In 1-2 pages, answer the questions described in the PDF here:

• AssignmentDescription1.pdf

Analytical Exercise: Equilibrium in an Oligopoly Market with Capacity Constraints Consider the economic environment we encountered in the online exercise on Monday, in which a set of firms engage in Bertrand competition in four distinct markets. Each firm produces a homogeneous good at a constant marginal cost = 4, up to a capacity constraint which determines each firm's maximum production. The firms compete in prices: each firm posts a price in each market, where prices must be in whole numbers. Capacity constraints and fixed costs of production vary by market according to the schedule below: Market 1: Capacity = 1000 per firm, no fixed cost of production; Market 2: Capacity = 1000 per firm, fixed cost = 35,000 per firm; Market 3: Capacity = 400 per firm, fixed cost = 35,000 per firm; Market 4: Capacity = 2000 per firm, fixed cost = 35,000 per firm. Demand is identical across markets and described by the schedule on the right (also provided in more detail in the Excel file attached). Consumers buy first from the firm with the lowest price until its capacity is exhausted, then buy from the firm with the second-lowest firm, and so on until no additional consumer wishes to purchase at the lowest price charged among firms with remaining free capacity. If two (or more) firms post the same price, they split the remaining quantity demanded at that price, after any firm charging a lower price has already sold the total quantity it can produce. You observe data on prices and quantities for a five-firm oligopoly in these four markets, given below (generated from play in our inclass exercise on Monday). In this particular market, it appears that four of the five firms are competing actively, while one firm (Firm 3) is playing passively. Let us say that the passive Firm 3 is a "Nonprofit," while the remaining four firms are "For-profit." Using the models of oligopoly behavior we have discussed, your assignment is to analyze the behavior of the four "For-profit" firms in this market, taking the prices of the "Nonprofit" as given. Assignment: In 1-2 pages, provide written answers to the following questions. 1. Analyze the Nash equilibrium of the pricing game between the four For-Profit players in each of the four markets above, taking the price charged by the Nonprofit (Firm 3) in each market as given. Based on this analysis, what theoretical predictions can you make about the price in each market? Market Demand Schedule Price Quantity 10 5120 20 4620 30 4190 40 3810 50 3470 60 3160 70 2880 80 2610 90 2360 100 2120 110 1890 120 1670 2. How do the observed prices charged by the four "For-profit" players compare with the Nash equilibrium predictions in Part 1? Which Nash equilibrium predictions are borne out in the data? Which predictions are not? In your answer to Question 1, it may be helpful to consider the following: Should unavoidable fixed costs matter for Nash equilibrium prices? Why or why not? (Note: By "unavoidable", we mean that firms cannot leave the market this period.) If there were no capacity constraints, and ignoring the fact that price must be an integer, what would be the Nash equilibrium price in each market? How do capacity constraints change our predictions about prices in each market? How would we expect prices to be ranked with high, medium, and low capacity constraints? Consider any potential price in the demand schedule below. Suppose that Firm 1's three for-profit rivals each charge this price (holding the Nonprofit's price fixed at its observed value). Consider two strategies for Firm 1: "matching" the price charged by its active rivals by setting . = , or "undercutting" all three active rivals by reducing price by $1 to . = 1. Bearing in mind Firm 1's capacity constraints, what is the *highest* price on the demand schedule at which Firm 1 prefers to match than undercut? How does this price vary with the capacity constraint ? And what does this tell you about Nash equilibrium prices in each market? [Hint: For a price to be a symmetric Nash equilibrium, it must be that no for-profit firm prefers to undercut when all for-profit rivals charge the given price. In this particular game there may in general be many Nash equilibria, but from the firms' perspective the best equilibrium will be the one with the highest price.] Evaluation: This assignment will count for 10 percent of your final course grade. In your answers, I will be looking for a clear discussion of both the key economic and strategic issues governing competition in this market, and how predictions of the underlying theory fit (or don't!) the actual prices observed. Note that data *will not* line up with theory on every dimension, although in some key dimensions it should. Long answers are not necessarily better; the key is to identify and analyze the core questions involved. Submissions are due via Canvas at midnight on Friday, April 10. Late submissions will receive a one letter grade penalty for each day late. Data on outcomes for each market is provided on the next page. Market 1: Moderate capacity, no fixed costs Firm Price Sales Capacity Revenues Variable Costs Fixed Costs Profit 1 39 1000 1000 39,000 4,000 0 35,000 2 40 889 1000 35,560 3,556 0 32,004 3 62 0 1000 0 0 0 0 4 38 1000 1000 38,000 4,000 0 34,000 5 40 950 1000 38,000 3,800 0 34,200 Market 2: Moderate capacity with fixed costs Firm Price Sales Capacity Revenues Variable Costs Fixed Costs Profit 1 42 1000 1000 42000 4000 35000 3000 2 43 887 1000 38141 3548 35000 -407 3 60 0 1000 0 0 35000 -35000 4 41 1000 1000 41000 4000 35000 2000 5 43 844 1000 36292 3376 35000 -2084 Market 3: Low capacity with fixed costs Firm Price Sales Capacity Revenues Variable Costs Fixed Costs Profit 1 119 317 400 37723 1268 35000 1455 2 110 400 400 44000 1600 35000 7400 3 82 400 400 32800 1600 35000 -3800 4 110 400 400 44000 1600 35000 7400 5 118 400 400 47200 1600 35000 10600 Market 4: High capacity with fixed costs Firm Price Sales Capacity Revenues Variable Costs Fixed Costs Profit 1 18 2000 2000 36000 8000 35000 -7000 2 19 375 2000 7125 1500 35000 -29375 3 63 0 2000 0 0 35000 -35000 4 17 2000 2000 34000 8000 35000 -9000 5 19 365 2000 6935 1460 35000 -29525

