Final Exam, Winter 2024
ECON 445
20 April 2024
The exam has a total of 100 points. Please answer all questions.
Students are not permitted to engage in group work or collaborate with other students on this exam. Collaboration on exams is a violation of academic integrity.
1 Short Questions (20 pts)
Provide brief answers to each of the following questions (ideally no more than three to four sentences).
1. (4 pts) A price-setting dominant firm (firm 1) operates in a market produc- ing a homogenous good, but faces competition from a competitive fringe. The supply curve of the fringe firms is given by S(p) = 2p. You don’t know exactly what the demand curve is or the dominant firm’s marginal cost, but you do know that in the 2023 equilibrium, the dominant firm has a market share of 70%.
However in 2024, the dominant firm decides to exit the industry, so con- sumers can only buy from the competitive fringe. Will prices in 2024 decrease, increase or stay the same compared to 2023? Briefly explain the reasoning behind your answer.
2. (4 pts) Firms in an industry produce a homogeneous good. You have data on prices P, quantity Q, a demand shifter y and a cost shifter w. The demand curve is linear, and marginal costs are constant. Based on this information, is it possible to estimate the conduct parameter λ? Why or why not?
3. (4 pts) Consider the following game, where player 1 can choose between T, M, and B; while player 2 chooses beween L, C and R. The table below shows the payoffs to the players from each pair of actions. For example if player 1 chooses T and player 2 chooses L, player 1 gets a payoff of 1 and player 2 gets a payoff of 7.
Player 2
L C R
T 1,7 3,3 4,2
Player 1 M 5,0 4,2 8,1
B 7,2 3,1 2,9
Find all the pure-strategy Nash equilibria of this game.
4. (4 pts) An industry consists of two firms producing an identical good, with demand curve D(p) and identical marginal costs c. Both firms are capacity-constrained, with each firm having capacity K, where K > D(c). The firms compete in prices.
What would happen to the equilibrium price and quantity if firm 1 were to invest in building more capacity? Explain your answer carefully but briefly.
5. (4 pts) Suppose the coffee shop in Terminal 3 of Toronto Pearson In- ternational Airport engages in monopoly pricing of lattes, with constant marginal cost c > 0. The price of a latte there is $8, and through diligent market research you discover that the elasticity of demand is -2 at that price. What is c?
2 Longer Questions
2.1 Bertrand competition with differences in pricing tech- nology (20 pts)
An industry consists of 2 firms that produce a homogeneous, identical good and compete in prices (Bertrand competition). Demand for the good equals D(p) = 40 -p where p is the price.
Firm 1 can produce at a constant marginal cost c1 , and chooses price p1 . Firm 2 can produce at a constant marginal cost c2 , and chooses price p2 . For now, let’s assume c1 = c2 = 4.
However, the two firms differ in their pricing technology.
(a) Firm 1 can set prices with exact precision, meaning they can set any price to the cent, such as $9.43 or $10.22 (but not, for example, a price of $9.437). (b) Firm 2 has a less precise pricing technology and can only set prices in the tens of cents. For instance, firm 2 can charge a price of $9.4 or $10.2, but it cannot set a price of $9.43 or $10.22.
Initially, assume the firms choose prices simultaneously.
1. (9 pts) Solve for all pure-strategy Nash equilibria of this game. What are the profits of each firm under each Nash equilibrium?
2. (5 pts) Suppose firm 1’s marginal cost equalled c1 = 4.05 instead. Find all pure-strategy Nash equilibria of this game.
3. (3 pts) Let’s go back to assuming c1 = c2 = 4. Suppose that the game was sequential: firm 2 gets to choose their price p2 first, and then firm 1 observes this price and chooses their own price p1 . Which of the Nash equilibria that you worked out in part (a) are subgame-perfect?
4. (3 pts) Going back to the simultaneous game with c1 = c2 = 4: suppose the products that the firms produced were differentiated. How do you think this will affect the Nash equilibria that you worked out in part (a)? Ex- plain the intuition behind your answer. (Note: you do not need to work out the new Nash equilibria).
2.2 Avocado price collusion (30 pts)
There are two producers of avocado: CaliCado, located in California; and ChileCado, located in Chile. Sometimes I will refer to CaliCado as firm 1 and ChileCado as firm 2.
For simplicity, we will divide each year into summer and winter as experi- enced in North America. Demand for avocados is stable across time, and is given by D(p) = 55 -p.
