Suppose that the perfectly competitive market for granola bars is made up of identical firms with long-run total cost functions given by TC(Q) = 8Q3-
Q2 + 200Q. Assume that these cost functions are independent of the number of firms in the market and that firms may enter or exit the market freely. Market demand is
, where price is in cents.
a. Using calculus, find the long-run equilibrium price, the quantity produced by each firm, and the number of firms in the industry.
b. Suppose that market demand decreases to
. Solve for the new long-run competitive equilibrium.
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