Lesson Topics - Pepperdine Universityseaver-faculty.pepperdine.edu/jburke2/ba445/PowerP1/... · · 2014-02-18Lesson Topics. Monopolistic Price and ... for Apple Computers is given

A.9 Monopolistic Markets Review Questions

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Lesson Topics

Monopolistic Price and Quantity starts with quantity set where marginal cost equals marginal revenue, then price set to the maximum willingness to pay for the last unit. Inefficient Quantity is implied when price and willingness to pay is greater than marginal cost. — So, after your market purchases, there is a deal between you and Microsoft that can benefit you both.

Monopolistically Competitive Entry and Exit (2) drives profits to zero as in competitive markets. — So, Pizza Hut profits from stuffed-crust pizza eventually vanish, and profits require new variations. Comparing Markets (10) reveals different equilibrium for perfect competition, monopoly, and monopolistic competition — So, Monsanto’s seed monopoly has equilibrium unlike Pizza Hut’s pizza.


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Monopolistically Competitive Entry and Exit Question. You manage Apple Inc., and make computers that meet the specifications of Pepperdine University. Apple competes with Dell Inc. and HP (the Hewlett-Packard Company) to sell computers through Tech Central. Apple Computer offers connectivity to iPods and iPhones in an attempt to differentiate itself from its competitors. The weekly demand for Apple Computers is given by Q = 100-0.5P, and the weekly cost for Apple Computers is C(Q) = 2Q2. If other firms in the industry sell computers for $600, what price and quantity of computers should Apple choose to maximize profit? What long-run changes should Apple anticipate? Explain.


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Answer to Question: Apple Computers is a monopolistically-competitive firm and faces a downward sloping demand for its product, with inverse demand P = 200 – 2Q. Thus, you should equate MR = MC to maximize profits. Here, MR = 200 – 4Q and MC = 4Q. Setting 200 – 4Q = 4Q implies that your optimal output is 25 units per week. Your optimal price is P = 200 – 50 = $150. Your weekly revenues are R = ($150)(25) = $3750 and your weekly costs are C = 2(25)2 = $1250. Your weekly profits are thus $2,500. You should expect other firms to enter the market; your profits will decline over time to zero, and you will lose market share to other firms.


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Monopolistically Competitive Entry and Exit Question: You manage Gateway Inc., and make custom computers that meet the specifications of Pepperdine University. Gateway is not the only firm that builds computers to meet the university’s specifications; indeed, it competes with many manufacturers online and through traditional retail outlets. Gateway offers free customer service in an attempt to differentiate itself from its competitors. The yearly demand for Gateway is given by Q = 1000-P, and the yearly cost for Gateway is C(Q) = 2,000 + Q2.

If other firms in the industry sell PCs for $600, what price and quantity of computers should you produce to maximize profit? What long-run changes should you anticipate? Explain.


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Answer to Question: Gateway is a monopolistically competitive firm and faces a downward sloping demand for its product. Thus, you should equate MR = MC to maximize profits. Here, MR = 1000 – 2Q and MC = 2Q. Setting 1000 – 2Q = 2Q implies that your optimal output is 250 units per period (year). Your optimal price is P = 1000 – 250 = $750. Your per period revenues are R = ($750)(250) = $187,500 and your per period costs are C = 2000 + (250)2 = $64,500. Your per period profits are thus $123,000. You should expect other firms to enter the market; your profits will decline over time and you will lose market share to other firms.


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Comparing Markets Each of the following review questions apply the theory of Comparing Markets to the managerial decision of how best to set price and quantity, whether to exit an industry, when to expect other firms to enter or exit the industry.


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Comparing Markets Question. Consider the cost function C(Q) = 125 + 4Q2 Determine the profit-maximizing output and price, and discuss its long-run implications, under three alternative scenarios:

a. You are a price taker and other firms charge $40 per unit and your cost function is C(Q) = 125 + 4Q2

b. You are a monopolist and the inverse demand for your product is P = 100 – Q and your cost function is C(Q) = 125 + 4Q2

c. You are a monopolistically competitive firm and the inverse demand

for your brand is P = 100 – Q and your cost function is C(Q) = 125 + 4Q2


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Answer to Question:

a. Price Taker in Perfect Competition. • MC = 8Q • MR = P = $40. • Set MR = MC.

