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) =8Q³-40Q² + 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 Q^D = 8,000 - 3.5P, where price is in cents. In the long-run equilibrium, there are ____ firms in the industry.

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In the long-run equilibrium, each firm will produce at the point where marginal cost equals price. The marginal cost curve is the derivative of the total cost curve, which is MC(Q) = 24Q² - 80Q + 200. Setting MC(Q) equal to the market price, P, we get:24Q² - 80Q + 200 = PSubstituting the market demand curve, Q^D = 8,000 - 3.5P, we get:24Q² - 80Q + 200 = 8,000 - 3.5(8,000 - 3.5Q)Simplifying, we get:24Q² - 80Q + 200 = 8,000 - 28,000 + 12.25Q24Q² - 92.25Q + 28,200 = 0Using the quadratic formula, we get:Q = 25 or Q = 480The only feasible solution is Q = 480, since Q cannot be negative.Therefore, each firm will produce 480 units of granola bars in the long-run equilibrium.To find the number of firms in the industry, we divide the total market demand by the output of each firm:N = Q^D / Q = (8,000 - 3.5P) / 480Substituting the market price, P = 2,400, we get:N = (8,000 - 3.5(2,400)) / 480 = 2,990Therefore, there are 2,990 firms in the industry in the long-run equilibrium.

Suppose That the Perfectly Competitive Market for Granola Bars Is