Ryan is choosing between three different types of golf balls. Each has a differe

Question

Ryan is choosing between three different types of golf balls. Each has a different price tag, but they also each have a different effect on his game. The Titleist golf balls have a constant Marginal Utility of 5, the Nike golf balls have a constant Marginal Utility of 7, and the Srixion a constant Marginal Utility of 4. 2. Write down a utility function that represents these preferences for golf balls. a. Ryan heads to GolfTec to buy some new golf balls, and they are selling each one individually. How many will he buy of each if the price of Titleist are $2 each, the price of Nike are $3 each, and the price of the Srixion are $2.502 He has a budget of $24 for golf balls. What is his utility? b. The price of Srixion goes on sale for $0.50. What happens to his consumption of each type of golf ball? What is his new utility? Is this change in consumption a result of an income effect, a substitution effect, or both? Explain? c.

Explanation / Answer

Answer 2

a) As Narginal Utility of Ryan is constant of all balls i.e. They must be a perfect substitutes of each other

Let T represents Titliest Golf Balls

N represents Nike Golf Balls

S represents Srixion golf Balls

Hence Utility Function is given by:

U(N,S,T) = 5T + 7T + 4S

b) Suppose Price of Titliest Ball is 2 i.e. PT = 2

Suppose Price of Nike Ball is 3 i.e. PN = 3

Suppose Price pf Srixion Ball is 2.5 i.e. PS = 2.5

Total Income =24

As goods ae perfect substtutes and MU is constant. Then She will purchase that ball whose MU/P is greatest

For Nike Balls MUN/PN = 7/3 = 2.33

For Titliest Balls MUT/PT = 5/2 = 2.5

For Srixion Balls MUS/PS = 4/2.5 = 1.6

As MU/P is largest fpr titliest balls Thenb he will buy Titliest balls only. Hence 2T = 24 => T = 12

Hence he will buy 12 units of Titliest balls , 0 units of Nike Balls and 0 units of srixion balls

Hence Her Utility will be

U = 5T + 7T + 4S = 5*12 + 7*0 + 4*0 = 60

Hence U = 60

c) Now Suppose Price of srixion Balls is 0.5, Henc MUS/P = 4/0.5 = 8. Hence Now MU/P is greatest for Srixion Balls Hence He will buy Srixion Balls Only.

So, 0.5S = 24 = > S = 48

Hence He will consume 0 units of Titliest ball, 0 unit of Nike ball and 48 unit of Srixion Balls and hence her Utility will be = 4*48 = 192

This change in consumption is a substitution effect only Because Goods are Perfect substitutes of each other and whenever goods are perfect substitutes then there is only Substitution effect and No income effect    

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