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Let market demand be given by the inverse demand curve P(Q) = 50−2Q, where Q = q1 +q2.

The cost function for each of the two firms in the industry is C(qi ) = 2qi . Firms are Cournot
competitors. (Show all calculations as detailed as possible)
(a) Define the best-response function of a firm. Derive the best-response function of each firm.

User CBBSpike
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Final answer:

The best-response function determines a firm's optimal output level considering its competitor's output to maximize profit. It relies on the market demand curve, the firm’s cost functions, and the output of the other firm. Specifying each firm’s best-response function needs additional cost function information and game theory analysis.

Step-by-step explanation:

The student's question is about determining the best-response function of a firm in the context of a market with two competing firms. The best-response function is an equation that tells a firm the optimal amount of an output to produce, given its competitor's level of output to maximize its own profit.

In the provided scenario, the inverse demand curve is P(Q) = 50 - 2Q. Assuming a duopoly where two firms (Firm 1 and Firm 2) compete, the total quantity Q is the sum of q1 (output of Firm 1) and q2 (output of Firm 2), such that Q = q1 + q2. To find the best-response function of each firm, we would calculate the optimal output for each firm while considering the expected output of the rival firm.

For each firm, the best-response function would be derived from their respective profit functions, which in turn depend on the given demand curve and the assumption about marginal costs, as well as the quantity produced by the other firm.

Important notes when deriving the best-response function:

  • The best-response function illustrates how each firm adjusts its output to the output level of the other firm.
  • Firms take the output level of their competitors as given and react to it with their optimal output to maximize profits.
  • The actual derivation of the best-response function requires knowledge of each firm's cost functions and further game theory analysis.
User Dillon Courts
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