Final answer:
The firm will produce 2 units of output at a market price of $10. To earn zero economic profit, the level of fixed cost must be $8.
Step-by-step explanation:
In a perfectly competitive market, a firm determines the output to produce by setting the market price equal to marginal cost (P = MC). Given the short-run marginal cost (SMC) curve is SMC = 2 + 4Q and the market price is $10, we set SMC equal to price to find the quantity produced. Therefore, 10 = 2 + 4Q, which simplifies to Q = 2. At this output level, the average variable cost (AVC) can be calculated using the given AVC curve, AVC = 2 + 2Q, which at Q = 2 is $6 per unit. Since the price ($10) is greater than the AVC ($6), the firm will continue producing in the short run. To earn zero economic profit, the firm's total cost (TC) must equal total revenue (TR). Total cost is composed of fixed costs (FC) and variable costs (VC), where TC = FC + VC. Variable cost at Q = 2 is 2 units * $6 = $12. Total revenue at Q = 2 is 2 units * $10 = $20. For TC to equal TR, and therefore to earn zero economic profit, FC must be $20 - $12 = $8.