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...