Final answer:
The firm is not currently maximizing profit because the marginal cost of producing the last unit is above the market price. It should produce 4 units to maximize profits. Long-term decisions should consider the relationship between average cost and market price for sustainability.
Step-by-step explanation:
In a competitive market, profit maximization occurs where marginal cost (MC) equals marginal revenue (MR), which is the product price for a competitive firm. Given the total cost (TC) function TC = 50 + 4Q + 2Q² and the marginal cost (MC) function MC = 4 + 4Q, we can determine profit-maximizing output by setting MC equal to the market price, which is $20 in this scenario.
At the current output of 5 units, the MC is 4 + 4(5) = $24, which is higher than the market price of $20, indicating that the firm is not maximizing profit because it costs more to produce the last unit than the revenue it generates. To maximize profits, the firm should adjust its output level so that MC is equal to the market price. Calculating this will require solving the equation 4 + 4Q = 20. Subtracting 4 from both sides gives us 4Q = 16, and dividing by 4 yields Q = 4. Hence, the firm should produce 4 units to maximize profit.
In the long run, to ensure continued profit maximization, the firm must consider the average cost (AC) in relation to the market price. It should only produce if the market price is above the minimum AC. If the market price falls below AC in the long run, the firm may incur losses and eventually exit the market.