Chapter 4: Problems
3. Suppose you are given the information about a monopoly that appears in the table.

Quantity_______________Price________________Marginal Cost


a. What is the firm's total revenue for each quantity?
b. What is the flrm's marginal revenue for each quantity?
c. What quantity and price should the firm choose to maximize its profit?
d. Suppose the monopolist is currently producing 5 units of the good. What actions should it undertake and why?
e. Use the information above to plot the demand curve faced by the monopolist, the monopoHst's marginal revenue and marginal cost curves, the profit-maximizing level of output, and the profits earned by the firm.

a. The firm's total revenue is price times quantity sold or P x Q. Applying this formula, the total revenue associated with the first unit of output is found to be 1 x $50 or $50. Using this formula the total revenue associated with each unit of output sold can be derived. These results are exhibited in column (a) in the table below.

b. The firm's marginal revenue shows the change in total revenue that is brought about by a one unit change in output. It is (TR1 - TRo)/(Q~ - Q0). The marginal revenue associated with increasing production from one to two units of output would be (90 - 50)/(2 - 1), or $40. Applying this formula to the various levels of output results in column (b) in the table below.


c. In order to maximize profit, the firm should produce where its marginal revenue and marginal cost are equal. The firm's marginal cost of production is $20 for each unit. When the firm produces 4 units, its marginal revenue is $20. Thus, the firm should produce 4 units of output. When it produces four units, the previous table indicates that people will be willing to pay $35 per unit. Thus output of 4 and price of $35 are the profit maximizing output and price.

d. If the monopolist is producing 5 units, her marginal cost is $20 while her marginal revenue is $10. The revenue received from the sale of this unit is less than the cost of producing this unit. Production of this unit will cause profits to fall by $10 ($20 - $10). In order to maximize profits, the firm should cut back on output. In this instance, as output falls, profits will rise.

e. In order to draw the monopolist's demand curve, simply plot the price and quantity combinations given in the above table. This is done in the diagram below. The marginal revenue curve is drawn by plotting the marginal revenue and quantity combinations in the table. Plotting the marginal cost and quanti~ combinations will give the marginal cost curve. The profit maximizing output, Q, is found by equating marginal revenue and marginal cost at point A. Q' is found by reading down from point A to the horizontal axis. Reading up from point A to the demand curve and then across to the vertical axis gives the price the monopolist will charge, P*. Profit is equal to total revenue minus total cost. Total revenue is equal to price times quantity, or area OP*BQ*. Total cost is equal to the sum of the marginal costs. It is the area under the marginal cost curve up to Q*. Thus, total cost is given by the area OC*AQ*. Total profit, total revenue

4. "A monopolist can charge whatever price it desires for its output." Is this statement true or false? Defend your answer.

The statement is false. While it is true that the monopolist is not a price taker and does exert control over the price of output, profit maximization mean~ she cannot charge any price she desires. In the previous question, the monopolist maximized profit by selling 4 units at a price of $35 per unit. If she were to raise the price to $45 per unit and still sell 4 units, profit would go up by $40. But at the price of $45 she can only sell 2 units. Even though she charges a higher price, her profit goes down by $10 because she sells fewer units. The law of demand puts a constraint on the price charged by a monopolist.
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