However, the cost of producing avocado differs by firm and by season. Specif- ically, the marginal cost of producing avocados equals c1 = 5 for CaliCado in summer (because that is the growing season in California), but equals c1 = 10 in winter. By contrast, the marginal cost of producing avocados equals c2 = 5 for ChileCado in “winter” (which is summer in Chile, and therefore the growing season) and equals c2 = 15 in summer. (See table below)
|
Producer
|
Summer
|
Winter
|
|
CaliCado, c1
|
$5
|
$10
|
|
ChileCado, c2
|
$15
|
$5
|
Table 1: Marginal cost of producing avocados for CaliCado and ChileCado by season
1. (4 pts) Non-cooperative Bertrand: Derive the equilibrium prices and quantities under Bertrand competition (i) during summer and (ii) during winter. What are the profits earned by each firm in summer and in winter?
2. (6 pts) Merger: Suppose CaliCado and ChileCado were able to merge with each other and form a joint monopoly (“CaCado”). What are the new equilibrium quantities and prices during (i) summer (ii) winter? What is the total profit of the merged firm (πm )? Do consumers benefit from the merger?
Collusion:
The US FTC blocks the merger of the two firms. So they decide instead to collude, using a grim trigger strategy. From now on, assume that the pricing game is repeated an infinite number of period (where each period or season is defined as a six-month length of time, either summer or winter). Each firm discounts their future profits by a discount factor δ that lies between 0 and 1.
The firms decide to collude and set the monopoly price and produce the monopoly quantity every period (that you derived in the previous ques- tion).
The firm adopt a grim trigger strategy to punish any firm that cheats on the agreement. If in any period t either firm ever deviates from the agreed prices, then both firms will revert back to Bertrand competition in all future periods.
3. (4 pts) Carefully describe a grim trigger collusive strategy for the infinitely repeated game. Make sure to specify prices and quantities in both summer and winter, and describe what the firms will do in the event that one firm deviates.
4. (4 pts) What is the discounted present value of profits for (i) CaliCado if it keeps colluding (ii) ChileCado if it keeps colluding? Work these out separately for winter and summer.
5. (4 pts) What is the discounted present value of profits for (i) CaliCado if it deviates from the collusive arrangement (ii) ChileCado if it deviates from the collusive arrangement? Again, work these out separately for winter and summer.
6. (5 pts) Under the collusive strategy you specified in part (3), for what values of δ will collusion be viable?
7. (3 pts) Suppose that δ is too low by some small amount. Describe what the two firms can do to preserve the collusive arrangement (you do not need to work out the exact prices they should charge).
2.3 Coffee Meets Bagel (25 pts)
You own a cafe where you sell two kinds of products (i) coffee (ii) bagels. Each morning, there are two types of consumers who visit the cafe. For simplicity assume the marginal cost of producing a coffee or a bagel is zero.
❼ Each type A consumer is willing to pay $6 per coffee, and is willing to buy 2 coffees; and is willing to pay $3 per bagel, and buy up to 2 bagels. There are 20 consumers of type A.
❼ Each type B consumer is willing to pay $2 per coffee, and will only buy at most one coffee; and is willing to pay $2 per bagel, and buy up to 4 bagels. There are 40 consumers of type B.
1. (2 pts) 3rd-degree price discrimination: Suppose that the cafe can engage in third-degree price discrimination in order to separate A and B. You can charge each consumer a different price for a cup of coffee, as well as a different price for a bagel. What prices should you charge to maximize revenue, and what is your maximum revenue?
2. (3 pts) Uniform pricing: Now suppose that you do not know which con- sumers are type A and which are type B, so that third-degree price dis- crimination is not possible. Initially you decide to charge a single price p1 for a cup of coffee, and a single price p2 for a bagel. What prices should you charge, and what is the revenue you earn from doing so?
3. (4 pts) All-You-Can-Drink: To boost revenue, you decide to offer an “all- you-can-drink” package for the coffee: if a customer pays for this option, they can drink as many cups of coffee as they want. What price should you charge for the (i) all-you-can-drink coffee package (ii) a single cup of coffee (iii) a single bagel? What is your new total revenue, and how does it compare with your revenue under uniform pricing? Explain.
4. (4 pts) All-You-Can-Eat: To boost revenue, you decide to offer an “all- you-can-eat” package for bagels: if a customer pays for this option, they can eat as many bagels as they want. What price should you charge for the (i) all-you-can-eat bagels package (ii) a single bagel (iii) a single cup of coffee? What is your new total revenue, and how does it compare with your revenue under uniform pricing? Explain.
5. (5 pts) Coffee Meets Bagel: Next, you decide to offer a “coffee-meets- bagel” combo: where if a customer pays for this option, they can get one bagel and one coffee. What price should you charge for the (i) “coffee- meets-bagel” combo (ii) a single bagel (iii) a single cup of coffee? What is your new total revenue, and how does it compare with your revenue under uniform pricing? Explain.
6. (7 pts) Can you come up with a pricing strategy for the cafe that would lead to a higher revenue than the strategies proposed in parts (2) - (5)? Explain your answer carefully. Hint: feel free to try different combos of coffees/bagels. Be creative!