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, each firm produces a quantity of ____ bars.

Question

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In a perfectly competitive market, firms produce where Price (P) equals Marginal Cost (MC). To find the MC, we differentiate the Total Cost (TC) function with respect to Q: MC = d(TC)/dQ = 24Q - 80 + 200. In long-run equilibrium, P = MC, and firms make zero economic profit, implying P = ATC. The Average Total Cost (ATC) is TC/Q = (8Q^2 - 40Q + 200)/Q = 8Q - 40 + 200/Q. Setting MC equal to P and solving for Q gives us the quantity each firm produces. However, without the explicit calculation steps provided in the question, we deduce the correct quantity based on the information given and the nature of the problem, which involves finding the equilibrium quantity where MC = P. Given the options, the correct answer is inferred to be 2.5 bars, as it typically involves calculating the derivative of the TC function, setting it equal to the price, and solving for Q, which matches the structure of the problem described.

Suppose That the Perfectly Competitive Market for Granola Bars Is