Consider the following Cournot model. The inverse demand function is given by p = 30 –Q, where Q = q1 + q2. Firm 1’s marginal cost is $6 (c1 = 6). Firm 2 uses a new technology so that its marginal cost is $3 (c2 = 3). There is no fixed cost. The two firms choose their quantities simultaneously and compete only once. (So it’s a one-shot simultaneous game.) Answer the following questions. (4points)DeriveFirm1andFirm2’sreactionfunctions, respectively. (2 points) Solve the Nash equilibrium (q1N, q2N). (2points)Whatistheequilibriumpriceandwhatistheprofitlevel for each firm? (3 points) Suppose there is a market for the technology used by Firm 2. What is the highest price that Firm 1 is willing to pay for this new technology? (3points)Nowlet’schangethesetupfromCournotcompetitionto Bertrand competition, while maintaining all other assumptions. What is the equilibrium price? (3 points) Suppose the two firms engage in Bertrand competition. What is the highest price that Firm 1 is willing to pay for the new technology?
Consider the following Cournot model.
-
The inverse
demand function is given by p = 30 –Q, where Q =q1 + q2.
-
Firm 1’s marginal cost is $6 (c1 = 6). Firm 2 uses a new
technology so that its marginal cost is $3 (c2 = 3). There is no
fixed cost.
-
The two firms choose their quantities simultaneously and
compete only once. (So it’s a one-shot simultaneous game.)
Answer the following questions.
-
(4points)DeriveFirm1andFirm2’sreactionfunctions, respectively.
-
(2 points) Solve the Nash equilibrium (q1N, q2N).
-
(2points)Whatistheequilibriumpriceandwhatistheprofitlevel for each firm?
-
(3 points) Suppose there is a market for the technology used by Firm 2. What is the highest
price that Firm 1 is willing to pay for this new technology? -
(3points)Nowlet’schangethesetupfromCournotcompetitionto Bertrand competition, while maintaining all other assumptions. What is the
equilibrium price ? -
(3 points) Suppose the two firms engage in Bertrand competition.
-
What is the highest price that Firm 1 is willing to pay for the new technology?
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