Let’s calculate the profit from price discrimination. The average daily demand for dinners at Paradise Grille, an upscale casual restaurant, is as follows:
Demand for dinners by senior citizens: P = 50 - 0.5QMR = 50 - Q
Demand for dinners by others: P = 100 – QMR = 100 - 2Q
Marginal cost = 10 in both cases.
a. What is the profit-maximizing price for each group?
b. Translate this into real-world jargon: If you owned this restaurant, what “senior citizen discount” would you offer, in percent?
c. Ignoring fixed costs, how much profit would Paradise Grille make if it did this?
d. If it became illegal to discriminate on the basis of age, you would face only one demand curve. Adding up these two demand curves turns out to yield:
P = 67 - (1/3)QMR = 67 - (2/3) Q
What is the optimal price and quantity in this unified market? Are the total meals sold in this discrimination-free market higher or lower than in part a?
e. What is the profit in this discrimination-free market?