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

A set of ﬁrms N = {1,...,n} select quantities of the same good to sell. Each ﬁrm i selects qi, and P(q1,...,qi,...,qn) = 1,000−(q1 +···+ qn). Assume they will choose q1 +···+ qn < 1,000. Each ﬁrm has the same linear cost for producing the goods, so C(qi) = cqi.

(a) Write down each ﬁrm’s set of strategies, and proﬁt function.

(b) Write the FOC’s for each ﬁrm.

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

(d) Solve for the market price, and each ﬁrm’s proﬁt. What happens when n is large?

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

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

(g) What are some diﬀerence between Bertrand and Cournot competition? Why are the results diﬀerent?

Expert Solution

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Colby Messinger answered 9 months ago

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