• DemandSchedule1.xlsx

Detailed Demand Schedule Price Quantity 10 5120 15 4870 20 4620 25 4400 30 4190 35 3990 40 3810 45 3640 50 3470 55 3320 60 3160 65 3020 70 2880 75 2740 80 2610 85 2480 90 2360 95 2230 100 2120 105 2000 110 1890 115 1780 120 1670 125 1560 130 1460 135 1350 140 1250 145 1160 150 1060 155 960 160 870 165 780 170 680 175 590 180 510 185 420 190 330 195 240 200 160 205 80 210 0

Analytical Exercise: Equilibrium in an Oligopoly Market with Capacity Constraints Consider the economic environment we encountered in the online exercise on Monday, in which a set of firms engage in Bertrand competition in four distinct markets. Each firm produces a homogeneous good at a constant marginal cost = 4, up to a capacity constraint which determines each firm's maximum production. The firms compete in prices: each firm posts a price in each market, where prices must be in whole numbers. Capacity constraints and fixed costs of production vary by market according to the schedule below: Market 1: Capacity Market 2: Capacity Market 3: Capacity Market 4: Capacity = 1000 per firm, no fixed cost of production; = 1000 per firm, fixed cost = 35,000 per firm; = 400 per firm, fixed cost = 35,000 per firm; = 2000 per firm, fixed cost = 35,000 per firm. Demand is identical across markets and described by the schedule on the right (also provided in more detail in the Excel file attached). Consumers buy first from the firm with the lowest price until its capacity is exhausted, then buy from the firm with the second-lowest firm, and so on until no additional consumer wishes to purchase at the lowest price charged among firms with remaining free capacity. If two (or more) firms post the same price, they split the remaining quantity demanded at that price, after any firm charging a lower price has already sold the total quantity it can produce. You observe data on prices and quantities for a five-firm oligopoly in these four markets, given below (generated from play in our inclass exercise on Monday). In this particular market, it appears that four of the five firms are competing actively, while one firm (Firm 3) is playing passively. Let us say that the passive Firm 3 is a \"Nonprofit,\" while the remaining four firms are \"For-profit.\" Using the models of oligopoly behavior we have discussed, your assignment is to analyze the behavior of the four \"For-profit\" firms in this market, taking the prices of the \"Nonprofit\" as given. Market Demand Schedule Price Quantity 10 5120 20 4620 30 4190 40 3810 50 3470 60 3160 70 2880 80 2610 90 2360 100 2120 110 1890 120 1670 Assignment: In 1-2 pages, provide written answers to the following questions. 1. Analyze the Nash equilibrium of the pricing game between the four For-Profit players in each of the four markets above, taking the price charged by the Nonprofit (Firm 3) in each market as given. Based on this analysis, what theoretical predictions can you make about the price in each market? 2. How do the observed prices charged by the four \"For-profit\" players compare with the Nash equilibrium predictions in Part 1? Which Nash equilibrium predictions are borne out in the data? Which predictions are not? In your answer to Question 1, it may be helpful to consider the following: Should unavoidable fixed costs matter for Nash equilibrium prices? Why or why not? (Note: By \"unavoidable\