Final answer:
The competitive firm will produce 2 units of output at a market price of $10. The level of fixed cost for the firm to earn zero economic profit is $8.
Step-by-step explanation:
To determine how many units of output the firm will produce at a market price of $10, we set the market price equal to the short-run marginal cost (SMC). Thus, we have 10 = 2 + 4Q. Solving for Q gives us Q = 2 units. This is the quantity at which marginal revenue (MR), which equals the market price for a competitive firm, is equal to marginal cost (MC).
For the second part of the question, to find the level of fixed cost at which the firm will earn zero economic profit, we must first calculate the total cost (TC) when producing the profit-maximizing quantity. Since TC = Total Fixed Cost (TFC) + Total Variable Cost (TVC) and TVC can be found by integrating the marginal cost curve, we can calculate TC. At Q = 2, TVC = ∫ (2 + 4Q)dQ = 2Q + 2Q^2 = 4 + 8 = 12. To earn zero economic profit, TC must equal total revenue (TR), which is price times quantity. At Q = 2 and P = $10, TR = 10×2 = 20. Therefore, TFC = TC - TVC = 20 - 12 = $8. This is the fixed cost level for zero economic profit.