Question

Consider a monopolist facing the daily demand curve displayed below. Use the line tool to draw the marginal revenue curve.

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Price 16 15 14 13 12 11 10 9 7 6 5 4 3 2 D 10600 1100 1200 1300 1400 1500 1600 Quantity

Part 2   (1 point)

See Hint

Suppose that the monopolist's cost function is given by ?(?)=4?c(y)=4y, where ?y stands for the amount of output produced daily. The firm's marginal cost equals $ _____   .

Part 3   (1 point)

See Hint

If the monopolist is a profit maximizer, the monopolist will produce and sell _____   units per day. (Round your answer to two decimals if necessary.)

Part 4   (1 point)

See Hint

If this is a profit-maximizing monopolist, the price per unit of the product will be $ _____ . (Round your answer to the nearest integer.)

Answer 1

The Demand Curve can be drawn as follows

(1400 - y) / 1400 = (0 - P) / (0 - 12)

or 1 - y/1400 = P / 1200

or 12 - 3/350*y = P

The marginal Revenue curve is

MR = 12 - 3/175y

The graph can be drawn as follows

Monopolist Chart 14 12 10 8 Price 6 4 2 0 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 Quantity Demand Curve Marginal Revenue

Part 2:

Cost function is given by c(y) = 4y where y is the output

Marginal cost = d/dy (c(y)) = d/dy (4y) = 4

Suppose that the monopolist's cost function is given by ?(?)=4?c(y)=4y, where ?y stands for the amount of output produced daily. The firm's marginal cost equals $ 4

Part 3:

At profit maximization, MR = MC

or 12 - 3/175y = 4

or 3/175y = 8

or y = 466.67

So the monopolist will sell 466.67 units per day

If the monopolist is a profit maximizer, the monopolist will produce and sell 466.67 units per day.

Part 4:

The price of each unit at profit maximization is given as

P = 12 - 3/350*y = 12 - 3*466.67 / 350 = 8

If this is a profit-maximizing monopolist, the price per unit of the product will be $ 8

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