Two firms compete by choosing price. Their demand functions are and Q₁ = 40-P₁ + P₂ Q₂ = 40 +P₁-P₂₁ where P₁ and P₂ are the prices charged by each firm, respectively, and Q₁ and Q₂ are the resulting demands. Note that the demand for each good depends only on the difference in prices; if the two firms colluded and set the same price, they could make that price as high a they wanted, and earn infinite profits. Marginal costs are zero. Suppose the two firms set their prices at the same time. Find the resulting Nash equilibrium. What price will each firm charge, how much will it sell, and what will its profit be? (Hint: Maximize the profit of each firm with respect to its price.) Each firm will charge a price of $ (Enter a numeric response rounded to two decimal places.) Each firm will produce units of output. In turn, each firm will earn profit of $ Suppose Firm 1 sets its price first and then Firm 2 sets its price. What price will each firm charge, how much will each sell, and what will be profits? Firm 1 will charge a price of $ Firm 2 will charge a price of $ Firm 1 will sell units and Firm 2 will sell units. Firm 1 will earn profit of $ and Firm 2 will earn profit of Suppose you are one of these firms and that there are three ways you could play the game: (i) Both firms set price at the same time: (ii) You set price first; or (iii) Your competitor sets price first. If you could choose among these options, which would you prefer? Explain why. You would choose O A. to set price simultaneously with the other firm to earn profit of $1.600.00.
Two firms compete by choosing price. Their demand functions are and Q₁ = 40-P₁ + P₂ Q₂ = 40 +P₁-P₂₁ where P₁ and P₂ are the prices charged by each firm, respectively, and Q₁ and Q₂ are the resulting demands. Note that the demand for each good depends only on the difference in prices; if the two firms colluded and set the same price, they could make that price as high a they wanted, and earn infinite profits. Marginal costs are zero. Suppose the two firms set their prices at the same time. Find the resulting Nash equilibrium. What price will each firm charge, how much will it sell, and what will its profit be? (Hint: Maximize the profit of each firm with respect to its price.) Each firm will charge a price of $ (Enter a numeric response rounded to two decimal places.) Each firm will produce units of output. In turn, each firm will earn profit of $ Suppose Firm 1 sets its price first and then Firm 2 sets its price. What price will each firm charge, how much will each sell, and what will be profits? Firm 1 will charge a price of $ Firm 2 will charge a price of $ Firm 1 will sell units and Firm 2 will sell units. Firm 1 will earn profit of $ and Firm 2 will earn profit of Suppose you are one of these firms and that there are three ways you could play the game: (i) Both firms set price at the same time: (ii) You set price first; or (iii) Your competitor sets price first. If you could choose among these options, which would you prefer? Explain why. You would choose O A. to set price simultaneously with the other firm to earn profit of $1.600.00.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:Two firms compete by choosing price. Their demand functions are
and
Q₁ = 40-P₁ + P₂
Q₂=40+P₁-P21
where P₁ and P₂ are the prices charged by each firm, respectively, and Q₁ and Q₂ are the resulting demands. Note that the demand for each good depends only on the difference in prices; if the two firms colluded and set the same price, they could make that price as high as
they wanted, and earn infinite profits. Marginal costs are zero.
Suppose the two firms set their prices at the same time. Find the resulting Nash equilibrium. What price will each firm charge, how much will it sell, and what will its profit be? (Hint: Maximize the profit of each firm with respect to its price.)
Each firm will charge a price of $
(Enter a numeric response rounded to two decimal places.)
Each firm will produce units of output.
In turn, each firm will earn profit of $
Suppose Firm 1 sets its price first and then Firm 2 sets its price. What price will each firm charge, how much will each sell, and what will be profits?
Firm 1 will charge a price of $
Firm 2 will charge a price of $
Firm 1 will sell
units and Firm 2 will sell
units.
Firm 1 will earn profit of $ and Firm 2 will earn profit of
Suppose you are one of these firms and that there are three ways you could play the game: (i) Both firms set price at the same time; (ii) You set price first; or (iii) Your competitor sets price first. If you could choose among these options, which would you prefer? Explain why.
You would choose
O A. to set price simultaneously with the other firm to earn profit of $1,600.00.
OB. to set price second to earn profit of $2,500.00.
OC. to set price first to earn profit of $1,800.00.
O D. to set price simultaneously with the other firm to earn profit of $2,500.00.
O E. to set price first to earn profit of $2,500.00.
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