A firm has a long-run cost function, C(q)= 8q² + 72.In the long run, this firm will supply a positive amount of output, as long as the price is greater than

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In the long run, a firm will supply a positive amount of output if the price covers the average cost. The average cost (AC) is found by dividing the total cost (C(q)) by the quantity (q). Given the cost function C(q) = 10 + 8q^1.2, the average cost is AC = (10/q) + 8q^0.2. To find the minimum average cost, we differentiate AC with respect to q and set it equal to zero. However, without going through the calculus, we understand that the firm's supply decision is based on covering its variable costs in the long run since fixed costs (the constant term) do not affect long-run decisions. The variable cost here is represented by the 8q^1.2 term. The question simplifies to finding the price that covers the minimum point of the variable cost curve, which is not directly calculable from the information given. However, the correct answer is determined by understanding that the firm will only supply if the price is above the minimum average variable cost, which, based on the options provided and understanding the nature of cost functions, would logically be $48, making option A the correct choice without the detailed calculation. This is because, typically, a higher price than the average variable cost is needed to ensure the firm covers all its costs and is willing to supply a positive amount of output.

A Firm Has a Long-Run Cost Function, C(q)= 8q2

A Firm Has a Long-Run Cost Function, C(q)= 8q²