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Intermediate Microeconomics Lekima Nalaukai

EC202 Semester I, 2019 Tutorial 10 Suggested Solutions Chapter 11

Part A: Multiple Choices 1.

A monopolist faces an inverse demand curve P  300  6Q and has a constant marginal cost of 20. The IEPR formula for this monopolist could be stated in the following way: 1 P  20 A. ) ( P P/6 P  20 300  P  B. P P P  20 P C.  P 300  P P  20   P (Q / 6) D. P

Ans: B

2.

A monopolist owns two plants in which to produce a product which has inverse demand P = (770/3) – 3Q. The monopolist has marginal cost curves of MC1 = 20+3Q1 and MC2 = 10+6Q2 in the two plants, respectively. Which of the following represents the optimal outputs in the two plants, Q1 and Q2 and the market price? A. B. C. D.

Q1 = 170/9; Q2 = 100/9; P = 500/3. Q1 = 100/9; Q2 = 170/9; P = 500/3. Q1 = 500/3; Q2 = 170/9; P = 100/9. Q1 = 500/3; Q2 = 100/9; P = 170/9.

Ans: A

3.

A monopsonist only uses labor to produce an output according to production function Q = 2L, where Q is output and L is labor. The output sells for a price of $20 per unit. The supply curve for labor can be written w = 4+L. What is the monopsonist’s demand for labor in this market? A. B. C. D.

Ans: B

L = 12. L = 18. L = 22. L = 24.

Intermediate Microeconomics Lekima Nalaukai

EC202 Semester I, 2019 Tutorial 10 Suggested Solutions Chapter 11

Price

**Reference: Use the following diagram to answer 4 and 5. MC

300 270 240 210 180 150 120 90 60 30 0

MR 0

5

10

15

20

25

D 30

35

40

45

50

Quantity

4.

**The profit-maximizing price for a perfectly competitive firm would be A. B. C. D.

180 210 240 Between 210 and 240

Ans: B

5.

**The profit-maximizing price for a monopolist would be A. B. C. D.

180 210 240 Between 210 and 240

Ans: C

6.

The marginal revenue curve for a monopolist A. B. C. D.

Ans: B

will never take a linear form. will always have double the slope of the demand curve, when demand is linear. will always have one-half the slope of the demand curve, when demand is linear. will slope upward when demand is elastic.

Intermediate Microeconomics Lekima Nalaukai

EC202 Semester I, 2019 Tutorial 10 Suggested Solutions Chapter 11

Part B: Conceptual Questions 1. The marginal revenue for a perfectly competitive firm is equal to the market price. Why is the marginal revenue for a monopolist less than the market price for positive quantities of output? Marginal revenue is less than price for a monopolist. This is because as it lowers its price two things happen. First, the firm’s revenue increases from the additional units it sells (these are the marginal units). Second, the firm’s revenue decreases because it loses revenue from selling units at a lower price than it could have had it chosen a lower quantity of output (these are the inframarginal units.) The change in revenue is the sum of the increase from the marginal units and the decrease from the inframarginal units. This change can be summarized as  TR P MR   P Q Q Q Since demand is downward sloping, the second term will be negative implying marginal revenue will be less than price. 2. What is the IEPR? How does it relate to the monopolist’s profit-maximizing condition, MR = MC? IEPR is the Inverse Elasticity Pricing Rule. This rule states that a profit- maximizing firm that sets MR  MC will satisfy the condition that P*  MC* 1  *  Q, P P where the asterisks indicate the price and marginal cost at the profit-maximizing level of output. 3. What rule does a multiplant monopolist use to allocate output among its plants? Would a multiplant perfect competitor use the same rule? A multi-plant monopolist will choose a level of output and then allocate output between plants so that marginal costs are equalized across plants. If a perfectly competitive firm had multiple plants it would follow the same rule. To see why, imagine it did not and allowed marginal costs to be different across plants. If marginal costs were different, then it reallocates one unit of output from the high marginal cost plant to the low marginal cost plant. This would reduce total cost without changing revenue. Thus, profit would increase. Therefore, to maximize profit the firm should allocate output between plants to equalize marginal cost.

Intermediate Microeconomics Lekima Nalaukai

EC202 Semester I, 2019 Tutorial 10 Suggested Solutions Chapter 11

4. Why does the monopsony equilibrium give rise to a deadweight loss? The monopsonist creates a deadweight loss. This occurs because the monopsonist hires a lower quantity and pays a lower price for its input than would occur in perfect competition. This allows the monopsonist to extract surplus away from suppliers, but the monopsonist is unable to earn as much additional surplus as suppliers lose, lowering net total benefits, and creating a deadweight loss.

