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 is the monopoly price in this industry?

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BlackTom AI · Accepted Answer

The problem presents an oligopoly with two firms and a linear demand function P = 20 − 2Q, where Q is total industry output (Q = Q1 + Q2). Since the question asks for the monopoly price in this industry, we should consider the joint profit maximization (i.e., the firms colluding to behave as a single monopoly).

Step 1: Express total revenue and total cost for the joint entity. The price is P = 20 − 2Q, so total revenue TR = P × Q = (20 − 2Q)Q = 20Q − 2Q^2. The marginal cost for each firm is 4, so the joint (industry) cost is TC = 4Q, and the total cost per unit is constant at MC = 4.

Step 2: Write the profit function for the monopolist on the industry level. Profit Π = TR − TC = (20Q − 2Q^2) − 4Q = 16Q − 2Q^2.

Step 3: Find the quantity that maximizes profit by taking the derivative with respect to Q and setting it to zero. dΠ/dQ = 16 − 4Q. Set 16 − 4Q = 0, which gives Q* = 4.

Step 4: Determine the monopoly price using the demand function. Substitute Q* = 4 into P = 20 − 2Q: P* = 20 − 2(4) = 20 − 8 = 12.

Step 5: Conclude. The monopoly-equilibrated price, under joint profit maximization for the two-firm industry, is 12. This result uses the monopoly condition on the combined market, not the competitive outcome, and aligns with the given demand and constant marginal cost.

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 is the monopoly price in this industry?

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