Part I: Discrimination decreases total surplus
Suppose a monopolist can practice third degree price discrimination. Suppose that you are a consultant for this monopolist who has information about her consumers’ age. In particular, monopolist asks every consumer to reveal if she is above 45 or not. Monopolist wants the highest profit possible and will pay you %10 of the profit, so you also like to find the highest profit.
After working with data and running regressions you find the inverse demand func- tions for consumers above 45: p1 = 10 − 2q1 , and for consumers below 45: p2 = 14 − 2q2 (so demand functions are: q1 = 15 − 3p1 and q2 = 7 − p2 ). Also monopolist tells you that she has constant marginal cost: MC = 2.
a. What price and quantity would you suggest the monopolist to charge in each mar-ket?
b. Now government has passed a new law which prohibits discrimination based on age. What price, and quantity would you suggest to be charged this time? (this is what we called p ¯ in our lectures).
c. Check if you are asking her to do: pmin ≤ p ¯ ≤ pmax, where pmin, and pmax are, re- spectively, low and high price you told her to charge when she can practice discrim- ination. Which market gains and which one loses from having price discriminating monopolist in the market?
d. Do you suggest the monopolist to produce a higher amount in total in the presence of price discrimination? What would you expect to be the change in total surplus with price discrimination?
e. Check if your answer in part c is actually right. In particular, find the total surplus under price discrimination (W2) and total surplus under governmental force to charge a uniform price (W1). What is the sign of ?W? Use a calculator if you need.
Part II: Discrimination increases total surplus
For this part assume two submarket demand functions are q1 = 10 − p1, and q2 = 5 − p2. Repeat all the parts previous section.
Hint: Remember that in order to find optimal uniform price we look at two cases: monopolist only sells in one market, or monopolist sells in both. Here you will find that both prices are in the valid range. In this case the price that gives higher profit is the optimal price.