Question

1. Jane enjoys waterskiing and scuba diving. She obtains the following utility from each of these sports:

Half-hours     Total Utility                                   Total Utility

     per month    Waterskiing                                   Scuba diving

            1                  60                                                     20

            2                100                                                     38

            3                150                                                     53

            4                180                                                     64   

            5                200                                                     70

            6                206                                                     75

a. Calculate the marginal utility Jane receives from waterskiing and scuba diving. Are the marginal utilities you have calculated consistent with what economic theory would predict. Explain.

b. Jane has $140 to spend. Equipment for windsurfing rents for $40 a half hour while scuba diving equipment rents for $20 per half hour. How long will Jane choose to waterski and scuba dive? Make it clear how you arrived at your answer, showing your work. Use economic reasoning in finding your answer, not trial and error.

Answer 1

Half Hour	Total Utility Uw	Marginal Utility (change in total utility/change in number of units consumed)
Per Month	Waterskiing
1	60	N.A
2	100	40
3	150	50
4	180	30
5	200	20
6	206	6

Marginal Utility for waterskiing should continue diminishing, however it increases at half hour per month=3 therefore it is not totally consistent with diminishing marginal utility, wher Marginal utility decreases with each additional unit

Half Hour	Total Utility (Us)	Marginal Utility (change in total utility/change in number of units consumed)
Per Month	Scuba Diving
1	20	N.A
2	38	18
3	53	15
4	64	11
5	70	6
6	75	5

The law of Diminishing Marginal utility holds here since Marginal utility decreases with each additional unit of half hour added.

b) Jane has $140 to spend

Rental cost of water ski equipment= $40 per half hour

Rental cost of scuba diving equipment= $20 per half hour

Number of half hours of Water ski denoted by: W

Number of half hours of Scuba Diving Denoted by: S

The budget constraint therefore looks as follows

→ 40W+20S= $140

If Jane spends her entire income and time on Water skiing then:

S=0

→ 40W=140

→ W=140/40

→ W=3.5 half hours

If Jane spends her entire income and time on Scuba diving then:

W=0

→ 20S=140

→ S=140/20

→ S= 7 half hours.

Now since, we only have utility values and not a proper utility function it is best if we compare both utilities based on assumptions from the table

Since at W=3.5 hours Jane’s utility would be between 150-180, which would give her a higher utility than what she would receive if she spends all her time in scuba diving since because of diminishing marginal utility the utility she will receive after 6 half hours=75 would not be significantly high (since MU must be less than 5 for scuba diving at 7 half hours) and certainly not high enough to be bigger than her utility at W=3.5 hours which will be between 150-180.

Therefore Jan will choose to spend 3.5 half hours water skiing