Assignment
1. Additional problem: Consider a market with the following demand function: PP = aa - 1 9 * QQ Alpha Inc. is currently a monopolist in this market. Alpha's marginal costs are equal to 2. Alpha has no fixed costs.
a) Beta Co. is considering whether it should enter the market. Alpha and Beta would produce homogeneous products and they would compete by choosing quantities. Beta would also have marginal costs of 2. Beta would have to pay a fixed cost of F=20 if it were to enter the market. Write down the profit functions for Alpha and Beta in general terms for the scenario where Beta enters the market. (Hint: You do not need to solve for anything yet.)
b) Derive the best response functions for both firms for the scenario in part (b) of this question. (Hint: You may use symmetry if appropriate.)
c) Using the best response functions from part (b), calculate the production quantities for both firms for the scenario in part (b) of this question.
d) Calculate the market price for the scenario in part (b) of this question. (continued on next page)
e) Alpha's managers wonder whether they should try to deter entry by Beta. They know that a =7. Given that a = 7, Alpha's monopoly price would be P = 4.5. But they have also calculated that if a were equal to 4, then Alpha's monopoly price would be P = 3. Assume that Beta chooses to stay out of the market if it observes that Alpha charges P=3.
Calculate the profits that Alpha earns if a =7, Alpha charges a price of P = 3 and Alpha remains the only firm in the market (i.e. entry by Beta is deterred).
f) Use your results from part (e) to calculate Alpha's profits in the case that a =7 and Beta enters the market.
g) Use your results from part (e) and part (f) to compare Alpha's profits in the scenario where a =7 and Beta enters vs. the scenario where a =7 and Alpha successfully deters entry by Beta. Is entry deterrence profitable for Alpha in this case?
2. Suppose that a hospital monopolizes the local market for heart surgery, charging $10,000 per procedure. The hospital does 1,000 heart surgeries annually, and the cost of heart surgery is $5,000 per procedure. The hospital is a duopolist in the market for cataract surgery. The hospital and its competitor both perform 2,000 cataract procedures annually, charge $2,000 per procedure, and have costs of $1,000 per procedure. The hospital plans to go to insurers and offer a bundled price. It will discount the price of heart surgery below $10,000 and hold the price of cataracts at $2,000, provided that it is given exclusivity in the cataract market. What price for heart surgery must the hospital charge to insure that its competitor cannot profitably compete in the cataract market? (Assume that the hospital would match its rival's price in the cataract market if the rival were to respond to this bundling arrangement by cutting its cataract price.)