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answer this question Top Notch Video Games Pty Ltd (a monopoly firm) has the fol...
May 15, 2024
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Solution
a
The Marginal Revenue (MR) function for a monopoly is derived from the demand (average revenue) function. Given the demand function AR=60−QAR = 60 - Q, the total revenue (TR) is TR=AR×Q=(60−Q)Q=60Q−Q2TR = AR \times Q = (60 - Q)Q = 60Q - Q^2. The MR is the derivative of TR with respect to Q: MR=d(TR)dQ=60−2QMR = \frac{d(TR)}{dQ} = 60 - 2Q To find the profit-maximizing level of output, set MR equal to the marginal cost (MC). Given MC=20MC = 20: 60−2Q=2060 - 2Q = 20 2Q=402Q = 40 Q=20Q = 20
b
The equilibrium monopoly price is found by substituting the profit-maximizing quantity back into the demand function: P=60−QP = 60 - Q P=60−20=40P = 60 - 20 = 40 To find the monopoly profit, calculate total revenue (TR) and total cost (TC): TR=P×Q=40×20=800TR = P \times Q = 40 \times 20 = 800 TC=MC×Q=20×20=400TC = MC \times Q = 20 \times 20 = 400 Profit=TR−TC=800−400=400Profit = TR - TC = 800 - 400 = 400
c
To illustrate the market demand, marginal cost, average cost, profit-maximizing price, quantity, and profit level on a diagram: - Draw the demand curve AR=60−QAR = 60 - Q. - Draw the MR curve MR=60−2QMR = 60 - 2Q. - Draw the MC curve as a horizontal line at MC=20MC = 20. - Identify the profit-maximizing quantity Q=20Q = 20 where MR=MCMR = MC. - Identify the price P=40P = 40 from the demand curve at Q=20Q = 20. - Shade the area representing profit, which is the rectangle with height P−MC=40−20=20P - MC = 40 - 20 = 20 and width Q=20Q = 20, giving an area of 20×20=40020 \times 20 = 400
Answer
The profit-maximizing output is 20 units, the equilibrium monopoly price is 40,andthemonopolyprofitis40, and the monopoly profit is 400.
Key Concept
Monopoly Pricing and Profit Maximization
Explanation
A monopoly maximizes profit where marginal revenue equals marginal cost. The price is then determined from the demand curve at this quantity.
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