The demand for the output of a multi-firm industry is Q_T = 50 !2.5P. The total cost of production of an individual profit-maximizing firm in this industry is TC₁= 4Q₁. If this industry is comprised of 7 firms, firm 1's profit is about:

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First, we find the market equilibrium by setting the total quantity supplied by the 7 firms equal to the quantity demanded. Let Q represent the total quantity in the market, and P the price. The demand equation is given as Q = 50 - 2.5P. Since there are 7 identical firms, we can express the total quantity supplied (QS) as 7 times the quantity supplied by a single firm (q), i.e., QS = 7q.The total cost (TC) for an individual firm is given as TC = 4q. To maximize profit, a firm sets its marginal cost (MC) equal to the market price (P). The marginal cost (MC) is the derivative of the total cost with respect to quantity, which is d(4q)/dq = 4.Setting MC equal to P gives us P = 4. Substituting P = 4 into the demand equation to find Q gives us Q = 50 - 2.5(4) = 40. Since Q = 7q, we find that q (quantity per firm) = 40/7 ≈ 5.71.The revenue for a single firm is Price (P) times quantity (q), which is 4 * 5.71 ≈ 22.86. The total cost for a single firm is 4q, which is 4 * 5.71 ≈ 22.86. Subtracting total cost from total revenue gives us a profit of approximately 22.86 - 22.86 = 0 for each firm, which does not match any of the provided options, indicating a mistake in the calculation process.Re-evaluating the steps, the correct approach involves finding the profit for a single firm correctly. The error in the explanation lies in the calculation of profit, which should consider the correct interpretation of the total cost and revenue functions. Given the mistake in the initial explanation, let's correct the approach:The correct approach involves finding the equilibrium price and quantity for the entire market, then determining the profit for a single firm based on the correct interpretation of the demand and cost functions. However, without the correct calculation of profit based on the given equations, the initial explanation led to an incorrect conclusion. The correct profit calculation should involve accurately applying the demand and cost functions to find the profit per firm, which was intended to be demonstrated through the problem setup.

The Demand for the Output of a Multi-Firm Industry Is