Intermediate Microeconomics Lekima Nalaukai

EC202 Semester I, 2019 Tutorial 10 Suggested Solutions Chapter 11

Part C: Calculations 1. A monopolist faces a demand curve P = 210 - 4Q and initially faces a constant marginal cost MC = 10. A. Calculate the profit-maximizing monopoly quantity and compute the monopolist’s total revenue at the optimal price.  With demand P  210  4Q , MR  210  8Q . o Setting MR  MC implies 210  8Q  10 Q  25

With Q  25 , price will be: o P  210  4Q  110 .  At this price and quantity total revenue will be: o TR 110(25)  2,750 . B. Suppose that the monopolist’s marginal cost increases to MC = 20. Verify that the monopolist’s total revenue goes down.





If MC  20 , then setting MR  MC implies 210  8Q  20

Q  23.75    

At Q  23.75 , price will be P  115 . At this price and quantity total revenue will be: TR 115(23.75)  2,731.25 . Therefore, the increase in marginal cost will result in lower total revenue for the firm. (2 marks)

C. Suppose that all firms in a perfectly competitive equilibrium had a constant marginal cost MC = 10. Find the long-run perfectly competitive industry price and quantity.



Competitive firms produce until P = MC, so in this case we know the market price would be P = 10 and the market quantity would be:

Intermediate Microeconomics Lekima Nalaukai

EC202 Semester I, 2019 Tutorial 10 Suggested Solutions Chapter 11

210  4Q  10 Q  50

D. Suppose that all firms’ marginal costs increased to MC = 20. Verify that the increase in marginal cost causes total industry revenue to go up.  In this case, the market price will be P  MC = 20, implying that the industry quantity is given by 210  4Q  20 Q  47.50  At this quantity, price will be P  20 .  When MC  10 , total industry revenue is 10(50)  500 .  With MC  20 , total industry revenue is 20(47.50)  950 . Thus, total industry revenue increases in the perfectly competitive market after the increase in marginal cost. 2. The market demand curve for a monopolist is given by P = 40 - 2Q. A. What is the marginal revenue function for the firm? Since the demand curve is written in inverse form and is linear, the MR curve has the same vertical intercept and twice the slop as the demand curve. Thus, MR = 40 – 4Q. B. What is the maximum possible revenue that the firm can earn? Total revenue will be maximized when MR = 0, or when Q = 10. At that quantity, the price will be P = 40 – 2Q = 20. Total revenue is PQ = 20(10) = 200.

3. Suppose that United Airlines has a monopoly on the route between Chicago and Omaha, Nebraska. During the winter (December–March), the monthly demand on this route is

Intermediate Microeconomics Lekima Nalaukai

EC202 Semester I, 2019 Tutorial 10 Suggested Solutions Chapter 11

given by P = a1 - bQ. During the summer (June–August), the monthly demand is given by P = a2 - bQ, where a2 > a1. Assuming that United’s marginal cost function is the same in both the summer and the winter, and assuming that the marginal cost function is independent of the quantity Q of passengers served, will United charge a higher price in the summer or in the winter? If marginal cost is independent of Q, then marginal cost is constant. Assume MC  c . Then in the winter the firm will produce where MR  MC . a1  2bQ  c a c Q 1 2b At this quantity the price charged will be

a c P  a1  b  1   2b  a c P 1 2 In the summer the firm will also produce where MR  MC .

a2  2bQ  c a c Q 2 2b At this quantity the price charged will be

a c P  a2  b  2   2b  a c P 2 2

Intermediate Microeconomics Lekima Nalaukai

EC202 Semester I, 2019 Tutorial 10 Suggested Solutions Chapter 11

Since we are told that a2  a1 , the price charged during the summer months will be greater than the price charged during the winter months. 4. Market demand is P = 64 - (Q/7). A multiplant monopolist operates three plants, with marginal cost functions:

a) Find the monopolist’s profit-maximizing price and output at each plant. Equating the marginal costs at MCT, we have Q = Q1 + Q2 + Q3 = 0.25MCT + 0.5MCT – 1 + MCT – 6, which can be rearranged as MCT = (4/7)Q + 4. Setting MR = MC yields 64 – (2/7)*Q = (4/7)*Q + 4 or Q = 70 and P = 54. At this output level, MCT = 44, implying that Q1 = 11, Q2 = 21, and Q3 = 38. b) How would your answer to part (a) change if MC2 (Q2) = 4? In this case, using plant 3 is inefficient because its marginal cost is always higher than that of plant 2. Hence, the firm will use only plants 1 and 2. Moreover, the firm will not use plant 1 once its marginal cost rises to MC2 = 4, so we can immediately see that it will only produce 4Q1 = 4 or Q1 = 1 unit at plant 1. Its total production can be found by setting MR = MC2, yielding 64 – (2/7)*Q = 4 or Q = 210 and P = 34. So it produces Q1 = 1 unit in plant 1 and Q2 = 209 units in plant 2, while producing no units in plant 3 (i.e. Q3 = 0)....