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  3. a set of ?rms n = {1,...,n} select quantities of t

A set of ?rms N = {1,...,n} select quantities of the same good to sell. Each...

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A set of ?rms N = {1,...,n} select quantities of the same goodto sell. Each ?rm i selects qi, and P(q1,...,qi,...,qn) = 1,000?(q1+···+ qn). Assume they will choose q1 +···+ qn < 1,000. Each ?rmhas the same linear cost for producing the goods, so C(qi) =cqi.

(a) Write down each ?rm’s set of strategies, and pro?tfunction.

(b) Write the FOC’s for each ?rm.

(c) Since ?rms are symmetric, let qi = qj for each pair i and j.Solve for qi.

(d) Solve for the market price, and each ?rm’s pro?t. Whathappens when n is large?

(e) Do you think this is reasonable/observed?

(f) What elements do you think are missing from the model? Writeas many as you can.

(g) What are some di?erence between Bertrand and Cournotcompetition? Why are the results di?erent?

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