Adi and Jill are the only doctors in a small Pennsylvania town who offer LASIK e

Question

Adi and Jill are the only doctors in a small Pennsylvania town who offer LASIK eye surgery. The table provides the demand schedule for eye surgeries in this town. Each doctor faces a constant marginal cost of $50 to perform the surgery; there are no fixed costs.

Price (Dollars) Quantity
500 3
450 4
400 5
350 6
300 7
250 8
200 9
150 10
100 11
50 12


3.1. If Adi and Jill collude to achieve the monopoly outcome, how many surgeries should each doctor perform? Assume they split the output evenly.

Please enter a whole number, with no decimal point.


3.2. If Adi believes that Jill will abide by their collusive agreement and perform only three surgeries, find a number of surgeries that Adi could perform that would maximize his profits. (Hint: There is more than one correct answer. You need only select one.)

A. 8

B. 4

C. 5

D. 2


3.3. Jill does not trust Adi to abide by the agreement and instead believes that he will perform four surgeries. How many surgeries should Jill provide to maximize her own profits?

Please enter a whole number, with no decimal point.


3.4. The strategy set in which Adi performs _____ surgeries and Jill performs ______ surgeries is a Nash equilibrium.


A. 4, 4

B. 3, 4

C. 4, 3

D. 3, 3

Explanation / Answer

They should perform 3 each because 6 surgeries at $350 each yields the maximum profit of $1800 split two ways ($900 each) $350 price - $50 marginal cost = $300 profit x 6 customers. The answer is A or D (4 or 5 surgeries at $300 or $250 respectively) 4 surgeries at $250 each for $800 profit. (remember to subtract $50 marginal cost for each surgery performed) A. 4 and 4. 3 and 3 is a better result for the players, but it's not an equilibrium because each can unilaterally increase profit by performing a 4th surgery. Since they both know that, they'll both do it. But if they both perform 4 surgeries, neither can increase his or her profit by performing a 5th, so 4 each is an equilibrium.

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