Analyzing Strategic Behavior in Business and Economics by Webster Thomas J.;

Author:Webster, Thomas J.; [Webster, Thomas J.]
Language: eng
Format: epub
Publisher: Lexington Books
Published: 2014-01-30T16:00:00+00:00

Solution

From condition (15.12), the equilibrium strategy profile from double marginalization is (15.19)

From Eq. (15.6), the firm’s total profit from this strategy profile is

(15.20)

From condition (15.16), the equilibrium strategy profile when divisions maximize joint profits is

(15.21)

From Eq. (15.17), the firm’s total profit at this strategy profile is

(15.22)

Practice Exercises

15.1: How would you describe the relationship between the firm’s products when c < 0?

15.2: A firm is organized into two divisions. The goods produced by these divisions are demand complements. The profit equations of the two divisions are

(PE15.2a)

(PE15.2b)

where x1 and x2 are the outputs of goods 1 and 2, respectively, and c = 0.5 is the degree of strategic complementarity.

a. What is the equilibrium strategy profile and total profit if each division is treated as a quasi-independent profit center?

b. What is the equilibrium strategy profile and total profit when the divisions maximize joint profits?

c. For what range of values of c are the profits from joint profit maximization greater than firm profits from double marginalization?

15.3: A firm’s profit depends on the separate and joint efforts of two partners, which is given by the equation

(PE15.3)

Suppose that the partners incur private opportunity costs of x12 and x22, and share equally in the firm’s profits.

a. Under what conditions are the partners strategic complements?

b. What is the equilibrium strategy profile if the partners maximize their share equally in the firm’s profits? What is the firm’s profit?

c. What equilibrium strategy profile will maximize the partners’ joint profits? What is the firm’s profit?

d. For what values of c will the firm’s profit from joint maximization exceed the profit from double marginalization?

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