In a perfectly competitive market, each firm has a long-run total cost given by LTC = 100Q - 10Q² + 1/3Q³ and long-run marginal cost curve given by LMC = 100 - 20Q + Q². What is the market's long-run equilibrium price?

Question

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In a perfectly competitive market, the long-run equilibrium price is determined where the long-run marginal cost (LMC) equals the market price. Setting LMC = 100 - 20Q + Q^2 equal to the price and solving for Q does not directly give us the price. However, given the options and understanding that in equilibrium, firms produce where price equals marginal cost, we can deduce that the correct answer must be one where the LMC formula would equate to a constant price across different quantities. Without the explicit demand function or further details, we infer the equilibrium price by recognizing that the LMC curve represents the supply side conditions. Since none of the provided options directly solve the equation given the complexity of solving for Q without additional information, we look for the most reasonable approximation based on the structure of the LMC equation. The correct answer, D) $25, is chosen based on the understanding of economic principles rather than a direct calculation from the given LMC equation, as the exact intersection point requires more information or a different approach to calculate directly.

In a Perfectly Competitive Market, Each Firm Has a Long-Run