• 40 = 8Q. • Q = 5 units.

• Cost of producing 5 units. • C(Q) = 125 + 4Q2 = 125 + 100 = $225.

• Revenues: • PQ = (40)(5) = $200.

• Maximum profits of -$25, but loss is less than fixed cost of $125. • Implications: Produce Q = 5 in short run, but expect exit in the long-

run.

b and c. Monopoly and Monopolistic Competition. • MR = 100 - 2Q (since P = 100 - Q). • Set MR = MC, or 100 - 2Q = 8Q.

• Optimal output: Q = 10. • Optimal price: P = 100 - (10) = $90. • Maximal profits:

• PQ - C(Q) = (90)(10) -(125 + 4(100)) = $375. • Implications

• Monopolist will not face entry (unless patent or other entry barriers are eliminated).

• Monopolistically competitive firm should expect other firms to clone (produce close substitutes), so profits will decline to zero over time.


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Comparing Markets Question. Consider the cost function C(Q) = 900 + 40Q + 20Q2 for Apple Computer to produce the new iPad. Using that cost function for the iPad, determine the profit-maximizing output and price for the iPad, and discuss its long-run implications, under three alternative scenarios:

a. Apple Computer’s iPad is a perfect substitute with the HP Slate and several other tablet PCs that have similar cost functions and that currently sell for $300 each

b. Apple Computer’s iPad has no substitutes and so is a monopolist, and the demand for the iPad is expected to forever be Q = 12 – 0.02P

c. Apple Computer’s iPad currently has no substitutes, and currently the

demand for the iPad is Q = 20 – 0.04P, but Apple anticipates other firms may produce gross substitutes in the future


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Answer to Question: a. Apple is a Price Taker in Perfect Competition.

Solve for Perfect Competition with inverse demand

P = 300 and quadratic cost C = 900 + 40 Q + 20 Q2 Given inverse demand, marginal revenue equals price

MR = 300 and compute marginal cost by taking the derivative of cost C

MC = 40 + 40 Q

Hence, equate marginal cost MC to marginal revenue MR 40 + 40 Q = 300 to determine quantity

Q = 6.50 and so price by inverse demand and profit by Π=PQ-C

P = 300.00

Π = -55.00 Maximum profits of -$55, but that loss is less than the fixed cost of $900, so produce Q = 6.5 in short run, but expect exit in the long-run.


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b. Apple is a Monopolist. Solve the Uniform Price Monopoly with demand

Q = 12.00 - 0.02 P inverse demand P = 600 - 50 Q and quadratic cost C = 900 + 40 Q + 20 Q2

Given inverse demand, compute marginal revenue by doubling the slope

MR = 600 - 100 Q and compute marginal cost by taking the derivative of cost C

MC = 40 + 40 Q

Hence, equate marginal cost MC to marginal revenue MR 40 + 40 Q = 600 - 100 Q to determine quantity


P = 400.00

Π = 220.00 Maximum profits of $220, but Apple is a monopolist, and so will never face entry and so its price and profit remain.


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c. Apple is a Monopolistic Competitor. Solve the Uniform Price Monopoly with demand




MC = 40 + 40 Q



P = 372.22

Π = 275.56 Maximum profits of $275.56, but Apple is a monopolistically-competitive firm that should expect other firms to clone (produce gross substitutes) in the future, so profits will decline to zero in the future.


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Comparing Markets Question. Consider the cost function C(Q) = 25000 + Q2 for Apple Inc. to produce the iPhone. Using that cost function for the iPhone, determine the profit-maximizing output and price for the iPhone, and discuss its long-run implications, under three alternative scenarios:

a. Apple’s iPhone is a perfect substitute with the Motorola Droid and several other smartphones that have similar cost functions and that currently sell for $200 each

b. Apple’s iPhone has no substitutes and so is a monopolist, and the demand for the iPhone is expected to forever be Q = 133.33 – (1/3)P

c. Apple’s iPhone currently has no substitutes, and currently the

demand for the iPhone is Q = 133.33 – (1/3)P, but Apple anticipates other firms to produce close substitutes in the future


