In this exercise, assume the same set-up as in exercise 15.3 except that this time we will assume that hamburgers are a nor- mal good for all consumers.
A: As in exercise 15.3, we’ll consider the long run impact of a license fee for fast food restaurants on consumer surplus. In (a) and (b) of exercise 15.3, you should have concluded that the long run price increases as a result of the license fee.
(a) Consider your graph from part (c) of exercise 15.3. Does the area you indicated over- or under- estimate the amount consumers would have to be compensated (in cash) in order to accept the license fee?
(b) Does the area over- or under-estimate the amount consumers are willing to pay to avoid the license fee?
(c) How would your answers to (a) and (b) differ if hamburgers were instead an inferior good for all consumers?
(d) Do any of your conclusions depend on the assumption (made explicitly in exercise 15.3) that all firms are identical?
B: Suppose that tastes by consumers are characterized by the utility function u(x,y)=x0.25y0.75 and that each consumer had $100 budgeted for hamburgers x and other goods y .
(a) Calculate how many hamburgers each consumer consumes — and how much utility (as measured by this utility function) each consumer obtains — when the price of hamburgers is $5 (and the price of “other goods” is $1).
(b) Derive the expenditure function for a consumer with such tastes.
(c) Suppose that the license fee causes the price to increase to $5.77 (as in exercise 15.3). How does your answer to (a) change?
(d) Using the expenditure function, calculate the amount the government would need to compensate each consumer in order for them to agree to the imposition of the license fee?
(e) Calculate the amount that consumers would be willing to pay to avoid the license fee.
(f) Suppose you used the demand curve to estimate the change in consumer surplus from the introduction of the license fee. How would your estimate compare to your answers in (d) and (e)?
(g) Can you use integrals of compensated demand curves to arrive at your answers from (d) and (e)?