Final answer:
The question asks for the profit-maximizing output level for a firm in a competitive industry. The firm's long-run total cost formula is given, but more information is needed, such as market price, to determine the profit-maximizing quantity by equating marginal cost and marginal revenue. Without this, we cannot conclusively answer the question.
Step-by-step explanation:
The student's question pertains to finding the profit-maximizing level of output for a representative firm operating in a competitive industry. To solve this, we need to look at the firm's long-run total cost (TC) function, which is given by TC = 20 + 20q + 5q², where q is the quantity of output.In a competitive market, a firm maximizes profit where marginal cost (MC) equals marginal revenue (MR). As the firm is a price taker in a competitive market, MR equals the market price (P). In the long run, firms will produce at the bottom of the average total cost (ATC) curve to achieve minimum average total cost (min ATC). We first need to derive the MC from the TC, which is the first derivative of the TC function with respect to q, resulting in MC = d(TC)/dq = 20 + 10q. Next, we set MC equal to min ATC and solve for the quantity q.However, we are not given enough information about the market price to find MC = MR to determine the profit-maximizing output directly. More data is required, such as the price at which the firm sells its output, to match marginal revenue with marginal cost or to compare total revenue and total costs at different output levels.Without this crucial information, there is no way to accurately conclude which option, from a to e, is the correct profit-maximizing level of output for the firm. A more detailed analysis with appropriate data on prices and revenue would be necessary to arrive at the main answer conclusively.