Below is the reaction function diagram for an oligopoly. There are two firms each has the marginal cost of 4 and the demand function is P=20-2Q.What are the monopoly profits in this industry?

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BlackTom AI · Accepted Answer

We start with the given demand function P = 20 − 2Q for the industry and a constant marginal cost MC = 4 for the firm(s).

To find the monopoly profit, treat the industry as a single monopolist facing the demand P = 20 − 2Q.

Step 1: Compute total revenue (TR) as a function of quantity Q.
TR(Q) = P × Q = (20 − 2Q)Q = 20Q − 2Q^2.

Step 2: Compute marginal revenue (MR) from TR.
MR(Q) is the derivative of TR with respect to Q: MR = d(TR)/dQ = 20 − 4Q.

Step 3: Set MR equal to MC to find the profit-maximizing quantity Q*.
20 − 4Q* = 4 ⇒ 4Q* = 16 ⇒ Q* = 4.

Step 4: Determine the monopoly price using the demand function.
P* = 20 − 2Q* = 20 − 2(4) = 12.

Step 5: Calculate monopoly profit.
Profit = (P* − MC) × Q* = (12 − 4) × 4 = 8 × 4 = 32.

If one were to compare to the oligopoly outcome shown in a two-firm Cournot setting, the total industry quantity would be smaller than the competitive level but the monopoly profit computation above directly uses the monopolist condition MR = MC. The resulting profit value here is 32, which reflects the deadweight loss typical of monopoly relative to more competitive outcomes.

ECON0015_ECON0013_ECON0014_25-26 Quiz 3b

Below is the reaction function diagram for an oligopoly. There are two firms each has the marginal cost of 4 and the demand function is P=20-2Q.What are the monopoly profits in this industry?

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