Suppose XER Inc. is a monopoly and produces a drug that cures the common cold. T
ID: 1106469 • Letter: S
Question
Suppose XER Inc. is a monopoly and produces a drug that cures the common cold. The weekly (inverse) market demand for its product takes the form P = 660 – 4Q, where Q is measured as number of tablets. The marginal costs (MC) and average total costs (ATC) are equal at $100 per tablet (that is, a horizontal marginal cost curve).
A. Given this information, solve for the level of output that will be produced by XER Inc. if it maximizes profits (you may need to consult footnote 2 in the chapter).
B. Solve for the price charged and amount of profits earned by XER Inc.
C. From a societal point of view, does the profit-maximizing level of output represent an efficient level of output? Why or why not? Calculate the social damages created by XER Inc. (Hint: You will have to know how to calculate the area of a triangle.)
D. Suppose the source of the entry barrier was removed so XER is no longer a monopoly. How would equilibrium change? Explain fully.
Explanation / Answer
P = 660 - 4Q
MC = ATC = $100
(a) Profit is maximized when Marginal revenue (MR) equals Marginal cost (MC).
Total revenue (TR) = P x Q = 660Q - 4Q2
MR = dTR/ dQ = 660 - 8Q
Equating with MC,
660 - 8Q = 100
8Q = 560
Q = 70
(B)
P = 660 - (4 x 70) = 660 - 280 = $380
Profit = Q x (P - MC) = 70 x $(380 - 100) = 70 x $280 = $19,600
(C)
This output is not socially optimal since Price charged is higher than marginal cost.
In efficient outcome, P = MC
660 - 4Q = 100
4Q = 560
Q = 140
P = MC = $100
Social damage = (1/2) x Difference in Price x Difference in quantity = (1/2) x $(380 - 100) x (140 - 70)
= (1/2) x $280 x 70
= $9,800
(D)
When XER is no monopoly and free entry is possible, eventual new equilibrium is by equating Price with MC, as obtained in part (C). Therefore,
New equilibrium price = MC = $100
New equilibrium quantity = 140
Price will be lower and quantity will be higher compared to monopoly outcome.
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