Ch9_Q&A

1 Chapter 9: Pricing Strategies (Suggested Questions) Question 1 A firm’s total cost function is TC = 8Q . The market demand function is Q = 20 – 0.5P. a) If the firm uses a single-pricing strategy : • W hat are the firm’s profit -maximizing output (Q S ) and price (P S )? • Determine the consumer surplus (CS), producer surplus (PS), total surplus (TS), and deadweight loss (DWL). b) If the firm uses a perfect price discrimination: • What is the firm’s profit -maximizing output (Q D )? • Determine the consumer surplus (CS), producer surplus (PS), total surplus (TS), and deadweight loss (DWL). Solution: a) A single price strategy Q S = 8 units, P S = $24, CS = $64, PS = $128, TS = CS + PS = $192, DWL = $64. b) A perfect price discrimination Q D = 16 units, CS = 0, PS = $256, TS = CS + PS = $256, DWL = 0.

2 Question 2 A firm sells its product to a market consisting of 1000 identical customers. The market demand for the product is Q = 10 – 2P . The firm has a constant marginal cost of $1 and no total fixed cost. To boost its total profit, the firm employs a two-part pricing strategy. (a) What will be the entry fee (A)? (b) What is the total profit (π)? Solution: (a) A = $16. (b) π = $16000.

4 Question 4 Consider the following scenario: A firm encounters two demand functions: • Strong demander: P S = 30 – Q S . • Weak demander: P W = 20 – Q W . The firm's marginal cost is $10, and there are no total fixed costs. To boost its total profit, the firm is considering a two-part pricing strategy. In this simplified setting, there is only one strong demander and one weak demander present in the market. a) If the firm assumes that there is only strong demander in the market , what will be the entry fee (A), price of the product (P), and total profit (π)? b) If the firm assumes that there are both strong and weak demanders in the market and sets P = MC , what will be the entry fee (A), price of the product (P), and total profit (π)? c) If the firm assumes that there are both strong and weak demanders in the market and sets P > MC , what will be the entry fee (A), price of the product (P), and total profit (π)? d) What would be the best option for the firm to select? Solution: e) A = $200, P = $10 , π = $ 200. f) A = $50, P = $10 , π = $ 100. g) A = $12.5, P = $15 , π = $ 125. h) The firm should select assumption (a) that yields the highest total profit.

5 Question 5 Consider the following scenario: A firm encounters two demand functions: • Strong demander: P S = 8 – Q S . • Weak demander: P W = 6 – Q W . The firm's marginal cost is $2, and there are no total fixed costs. In this simplified setting, only one strong demander and one weak demander are present in the market. To boost its total profit, the firm employs a two-part pricing strategy. (a) What would be the optimal entry fee (A*)? (b) What is the optimal price of the product (P*)? Solution: (a) A* = $18. (b) P* = $2.

7 Question 7 A firm sells its product in two groups of customers: A and B. The market demand functions in the two groups are as follows: Group A: Q A = 55 – 0.5P A . Group B: Q B = 100 – 2P B . The total cost is TC = 20 + 10Q , where Q = Q A + Q B . (a) If the firm can prevent resale , what are the profit-maximizing prices in Group A and Group B, respectively? (b) If the firm cannot prevent resale , what is the profit-maximizing price? Solution: (a) P A * = $60. P B * = $30. (b) P* = $36. Question 8 Taylor Swift is planning to hold the Eras Tour in Montreal, Canada. An analysis of the ticket demand for her concert has provided the following market demand functions: • The standing audience demand: Q 1 = 𝟓??? ? −?.𝟓 . • The sitting audience demand: Q 2 = 𝟓?? ? −𝟓 . Given a marginal cost of $40 per ticket, what is the profit-maximizing price of a standing ticket (P 1 ) and a sitting ticket (P 2 )? Solution: • P 1 = $120. • P 2 = $50.

8 Question 9 Olivia Rodrigo plans to hold the Guts World Tour in Montreal, Canada. An analysis of the ticket demand for her concert has provided the following demand functions: • The standing audience demand: Q 1 = 𝟓??? ? −?.𝟓 . • The sitting audience demand: Q 2 = 𝟓?? ? −𝟓 . If the price for a standing ticket (P 1 ) is $120, what is the profit-maximizing price for a sitting ticket (P 2 )? Solution: • P 2 = $50. Question 10 The firm has estimated the following demand functions for Peak and Off-peak demand car users: Peak demand: Q P = 500 – 50P P . Off-peak demand: Q OP = 100 – 20P OP . where P is the fee charged and Q is the number of cars crossing the bridge per minute. The marginal cost of operating the bridge is $2 per car. The peak capacity of the bridge has been estimated at 50 cars per minute. (a) What is profit-maximizing fee during Peak (P P *)? (b) What is profit-maximizing fee during Off-peak (P OP *)? Solution (a) P P * = $9. (b) P OP * = $3.5.

