball tickets cost $10 per game and football tickets cost $40 per game.

Illustrate both constraints on the coordinate system below. Be as mathematically accurate as possible. Shade the feasible consumption set.

a.         If Evan exhausts all of his allotted time per month attending games as well as his monthly budget, how many football and baseball games would he attend (fractional answers are mathematically possible here).

b.         Illustrate on the above graph a utility-maximizing choice where Evan would be using all of his budget but not all of his time allotment.

Explanation / Answer

Total time to be spent on games = 24 hrs/month

Total spending on tickets = 120$/month

The two constraints for Evan are:

Time constraint

4B + 5F 24

Spending constraint

10B + 40F 120

Hours spent in Baseball

6B, 0F

1B, 4F

0B, 4.8F

Hours spent in Football

Hours spent in Baseball

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