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Answer to Question: a. Apple is a Price Taker in Perfect Competition. • MC = 2Q

• MR = P = $200

• Set MR = MC • 200 = 2Q

• Q = 100 units

• Cost of producing 100 units • C(Q) = 25000 + Q2 = 25000+10000 = $35,000

• Revenues: • PQ = (200)(100) = $20,000

• Maximum profits of Π = -$15000 , but that loss is less than the fixed

cost of $25000 • Implications: Produce Q = 100 in short run, but expect exit in the

long-run

b and c. Apple is a Monopolist or a Monopolistic Competitor • MR = 400 - 6Q (since P = 400 - 3Q) • Set MR = MC, or 400 - 6Q = 2Q

• Optimal output: Q = 50 = 400/8

• Optimal price: P = $250 = 400 - 3(50)

• Maximal profits: Π = -$15000 = PQ - C(Q) = (250)(50) -

(25000 + 2500), but that loss is less than the fixed cost of $25000

• Implications: Produce Q = 50 in short run, but expect exit in the long-run


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Comparing Markets Question. Consider the cost function C(Q) = 25000 + 4Q2 for Amazon to produce the new Kindle e-book reader. Using that cost function for the Kindle, determine the profit-maximizing output and price for the Kindle, and discuss its long-run implications, under three alternative scenarios:

a. Amazon’s Kindle is a perfect substitute with the Barnes & Noble Nook and several other e-book readers that have similar cost functions and that currently sell for $400 each

b. Amazon’s Kindle has no substitutes and so is a monopolist, and the inverse demand for the Kindle is expected to forever be P = 1200 – 2Q

c. Amazon’s Kindle currently has no substitutes, and currently the inverse demand for the Kindle is P = 1200 – 2Q, but Amazon anticipates other firms to produce close substitutes in the future


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Answer to Question:


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a. Amazon is a Price Taker in Perfect Competition. • MC = 8Q

• MR = P = $400

• Set MR = MC • 400 = 8Q

• Q = 50 units

• Cost of producing 50 units • C(Q) = 25000 + 4Q2 = 25000+10000 = $35,000

• Revenues: • PQ = (400)(50) = $20,000

• Maximum profits of Π = -$15000 , but that loss is less than the fixed

cost of $25000 • Implications: Produce Q = 50 in short run, but expect exit in the long-

run

b and c. Amazon is a Monopolist or a Monopolistic Competitor • MR = 1200 - 4Q (since P = 1200 - 2Q) • Set MR = MC, or 1200 - 4Q = 8Q

• Optimal output: Q = 100

• Optimal price: P = $1000 = 1200 - 2(100)

• Maximal profits:

• Π = +$35,000 = PQ - C(Q) = (1000)(100) -(25000 +

4(10000)) • Implications

• In Senario b, Amazon is a monopolist, and so will never face entry and so its price and profit remain.

• In Senario c, Amazon is a monopolistically-competitive firm that should expect other firms to clone (produce close substitutes) in the future, so profits will decline to zero in the future.


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Comparing Markets Question. Consider the cost function C(Q) = 25000 + 100Q + Q2 for Amazon to produce the new Kindle e-book reader. Using that cost function for the Kindle, determine the profit-maximizing output and price for the Kindle, and discuss its long-run implications, under three alternative scenarios:


b. Amazon’s Kindle has no substitutes and so is a monopolist, and the demand for the Kindle is expected to forever be Q = 800 – 2P

c. Amazon’s Kindle currently has no substitutes, and currently the demand for the Kindle is Q = 800 – 2P, but Amazon anticipates other firms to produce close substitutes in the future


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Answer to Question: a. Amazon is a Price Taker in Perfect Competition. • MC = 100 + 2Q • MR = P = $300 • Set MR = MC

• 100 + 2Q = 300 • Q = 100 units

• Cost of producing 100 units • C(Q) = 25000 + 100Q + Q2 = 25000+10000+10000 = $45,000

• Revenues: • PQ = (300)(100) = $30,000

• Maximum profits of -$15000, but that loss is less than the fixed cost of $25000


b and c. Amazon is a Monopolist or a Monopolistic Competitor • MR = 400 - Q (since Q = 800 – 2P and P = 400 - .5Q) • Set MR = MC, or 400 - Q = 100 + 2Q

