Calculating Profit in the Two-Firm Price-Setting Game
In a symmetric two-firm price-setting game, a single firm's total profit is calculated by multiplying its per-unit profit by its share of the total market sales:
where is the chosen price, is the constant production cost per unit, and is the total market sales at price . Using the given parameters (), the profit per unit is $3 when the price is high ($4) and $1 when the price is low ($2).
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The Economy 2.0 Microeconomics @ CORE Econ
Ch.8 Supply and demand: Markets with many buyers and sellers - The Economy 2.0 Microeconomics @ CORE Econ
The Economy 2.0 Macroeconomics @ CORE Econ
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Payoff Matrix for the Two-Firm Price-Setting Game (Figure 8.20)
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Two firms, Firm 1 and Firm 2, sell an identical product and must simultaneously decide whether to set a high price or a low price. Their potential profits are shown in the matrix below, with Firm 1's profit listed first in each pair.
Firm 2: High Price Firm 2: Low Price Firm 1: High Price ($100, $100) ($0, $0) Firm 1: Low Price ($0, $0) ($50, $50) Why is the outcome where both firms choose a 'High Price' considered a stable equilibrium?
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Consider a market with two firms selling an identical product. Their price-setting interaction can be modeled as a game with two stable outcomes: one where both set a high price (leading to high profits for both) and one where both set a low price (leading to low profits for both). If the firms are currently in the high-price outcome, a single firm has a strong incentive to unilaterally lower its price to capture more market share and increase its individual profit.
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In a market with two firms selling an identical product, their simultaneous price-setting decisions can be represented by a game. Match each strategic element or outcome of this game with its correct description.
In a market with two firms selling an identical product, their price-setting interaction can be modeled as a game with two stable outcomes. The outcome where both firms set a high price is considered a __________ because neither firm can improve its own profit by changing its price, assuming the other firm's price remains high.
Two firms, Innovate Inc. and TechCorp, are the only producers of a specialized microchip. They must decide simultaneously whether to set a high price or a low price for their product. The table below shows the daily profits for each firm based on their combined decisions. The first number in each pair is Innovate Inc.'s profit, and the second is TechCorp's profit.
TechCorp: High Price TechCorp: Low Price Innovate Inc.: High Price ($200,000, $200,000) ($0, $0) Innovate Inc.: Low Price ($0, $0) ($80,000, $80,000) Based on this information, what is the primary strategic challenge these two firms face?
Two companies, AquaPure and HydroFresh, are the only sellers of a premium water filtration system. They must decide whether to price their systems high or low. The matrix below shows their potential weekly profits, with AquaPure's profit listed first in each pair.
HydroFresh: High Price HydroFresh: Low Price AquaPure: High Price ($50,000, $50,000) ($10,000, $70,000) AquaPure: Low Price ($70,000, $10,000) ($25,000, $25,000) In this scenario, an agreement for both firms to set a high price is unstable because each has an incentive to lower its price. Which of the following changes would most effectively transform this situation into one where both firms setting a high price is a stable outcome?
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Payoff Matrix for the Two-Firm Price-Setting Game (Figure 8.20)
Calculating Profit in the Two-Firm Price-Setting Game
Learn After
Following a sudden, sharp increase in the price of a primary raw material like cotton, a series of economic consequences unfolded for the British textile industry. Arrange the following events in the correct chronological sequence.
Two firms, Firm A and Firm B, are the only producers of an identical product. The cost to produce each unit is $1. If both firms agree to set a high price of $4 per unit, a total of 60 units will be sold in the market, with the sales split evenly between the two firms. What would Firm A's total profit be in this scenario?
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Two firms, operating as a duopoly, sell an identical product. The cost to produce each unit is $1. If both firms decide to set a low price of $2, the total market demand is 72 units, which they split equally. In this case, the total profit for a single firm would be $____.
Consider a market with two firms selling an identical product that costs $1 per unit to produce. If both firms set a high price of $4, they sell a total of 60 units. If they both set a low price of $2, they sell a total of 72 units. In both scenarios, sales are split evenly between the two firms.
Statement: A single firm earns a higher total profit when both firms set the low price because the increase in the number of units it sells outweighs the smaller profit earned on each unit.
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A market has two firms selling an identical product that costs $1 per unit to produce. They can either both set a high price of $4, resulting in 60 total units sold, or both set a low price of $2, resulting in 72 total units sold. In either case, sales are split evenly. Match each calculation component to its correct value for a single firm.
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Two firms, operating as a duopoly, sell an identical product. The cost to produce each unit is $1. If both firms decide to set a low price of $2, the total market demand is 72 units, which they split equally. In this case, the total profit for a single firm would be $____.