Question

Jimmy has the following utility function for hot dogs: U(H) =10H-H^2. (a)What is the equation for Jimmy’s Marginal Utility of Hot Dogs? (Show your work.) (b)Jimmy’s total utility for hot dogs eventually decreases as the number of hot dogs increases. How can we tell this using your answer in part (a)? (c)At what number of hot dogs does Jimmy’s total utility begin to decrease? (Show your work.) Explain how we can tell. (d)Which of our Three Rules for Preferences does this utility function violate? Briefly explain.

Answer 1

A) MUH = dU/dH = 10-2H

B) Since MU has a negative relationship with H, it means as H increases, MU decreases, implying falling TU (since TU is nothing but the sum of MU)

C) Calculate MU and equate it to 0

That is, 10-2H = 0

H = 5

This means at H = 5, TU is maximum and it starts to fall post that

D) The rule: More is better is violated here

This is because one can clearly see, more of H is decreasing TU and is thus not preferred by the consumer.