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?
