Ch9 Q&A - chapter 9 questions and answers PDF

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Chapter 9 Pricing Strategies (Suggested Questions) (from Chapter 9 by Allen et al., 2017)

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(from Chapter 9 by Allen et al., 2017)

P = 580 – (10/3)(85.8) = $294.

2

Price-Discriminating Profit (PD)

PD = TRC + TRM – TC = PCQC + PMQM – (410 + 8(QC + QM)) PD = ($251.5)(48.7) + ($379)(37.1) – (410 + 8(48.7 + 37.1)) PD = $25,212.55. Single-Price Profit (SP)

SP = TR – TC = PQ – (410 + 8Q) SP = ($294)(85.8) – (410 + 8(85.8)) SP = 24,128.8. This implies that the monopolist earns $1083.75 (π = SP - PD) less than when not allowed to price discriminate.

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(from Chapter 9 by Allen et al., 2017)

In this case, P = 2, Qw = 2, the entry fee = CS’s weak demander = (0.5)*2*(4-2)) = $2. So, the variable cost profit = 2*($2) = $4. Strategy 3: Charge a price greater than MC that maximized variable cost profit and charge an entry fee based on weak demand. In this case, P = $3, Q = 4. The entry fee = (0.5)(4 – P)(4 – P) = (0.5)(4 – $3)(4 – $3) = $0.5. Use fee = (Qs + Qw)(P – 2) = (10 – 2P)(P – 2) = (10 – 2($3))($3 – 2) = $4. So, the variable cost profit = 2(entry fee) + use fee = 2($0.5) + $4 = $5. Strategy 1 is the best alternative (highest variable cost profit). 4

(from Chapter 9 by Allen et al., 2017)

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Extra questions: A1) A monopoly book publisher with a constant marginal cost MC = $1 sells a novel in only two countries and faces linear inverse demand curves: P1 = 6 - (1/2)Q1 in Country 1 and P2 = 9 – Q2 in Country 2. a) What price would a profit-maximizing monopoly charge in each country with a ban against shipments between the countries (i.e., the firm can prevent resale)? b) If the firm cannot prevent resale, what would be the profit-maximizing output and price? Solution: a) Q1 = 5, P1 = $3.5 and Q2 = 4, P2 = $5 b) Q = 9 and P = $4.

A2) Suppose that Post Malone has scheduled the “Runaway Tour” concert in Montreal, Canada. A careful analysis of demand for tickets to his concert suggests that demand for standing audience is described by Q1 = 𝟓𝟎𝟎𝐏𝟏−𝟏.𝟓 while demand for sitting audience by Q2 = 𝟓𝟎𝐏𝟐−𝟓 . If the marginal cost of a ticket is $40, how should standing and sitting tickets to Post Malone’s concert be priced to maximize profits? Solution: •

Standing ticket price, P1 = $120.

•

Sitting ticket price, P2 = $50.

A3) Suppose that Post Malone has scheduled the “Runaway Tour” concerts in Montreal, Canada. A careful analysis of demand for tickets to his concert suggests that demand for standing audience is described by Q1 = 𝟓𝟎𝟎𝐏𝟏−𝟏.𝟓 while demand by sitting audience is Q2 = 𝟓𝟎𝐏𝟐−𝟓 . If the standing ticket price (P1) is $120, how should sitting ticket to Post Malone’s concerts be priced to maximize profits? Solution: •

Sitting ticket price, P2 = $50.

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(From Chapter 10, Allen et al., 2017)

Solution: a) Q* = 4300 units b) P* = $57 c) PU = $10

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(From Chapter 8, Allen et al., 2017)

Solution: •

A firm produces two units of good Y for each unit of good X. That is QY = 2QX.

a) π = PXQX + PYQY – TC = (400 – QX)QX + (300 – 3QY)QY – (500 + 3Q + 9Q2) Setting QY = 2QX, π = (400 – QX)QX + (300 – 3(2QX)) (2QX) – (500 + 3Q + 9Q2). Setting QX = Q; π = (400 – Q)Q + (300 – 3(2Q)) (2Q) – (500 + 3Q + 9Q2). π = 997Q – 500 – 22Q2. Finding Profit-maximizing output (Q*): dπ/dQ = 997 – 44Q = 0; Q* = 22.66. So, Q* = QX*= 22.66, and QY* = 2(QX*) = 2(22.66) = 45.32

b)

PX* = 400 – QX* = 400 – 22.66 = $377.34. PY* = 300 – 3QY* = 300 – 3(45.32) = $164.04.

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Extra Question: A3) Suppose that a firm jointly produces two goods. Good B is a by-product of the production of good A. The demand equations for the two goods are QA = 40,000 – 100PA. QB = 23,333.33 – 66.67PB. The firm’s total cost equation is TC = 2,000,000 + 50Q + 0.01Q2. (a) How many units of each product should the firm produce to maximize profit? (b) How much are the prices of the two products at maximum profit?

Solution: (a) Q* = QA = QB = 10,000 units. (b) PA = $300, PB = $200.

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(from Chapter 10 by Allen et al., 2017)

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Solution: There are three strategies. You have to do all strategies and select the optimal pricing strategy that is the most profitable. 1. Separate Pricing: In order to get maximum profit for this strategy, Kansas ticket price (Pk) = $40; Nowhere ticket price (Pn) = $30; total profit of separate pricing strategy = $95. 2. Pure Bundling: In order to get maximum profit for this strategy, the bundle price (Pb) = $52; total profit of pure bundling strategy = $84. 3. Mixed Bundling: for this strategy, there are many cases of setting prices. We will do only one case by assuming that one consumer buys Kansas ticket, one consumer buy Nowhere ticket, and one spectator buys a bundle. So, Pk = $49; Pn = $30; Pb = $53. Total profit of mixed bundling = $112. The optimal pricing strategy is “mixed bundling” because it is the most profitable.

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Extra Question A4) You are selling two goods, Good 1 and Good 2, to a market consisting of three consumers with reservation prices as follows: Reservation Price ($) Consumer

For 1(r1)

For 2 (r2)

A

60

10

B

50

40

C

30

50

Marginal costs (MC) of Good 1, Good 2, and a bundle are as follows: MC1 = $10 and MC2 = $10, MCB = $20. a) Determine the optimal prices and profits for selling the goods separately. b) Determine the optimal prices and profits for pure bundling. c) Determine the optimal prices and profits for mixed bundling. d) Which pricing strategy would you select? Why?

Answer: a) Separate Pricing: In order to get maximum profit for this strategy, P1 = $50, P2 = $40, and total profit of separate pricing, πS = $140. b) Pure Bundling: In order to get maximum profit for this strategy, PB = $70; total profit of pure bundling, πB = $150. c) Mixed Bundling: for this strategy, there are many cases of setting prices of Good 1, Good 2, and a bundle. We will do only one case by assuming at least one consumer buys Good 1, one consumer buys Good 2 and one consumer buys a bundle. The optimal prices are as follows: P1 = $60, P2 = $50, PB = $90 and total profit of mixed bunding, πM = $160. d) The optimal pricing strategy is “mixed bundling” because it is the most profitable.

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