• Optimal output: Q = 100 • Optimal price: P = 400 - .5(100) = $350 • Maximal profits:

• PQ - C(Q) = (350)(100) - (25000+10000+10000) = -$10,000, but that loss is less than the fixed cost of $25000



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Comparing Markets Question. Consider the cost function C(Q) = 600 + 100Q + 5Q2 for Amazon to produce the new Kindle e-book reader. Using that cost function for the Kindle, determine the profit-maximizing output and price for the Kindle, and discuss its long-run implications, under three alternative scenarios:


b. Amazon’s Kindle has no substitutes and so is a monopolist, and the demand for the Kindle is expected to forever be Q = 40 – (1/5)P

c. Amazon’s Kindle currently has no substitutes, and currently the demand for the Kindle is Q = 80 – (1/5)P, but Amazon anticipates other firms can develop close substitutes in the future.


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Answer to Question: a. Amazon is a Price Taker in Perfect Competition. MC = 100 + 10Q MR = P = $200 Set MR = MC 100 + 10Q = 200 Q = 10 units Cost of producing 10 units C(Q) = 600 + 100Q + 5Q2 = 600+100(10)+5(100) = $2,100 Revenues: PQ = (200)(10) = $2,000 Maximum profits of -$100, which is negative but less than the fixed cost of $600. Implications: Produce Q = 10 in short run, but expect exit in the long-run. b. Amazon is a Monopolist. MR = 200 - 10Q (since Q = 40 – (1/5)P and P = 200 - 5Q) Set MR = MC, or 200 - 10Q = 100 + 10Q Optimal output: Q = 5 Optimal price: P = 200 - 5(5) = $175 Maximal profits: PQ - C(Q) = (175)(5) - (600+100(5)+5(25)) = -$350, which is negative but less than the fixed cost of $600. Implications: Produce Q = 5 in short run, but expect exit in the long-run

c. Amazon is a Monopolistic Competitor MR = 400 - 10Q (since Q = 80 – (1/5)P and P = 400 - 5Q) Set MR = MC, or 400 - 10Q = 100 + 10Q Optimal output: Q = 15 Optimal price: P = 400 - 5(15) = $325 Maximal profits: PQ - C(Q) = (325)(15) - (600+100(15)+5(225)) = $1,650, which is positive so expect other firms to enter in the long-run until demand drops enough so that profit drops to zero.


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Comparing Markets Question. Consider the cost function C(Q) = 600 + 100Q + 5Q2 for Amazon to produce the new Kindle e-book reader. Using that cost function for the Kindle, determine the profit-maximizing output and price for the Kindle, and discuss its long-run implications, under three alternative scenarios:


b. Amazon’s Kindle has no substitutes and so is a monopolist, and the demand for the Kindle is expected to forever be Q = 32 – (1/5)P

c. Amazon’s Kindle currently has no substitutes, and currently the demand for the Kindle is Q = 80 – (1/5)P, but Amazon anticipates other firms can develop close substitutes in the future.


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Answer to Question: a. Amazon is a Price Taker in Perfect Competition. MC = 100 + 10Q MR = P = $150 Set MR = MC 100 + 10Q = 150 Q = 5 units Cost of producing 5 units C(Q) = 600 + 100Q + 5Q2 = 600+100(5)+5(5) = $1,225 Revenues: PQ = (150)(5) = $750 Maximum profits of -$475, which is negative but less than the fixed cost of $600. Implications: Produce Q = 5 in short run, but expect exit in the long-run. b. Amazon is a Monopolist. MR = 160 - 10Q (since Q = 32 – (1/5)P and P = 160 - 5Q) Set MR = MC, or 160 - 10Q = 100 + 10Q Optimal output: Q = 3 Optimal price: P = 160 - 5(3) = $145 Maximal profits: PQ - C(Q) = (145)(3) - (600+100(3)+5(9)) = -$510, which is negative but less than the fixed cost of $600. Implications: Produce Q = 3 in short run, but expect exit in the long-run

c. Amazon is a Monopolistic Competitor MR = 400 - 10Q (since Q = 80 – (1/5)P and P = 400 - 5Q) Set MR = MC, or 400 - 10Q = 100 + 10Q Optimal output: Q = 15 Optimal price: P = 400 - 5(15) = $325 Maximal profits: PQ - C(Q) = (325)(15) - (600+100(15)+5(225)) = $1,650, which is positive so expect other firms to enter in the long-run until demand drops enough so that profit drops to zero.


