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Econ 101: Intro to Microeconomics

Spring 2012, Handout 8 Solutions

More on Monopolies

1. A monopoly faces a market demand curve given by P = 42 − Q. Its marginal cost curve is given by M C = Q. (a) Find an equation for the marginal revenue curve. Graph market demand, marginal revenue, and marginal cost for this monopoly. Double the slope of the demand curve to get the MR: M R = 42 − 2Q. The

graph should show a line twice as steep as the original demand curve, but with the same price intercept. Note: the “double the slope” rule only works when the equation is solved for P! (b) Find the proﬁt-maximizing level of production for this monopolist. M R = M C to get 42 − 2Q = Q ⇒ Q = 14. ...view middle of the document...

Most ATC curves will eventually curve back up.) (b) What is the ﬁxed cost? Might this indicate high barriers to entry? FC=$400. Yes, there are high barriers to entry. This is much higher than the price at any level of production. (c) What is the socially optimal level of production and price? Social optimum where P = M C ⇒ 120 − 4Q = 4 ⇒ Q = 29, P = $4. (d) At the social optimum found in part (b), is the perfect competition long run equilibrium possible? Why or why not? No: AT C = 400/Q + 4 > 4 = M C for the range of Q that we have demand for. Thus there is no “break-even point” where AT C = M C as in perfect competition. (e) Suppose this industry operates as a monopoly. Find the equilibrium price and quantity. MR for a monopoly = 120 − 8Q M R = M C ⇒ 120 − 8Q = 4 ⇒ Q = 14.5 ⇒ P = 120 − 4(14.5) = $62 (f) The government, bowing to public pressure to regulate monopolies, decides to force ﬁrms to charge their marginal cost just like they would in perfect competition. How much will the monopolist produce? What is their TR? What is their TC? Proﬁts? The monopolist will produce at the social optimum quantity of 29 units. T C = 400 + 4(29) = $516. T R = (4)(29) = $116, Proﬁt= -$400 ⇒ A government subsidy will be required to keep this ﬁrm in business (or the ﬁrm will not produce at all). (g) Suppose the government instead chooses to force the monopolist to charge a price equal to their average total cost. How much will the ﬁrm produce, assuming it produces more than its unregulated equilibrium? What will be their proﬁts? 2

Econ 101: Intro to Microeconomics

Spring 2012, Handout 8 Solutions

(Note: This problem involves a quadratic equation. The numbers are chosen to work out nicely, but it may be diﬃcult to do by hand, so feel free to use a calculator.) Set average total cost equal to the demand price: 400/Q + 4 = 120 − 4Q ⇒ 400 = 116Q − 16Q2 ⇒ 4Q2 − 116Q + 400 = 0 ⇒ Q2 − 29Q + 100 = 0 ⇒ Q = 25. The ﬁrm will earn zero proﬁt.

Price Discrimination

3. Suppose you are a monopolist that is debating charging a single price for your product or diﬀerent prices to diﬀerent customers based on their demand elasticities. The marginal cost of production for your ﬁrm is equal to $200 and is constant for all levels of output. The market demand curve is P = 1, 000 − 2Q. (a) If you charge a single price, what price and quantity would you select given the above information? What does the ﬁrms total revenue equal? What do the ﬁrm’s proﬁts equal with this pricing policy? The monopolist would produce the proﬁt-maximizing level of output where M R = M C. For this monopolist the MR curve is M R = 1, 000 − 4Q and M C = 200. Thus, the proﬁt-maximizing level of output is Q = 200. The proﬁt-maximizing price can be found by substituting this level of output into the demand equation and solving for price: P = $600. The ﬁrm’s total revenue is equal to $120,000. Since the MC curve is a horizontal line, this implies that the ﬁrms ATC is also a horizontal line at AT C =...

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