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In: Economics

Q. Two rival companies sell software packages that are perfect substitutes. The software is sold over...

Two rival companies sell software packages that are perfect substitutes. The software is sold over the web as a download, so the marginal cost is zero. The demand for the software is Q = 900 – P. Assume that these firms are Cournot duopolists. Derive the reaction functions for the two firms, the quantity each will produce, and the market price that will be charged

Solutions

Expert Solution

Demand function is as follows -

Q = 900 - P

Inverse demand function is as follows -

P = 900 - Q

Where,

Q is the market demand

Q = q1 + q2

q1 = Output of Firm 1

q2 = Output of Firm 2

Determining market demand by equating inverse demand function and marginal cost

P = MC

900 - Q = 0

Q = 900

Reaction function of firm 1 is as follows -

q1 = 1/2(Market demand - Output produced by Firm 2) = 1/2(900 - q2) = 450 - 0.5q2 ---- Equation(1)

Reaction function of firm 2 is as follows -

q2 = 1/2(Market demand - Output produced by Firm 1) = 1/2(900 - q1) = 450 - 0.5q1

Put value of q2 in Equation 1

q1 = 450 - 0.5q2

q1 = 450 - [0.5(450 - 0.5q1)]

q1 = 450 - [225 - 0.25q1]

q1 - 0.25q1 = 225

0.75q1 = 225

q1 = 225/0.75 = 300

The Firm 1 will produce 300 software packages.

q2 = 450 - 0.5q1 = 450 - (0.5*300) = 450 - 150 = 300

The Firm 2 will produce 300 software packages.

P = 900 - Q = 900 - (q1 + q2) = 900 - (300+300) = 900 - 600 = 300

The market price that will be charged is $300 per software package.

Rahul Sunny answered 1 year ago

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