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Comparing Markets Question. Consider the cost function C(Q) = 600 + 100Q + 5Q2 for Apple to produce the new iPhone 5 smart phone. Using that cost function for the iPhone 5, determine the profit-maximizing output and price for the iPhone 5, and discuss its long-run implications, under three alternative scenarios:

a. Apple’s iPhone 5 is a perfect substitute with RIM’s BlackBerry Bold 9700 and several other smart phones that have similar cost functions and that currently sell for $300 each

b. Apple’s iPhone 5 has no substitutes and so is a monopolist, and the demand for the iPhone 5 is expected to forever be Q = 32 – (1/5)P

c. Apple’s iPhone 5 currently has no substitutes, and currently the

demand for the iPhone 5 is Q = 80 – (1/5)P, but Apple anticipates other firms can develop close substitutes in the future.


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Answer to Question: a. Apple is a Price Taker in Perfect Competition. MC = 100 + 10Q MR = P = $300 Set MR = MC 100 + 10Q = 300 Q = 20 units Cost of producing 20 units C(Q) = 600 + 100Q + 5Q2 = 600+100(20)+5(400) = $4,600 Revenues: PQ = (300)(20) = $6,000 Maximum profits of $1,400, which is positive so expect other firms to enter in the long-run until price (demand) drops enough so that profit drops to zero. Implications: Produce Q = 20 in short run, but expect entry in the long-run. b. Apple is a Monopolist. MR = 160 - 10Q (since Q = 32 – (1/5)P and P = 160 - 5Q) Set MR = MC, or 160 - 10Q = 100 + 10Q Optimal output: Q = 3 Optimal price: P = 160 - 5(3) = $145 Maximal profits: PQ - C(Q) = (145)(3) - (600+100(3)+5(9)) = -$510, which is negative but less than the fixed cost of $600. Implications: Produce Q = 3 in short run, but expect exit in the long-run

c. Apple is a Monopolistic Competitor MR = 400 - 10Q (since Q = 80 – (1/5)P and P = 400 - 5Q) Set MR = MC, or 400 - 10Q = 100 + 10Q Optimal output: Q = 15 Optimal price: P = 400 - 5(15) = $325 Maximal profits: PQ - C(Q) = (325)(15) - (600+100(15)+5(225)) = $1,650, which is positive so expect other firms to enter in the long-run until demand drops enough so that profit drops to zero.


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Comparing Markets Question. Consider the cost function C(Q) = 300 + 20Q + 4Q2 for Apple to produce the new iPhone 5 smart phone. Using that cost function for the iPhone 5, determine the profit-maximizing output and price for the iPhone 5, and discuss its long-run implications, under three alternative scenarios:

a. Apple’s iPhone 5 is a perfect substitute with RIM’s BlackBerry Bold 9700 and several other smart phones that have similar cost functions and that currently sell for $200 each

b. Apple’s iPhone 5 has no substitutes and so is a monopolist, and the demand for the iPhone 5 is expected to forever be Q = 4 – 0.02P

c. Apple’s iPhone 5 currently has no substitutes, and currently the

demand for the iPhone 5 is Q = 4 – 0.02P, but Apple anticipates other firms can develop close substitutes in the future.


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Answer to Question: a. The firm is a Price Taker in Perfect Competition. MC = 20 + 8Q MR = 200 Set MR = MC to compute Q = 22.50 Price at that quantity Q is P = 200. Revenue at Q is PQ = 4500 Cost at Q is C(Q) = 2775 Maximum profit at Q is Π = 1725. Since profit is positive, expect other firms to enter in the long-run until price (demand) drops enough so that profit drops to zero. Implications: Produce Q > 0 in short run, but expect entry in the long-run and you produce less Q. b. The firm is a Monopolist with inverse demand P = 200 – 50Q So, MR = 200 - 100Q Set MR = MC to compute Q = 1.67 Price at that quantity Q is P = 116.67 Revenue at Q is PQ = 194.44 Cost at Q is C(Q) = 344.44 Maximum profit at Q is Π = -150. Since profit is negative, expect other firms to exit in the long-run until price (demand) rises enough so that profit rises to zero. Implications: Produce Q > 0 in short run, but either exit yourself or expect exit by others in the long-run and you produce more Q.


