51. If your household income is $63.785 consummers, the price of a pair of tenni

Question

51. If your household income is $63.785 consummers, the price of a pair of tennis shoes Reebok is $3.319, the price of a Nike training shirt is $872 anc the utility function of a consumer is represented by where A=11 ,619, = 0.36 y = 0.4, a) Calculate the maximum number of t-shirts you can buy the consumer if you do not purchase any tennis courts. b) Calculate the maximum number of pairs of tennis that you can purchase the consumer if you don't buy any shirt. c) Calculates the Marginal Rate of Substitution of market when the pairs of tennis are represented in the "y" axis and the t-shirts are identified in the x d) Calculates the number of tennis you should consume the home to axis maximize its usefulness c) Calculates the number of t-shirts you should consume the home to maximize its usefulness 124%

Explanation / Answer

(a) The budget line is 3.319R+8.72N = 63.785

If tennis shoes = 0 this imply R = 0, put R = 0 in the budeget constraint:

8.72N = 63.785

N = 63.785/8.72

N = 7.315

(b)If doesn’t buy the T-shirt then N = 0, putting N = 0 in the bUdget Constraint:

3.319R = 63.785

R = 19.218

(c)MRS = Mux/MUy

Mux = dU/dN

Mux = AN^-1R^

MUx = 11619*0.36N^-0.64R^0.4

MUx = 4182.84N^-0.64R^0.4

MUy = dU/dR

= AN^R^-1

MUy = 11619*0.4*N^0.36R^-0.6

MUy = 4647.6 N^0.36R^-0.6

MRS= 9*(R/N)

(d)

Consumes such that MRS = Px/Py

9(R/N) = 8.72/3.319

N = 3.426R

From Budget constraint:

3.319*R+8.72(3.426R)= 63.785*8.

R = 1.922

(E) N = 3.426*R

N = 6.583

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