1. Suppose that a monopolist firm’s demand curve is given by P = 210 4y and it f

Question

1. Suppose that a monopolist firm’s demand curve is given by P = 210 4y and it faces a constant marginal cost of $10. Answer the following questions: a. What is the profit-maximizing output for this monopolist? How much total revenue does it earn at this profit-maximizing level of output? b. Suppose that the marginal cost increases to $20. How does total revenue change? c. Now consider a perfectly competitive industry with a constant marginal cost of $10 for each firm. Find the optimal level of market output and the corresponding price in this industry. d. Suppose that the marginal cost of each firm in this perfectly competitive industry increases to $20. How does total industry revenue change? e. Compare and discuss your answers to parts (b) and (d).

Explanation / Answer

Demand curve P = 210 – 4y

MC = $10

Revenue = PY

Revenue = 210y – 4y2

Marginal Revenue (by differentiating for y) = 210 – 8y

For profit maximization

MR = MC

210 – 8y = 10

8y = 200

y = 200/8

y = 25

How much total revenue does it earn at this profit-maximizing level of output?

Equating the quantity in the revenue = 210y – 4y2

Price = 210 * 25 – 4 * (25*25)

5250 – 2500

2750

Total revenue =    2750 *25

                             68750

b. Suppose that the marginal cost increases to $20. How does total revenue change?

Calculating for quantity for increased MC

MR = MC

210 – 8y = 20

8y = 190

y = 190/8

y = 23.75

Equating the quantity in the revenue = 210y – 4y2

Price = 210 * 23.75 – 4 * (23.75*23.75)

4987.5 – 2256.25

2731.25

Total revenue =    2731.25 *23.75

                             64867.19

The total revenue of the monopolist decreases when the marginal cost of production n of the firm goes up.

c. Now consider a perfectly competitive industry with a constant marginal cost of $10 for each firm. Find the optimal level of market output and the corresponding price in this industry.

Competitive firms produce until P = MC, so in this case we know the market price would be P = 10 and the market quantity would be:

210 4y = 10

y = 200/4

y = 50

d. Suppose that the marginal cost of each firm in this perfectly competitive industry increases to $20. How does total industry revenue change?

P = MC = 20

210 4y = 20

y = 190/4

y = 47.5

At this quantity, price will be P = 20 . When MC =10, total industry revenue is 10(50) 500 = . With MC = 20, total industry revenue is 20(47.50) 950 = . Thus, total industry revenue increases in the perfectly competitive market after the increase in marginal cost.

e. Compare and discuss your answers to parts (b) and (d)

For a monopolist, with increase in the marginal cost, the revenue of the firm decreases as the marginal cost increases whereas with the perfect competition the revenue of the firm increase with increase in the marginal cost. When the marginal cost of the product increases the monopolist decreases the production whereas in the case of perfect competition, the firms are price taker and cannot alter the level of production according to their will, the quantity supplied in the market remains the same and hence earns a higher revenue than in the case of monopoly

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