Question

1. Joseph Jorgensen was an outstanding collegiate ping-pong player. He has a true love for the game. After injuring his wrist in a tragic carpal tunnel syndrome incident, he no long has the physical skills to excel at the collegiate level and just plays recreationally. Suppose that Joseph's utility function is U = F +10N - N2, where Fis food and N is the amount of ping-pong Joseph plays. Suppose further that the price of food is P and the price of ping-pong is P. Joseph's income is I. (30 points)

a) Solve for the optimal amount of food and ping-pong. (Assume that prices and income are such that some of both goods are consumed.)

b) What is the marginal utility of ping-pong (at the optimal bundle)? Does Joseph enjoy ping-pong on the margin?

c) Now suppose that Joseph undergoes surgery to get a prosthetic wrist. He once again achieves a high level of performance and is able to secure a contract playing ping-pong professionally in Albania. Is the price of ping-pong for Joseph positive or negative? Explain.

d) At the new equilibrium level of ping-pong playing, does Joseph enjoy ping-pong on the margin? Explain intuitively?

Answer 1

1 Jesek's utitiry dnction s Aus HOn C f+1o N. N - Food Naw ean fo Joseth N - Bundger Oime Pe F PN N+ Profit monimisastion JIF,NJT TN,F]-NfF) fo.C dipperemciasing 下= (F +io N-N2)+Ala 2 N +入(エ-Pu-N-Pe F) 10-2N-APN= エーPu. N-BF F O Naw, Seluing ea"

from e4'n 10-1 PM N- Now, from e PrM.Nt PA f PN XI 10-PHIP+ PE F PN (10 PE-A 2Pp F = 1[I F

MUM 10-N MUN10-2 10 Pr- PN far Optienal Jesal On Jaseth emjay MUNYO 0-2NYO N 5 Negative Josebh will entoy peite Price m crsease lis tncome, Now lauld get 9eulard Lontract wi Tncease iA mcome Jevel dyes, Ad ned equiibrium Jerel Piny-Pag iayingaseth win at Buok -bhrd Repwa

Pofessionas ing a Because he daving Contoat, Inich mears he fing-Pong lae wauLkPay the ueilidy he uousd get mose at