2. Consider two firms facing the market demand curve P = 100 – Q, where P is in $/unit, Q is total...

Question

2. Consider two firms facing the market demand curve P = 100 – Q, where P is in $/unit, Q
is total output, Q = Q1 + Q2, Q1 is the output of firm-1 and Q2 is the output of firm-2. Both
firms have identical cost functions. Marginal cost of production is $10.
a. Suppose (as in the Cournot model) that each firm chooses its profit-maximizing level of
output on the assumption that its competitor’s output is fixed.
I. Find each firm’s “reaction function”. (6 marks)
Answer:
Demand curve: P = 100 – Q, Q = Q1+Q2
Marginal cost = average cost = $10
Firm1 will maximize;
1 = 100Q1-Q1^2 – Q2Q1 – 10Q1
At maximum, d 1/dQ1 = 0 implies
100 – 2Q1 – Q2 -10 = 0, simplifying this we get reaction function for firm 1 as:
Q1 = 45 – 0.5Q2 ……………. (1)
Since two firms are symmetric in terms of cost and demand function, so reaction function...

David · Accepted Answer

2. Consider two firms facing the market demand curve P = 100 – Q, where P is in $/unit, Q 
is total output, Q = Q1 + Q2, Q1 is the output of firm-1 and Q2 is the output of firm-2. Both 
firms have identical cost functions. Marginal cost of production is $10. 
a. Suppose (as in the Cournot model) that each firm chooses its profit-maximizing level of 
output on the assumption that its competitor’s output is fixed. 
I. Find each firm’s “reaction function”. (6 marks) 
Answer: 
Demand curve: P = 100 – Q, Q = Q1+Q2 
Marginal cost = average cost = $10 
Firm1 will maximize; 
  1 = 100Q1-Q1^2 – Q2Q1 – 10Q1 
At maximum, d   1/dQ1 = 0 implies 
100 – 2Q1 – Q2 -10 = 0, simplifying this we get reaction function for firm 1 as: 
Q1 = 45 – 0.5Q2 ……………. (1) 
Since two firms are symmetric in terms of cost and demand function,

2. Consider two firms facing the market demand curve P = 100 – Q, where P is in $/unit, Q is total output, Q = Q1 + Q2, Q1 is the output of firm-1 and Q2 is the output of firm-2. Both firms have...

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