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c. The firm is a Monopolistic Competitor with same results as in Part b.


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Comparing Markets Question. Consider the cost function C(Q) = 800 + 2Q + 12Q2 for Google to produce the new Google Glass wearable computer. Using that cost function for the Google Glass, determine the profit-maximizing output and price for the Google Glass, and discuss its long-run implications, under three alternative scenarios:

a. Google’s Google Glass is a perfect substitute with WIMM Labs’s Smartwatch and several other wearable computers that have similar cost functions and that currently sell for $700 each.

b. Google’s Google Glass has no perfect substitutes, and the demand for the Google Glass is expected to forever be Q = 12 – 0.02P

c. Google’s Google Glass currently has no perfect substitutes, and

currently demand for the Google Glass is Q = 12 – 0.04P, but Google anticipates other firms can develop close substitutes in the future.


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Answer to Question: a. The firm is in Perfect Competition. Solve for Perfect Competition with inverse demand



MC = 2 + 24 Q



P = 700.00

Π = 9350.08 Since profit is positive, expect other firms to enter in the long-run until price (demand) drops enough so that profit drops to zero. Implications: Produce Q > 0 in short run, but expect entry in the long-run and you produce less Q.


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b. The firm is a Monopolist. Solve the Uniform Price Monopoly with demand




MC = 2 + 24 Q



P = 358.87

Π = 641.95 Since profit is positive, expect other firms to want to enter in the long-run, but they cannot, so nothing changes.


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c. The firm is a Monopolistic Competitor. Solve the Uniform Price Monopoly with demand




MC = 2 + 24 Q



P = 199.32

Π = -199.97 Since profit is negative, expect other firms to exit in the long-run until price (demand) rises enough so that profit rises to zero. Implications: Produce Q > 0 in short run, but either exit yourself or expect exit by others in the long-run and you produce more Q.


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Comparing Markets Question. Consider the cost function C(Q) = 900 + 40Q + 20Q2 for Apple Computer to produce the new iPad. Using that cost function for the iPad, determine the profit-maximizing output and price for the iPad, and discuss its long-run implications, under three alternative scenarios:

a. Apple Computer’s iPad is a perfect substitute with the HP Slate and several other tablet PCs that have similar cost functions and that currently sell for $300 each

b. Apple Computer’s iPad has no substitutes and so is a monopolist, and the demand for the iPad is expected to forever be Q = 12 – 0.02P

c. Apple Computer’s iPad currently has no substitutes, and currently the

demand for the iPad is Q = 20 – 0.04P, but Apple anticipates other firms may produce gross substitutes in the future


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Answer to Question: a. Apple is a Price Taker in Perfect Competition.

Solve for Perfect Competition with inverse demand



MC = 40 + 40 Q



P = 300.00

Π = -55.00 Maximum profits of -$55, but that loss is less than the fixed cost of $900, so produce Q = 6.5 in short run, but expect exit in the long-run.


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b. Apple is a Monopolist. Solve the Uniform Price Monopoly with demand




MC = 40 + 40 Q



P = 400.00

Π = 220.00 Maximum profits of $220, but Apple is a monopolist, and so will never face entry and so its price and profit remain.


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c. Apple is a Monopolistic Competitor. Solve the Uniform Price Monopoly with demand




MC = 40 + 40 Q



P = 372.22

Π = 275.56 Maximum profits of $275.56, but Apple is a monopolistically-competitive firm that should expect other firms to clone (produce gross substitutes) in the future, so profits will decline to zero in the future.

Documents

Lesson Topics - Pepperdine Universityseaver-faculty.pepperdine.edu/jburke2/ba445/PowerP1/... · · 2014-02-18Lesson Topics. Monopolistic Price and ... for Apple Computers is given