10 Solution: (a)  D = TR D – TC D – P U Q = (20,000 - Q)Q – 8000Q - P U Q U .  U = P U Q U – TC U = P U Q U - 2Q U 2 .  =  D +  U = (20,000 - Q)Q – 8000Q – 2Q U 2 There is no external market, i.e., Q U = Q. Substituting Q U = Q. into the total profit function.  = (20,000 - Q)Q – 8000Q – 2Q 2 = 12000Q – 3Q 2 . (b) Q* = Q U * = 2000 units. (c) P* = $18000. (d) PU* = $8000. (e) •  D = P*Q* – TC D – P U ∗ Q U ∗ = 18,000(2,000) - 8,000(2,000) – 8,000(2,000).  D = $4,000,000. •  U = P U ∗ Q U ∗ - 2 (Q U ∗ ) 2 = (8,000)(2,000) - 2(2,000) 2 = $8,000,000. •  =  D +  U = $4,000,000 + $8,000,000 = $12,000,000.

11 Question 12 The Tesla Model Y is an electric car produced and sold by Tesla Inc. The marketing division (i.e., the downstream division) estimates that the market demand function of Model Y is Q = 80 – 0.5P , where Q is the quantity of Model Y demanded, and P is the price per unit of Model Y. The total cost of assembling and selling Model Y to customers is TC D = 2Q + 200 . Each Model Y requires 1 structural battery pack. The structural battery pack is produced by the manufacturing division (i.e., the upstream division). The total cost function for producing a structural battery pack is ?𝐂 ? = ?. 𝟓? ? ? + 𝟖? ? + 𝟓? , where Q U is the quantity of battery packs produced per period. There is no external market. All costs and price units are in thousands (don’t put “000” in the functions). Also, all cost and demand functions are per period. (a) Determine the profit-maximizing quantity of Model Y (Q*), quantity of structural battery packs ( Q U ∗ ) and price of a Model Y (P*). (b) Determine the optimal transfer price ( P U ∗ ). (c) Determine the profit earns by the downstream division (  D ). Solution: (a) Q* = Q U ∗ = 30 units. P* = $100. (b) P U ∗ = $38. (c)  D = $1600.

13 Question 14 A firm sells two goods, Good 1 and Good 2, to a market. There are three groups of customers with reservation prices as follows: Reservation Price ($) Consumer Good 1 Good 2 A 40 13 B 49 3 C 3 30 The marginal costs of Good 1, Good 2, and a bundle are as follows: MC 1 = $5, MC 2 = $5, and MC B = $10. If the firm employs a bundling strategy, (a) Determine the optimal prices and total profit of a separate pricing strategy. (b) Determine the optimal prices and total profit for a pure bundling strategy. (c) Determine the optimal prices and total profit for a mixed bundling strategy. Solution: (a) Separate Pricing: P 1 = $40, P 2 = $30, π S = $95. (b) Pure Bundling: P B = $52, π B = $84. (c) Mixed Bundling: P 1 = $49, P 2 = $30, P B = $53, π M = $112.

14 Question 15 You are selling two goods, Good 1 and Good 2, to a market. There are three groups of consumers with reservation prices as follows: Reservation Price ($) Consumer Good 1 Good 2 A 60 10 B 40 35 C 24 40 The marginal costs of Good 1, Good 2, and a bundle are as follows: MC 1 = $10, and MC 2 = $10, and MC B = $20. If the firm utilizes a bundling strategy, a) Determine the optimal prices and total profit of a separate pricing strategy. b) Determine the optimal prices and total profit for a pure bundling strategy. c) Determine the optimal prices and total profit for a mixed bundling strategy. Solution: a) Separate Pricing: P 1 = $40, P 2 = $35 , π S = $110. b) Pure Bundling: P B = $64 , π B = $132. c) Mixed Bundling: P 1 = $60, P 2 = $40, P B = $75 , π M = $135.