Suppose the demand for pizza in a small isolated town is p = 10 - Q. The only two firms, A and B, behave as Cournot duopolists. Each has a cost function TC = 2 + Q. If the government wants to subsidize firm A to raise its output to that of a Stackelberg leader, how large should the subsidy be?
What will be an ideal response?
Firm B's profit is ? = [10 - (qA + qB)]qB - 2 - qB. Maximizing with respect to its own output yields firm B's best response qB = 4.5 - qA/2. Knowing this, firm A substitutes this into demand and maximizes its profit. ? = [10 - qA - (4.5 - qA/2)]qA - 2 - qA. Maximizing with respect to qA yields qA = 4.5. Firm B responds by producing 2.25. The subsidy (S) must make firm A choose 4.5 units while acting as a Cournot firm. Firm A's reaction function as a Cournot firm is qA = [10 - 1 + S - qB]/2. Setting qA= 4.5 and qB = 2.25 yields a subsidy of 2.25 per unit.
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Refer to Figure 12-11. Suppose the prevailing price is $20 and the firm is currently producing 1,350 units. In the long-run equilibrium
A) there will be fewer firms in the industry and total industry output decreases. B) there will be fewer firms in the industry but total industry output increases. C) there will be more firms in the industry and total industry output remains constant. D) there will be more firms in the industry and total industry output increases.
A direct relationship exists when:
a. there is no association between two variables. b. one variable increases and there is no change in the other variable. c. one variable increases and the other variable increases. d. one variable increases and the other variable decreases.