# How to derive MR from demand and find optimal output

Assume the graph attached represents the market demand for a patented prescription drug together with the long run marginal cost and average cost functions for producing the drug. (note: the diagram assumes that at output levels over 50 million AFC ~ 0, and MC is constant so that ATC = AVC =MC = $20)

A) Draw the marginal revenue function for this firm.

B) What is the profit maximizing price for this firm?

C) On the graph show the area which represents the net loss to society resulting from the monopoly power conferred by the patent.

D) What do you predict will happen to the structure of competition and to the price in this market when the patent expires ? (Hint: use the concept of "Minimum efficient scale " of production in your answer.) .

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#### Solution Preview

Please see the attached file for full explanations and graph.

Assume the graph below represents the market demand for a patented prescription drug together with the long run marginal cost and average cost functions for producing the drug. (note: the diagram assumes that at output levels over 50 million AFC ~ 0, and MC is constant so that ATC = AVC =MC = $20)

A)Draw the marginal revenue function for this firm.

Recall that MR is just the change in TR divided by the change in Output. The rule of thumb is that MR is twice as steep and demand. This can also be solved by taking the derivative of TR = P*Q where you would plug in the ...

#### Solution Summary

The question begins with cost and demand data for a firm. from demand marginal revenue is derived. given marginal revenue the optimal level of output for the firm is solved for. The results are graphed and a brief discussion regarding the loss of surplus is provided. the question compares outcomes under perfect competition with those of monopoly.

Determining the Optimal Price and Output Combination

1. A firm under monopolistic competition faces the demand curve: P = 500 - 12.5Q. The firm's marginal cost is MC = 200 + 5Q.

a. Find the firm's profit-maximizing output and price.

b. Assuming that the firm is at its long-run equilibrium position, estimate total revenue, total cost, and total profit.

2. A monopolist faces the demand curve: P = 8,400 - 3Q, and has long-run average cost

LAC = 900 - 3Q + Q2.

a. Derive equations for revenue, marginal revenue, total cost, and marginal cost.

b. Determine the monopolist's profit-maximizing output, price, and profit.

3. Industry demand for a good is given by: P = 60 - .5Q. The industry's long-run cost is $10 per unit: LAC = LMC = $10.

a. A monopolist controls the industry. Find its output and price.

b. Instead, suppose that the same industry is perfectly competitive. Find the long-run equilibrium price and output. Comment on the differences between the monopoly and competitive results.

4. A 5-member commodity cartel faces the demand curve: P = 60 - .4Q. Each member can produce output at (constant) LAC = LMC = $20 per unit.

a. Describe how the cartel should operate to maximize its total group profit.

b. Under the group profit-maximizing cartel agreement in part a, one member produces 10 units of output. It is tempted to secretly increase its output to 20 units. Assess this strategy and comment on cartel stability.