The only theater in a small college town has a constant marginal cost of $4 per
ID: 1245905 • Letter: T
Question
The only theater in a small college town has a constant marginal cost of $4 per person. The town has two types of people: professors and students. Demand by professors is 500 – 4p and demand by students is 500 – 50p.a. If the theater can’t differentiate between professors and students (that is to say they can’t price discriminate), what price should it set? What will its profit be?
b. If the theater can price discriminate, what price should it charge professors? What price should it charge students? How much profit will it make?
c. How did total surplus change when the theater could price discriminate? In general, is price discrimination efficient?
Explanation / Answer
the first's suply curve is its total cost curve. total cost = marginal cost times quantity supplied (i.e.) 4Q. thus, p=4Q. total demand curve will be Q=500 - 5p + 500 - 50p = 1000-54p. thus, Q = 1000-54(4Q). Q = 1000/217. similarly, p/4 = 1000-54p. p = 18.4. revenue = Q x 18.4 and cost = Q x 4. profit = revenue - cost (b) if it can charge different prices, total cost curve is same but demand for professors is 500-4p. do the above procedure for these 2 curves and find profit using same way as above. also, do the same with 500-50p. calculate total profit. (c) surplus is profit with price discrimination - profit without price discrimination. in general, it is efficient because we know that on either side of equilibrium, there is surplus LOST. thus, when we sell equilibrium price and quantity for each customer segment, we never lose any surplus. let me know if you want me to show all steps.
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