The short-run marginal and average variable cost curves for a competitive firm are given by MC = 2+2q and AVC = 2+q. The profit-maximizing level of output for a firm is 4 and its total fixed cost is $18. Which of the following must be true about the firm? Group of answer choices The firm is charging a price of $4 and covering its average variable cost, hence it should continue operating in the short-run. The firm is charging $10 and will remain in the industry in the short-run; but it is not covering its total costs and will consider leaving the industry in the long run. The firm is charging a price of $4 and making a short-run loss, hence it should shut down immediately. The firm is charging a price of $10 and making a zero profit, hence it should shut down eventually. The firm is charging a price of $10 and making a positive profit, hence it will remain in the industry in the long-run.
Question
The short-run marginal and average variable cost curves for a competitive firm are given by
MC = 2+2q and AVC = 2+q. The profit-maximizing level of output for a firm is 4 and its total fixed cost is $18. Which of the following must be true about the firm?
Group of answer choices
The firm is charging a price of $4 and covering its average variable cost, hence it should continue operating in the short-run.
The firm is charging $10 and will remain in the industry in the short-run; but it is not covering its total costs and will consider leaving the industry in the long run.
The firm is charging a price of $4 and making a short-run loss, hence it should shut down immediately.
The firm is charging a price of $10 and making a zero profit, hence it should shut down eventually.
The firm is charging a price of $10 and making a positive profit, hence it will remain in the industry in the long-run.
Solution
In a competitive market, a firm maximizes its profit by producing at the level where marginal cost equals the price. Given that the profit-maximizing level of output for the firm is 4, we can substitute q=4 into the MC equation to find the price:
MC = 2 + 2q MC = 2 + 2(4) MC = 2 + 8 MC = 10
So, the firm is charging a price of $10.
Next, we need to determine whether the firm is covering its average variable cost (AVC) at this price. Substituting q=4 into the AVC equation gives:
AVC = 2 + q AVC = 2 + 4 AVC = 6
Since the price (6), the firm is covering its average variable cost and should continue operating in the short-run.
However, to determine whether the firm is covering its total costs and making a profit, we need to consider its total fixed cost (TFC), which is given as $18. The total cost (TC) is the sum of the total fixed cost and the total variable cost (TVC), which is the product of the AVC and the quantity of output:
TVC = AVC * q TVC = 6 * 4 TVC = 24
TC = TFC + TVC TC = 18 + 24 TC = 42
The total revenue (TR) is the product of the price and the quantity of output:
TR = P * q TR = 10 * 4 TR = 40
Since the total cost (40), the firm is not covering its total costs and is making a loss. Therefore, it will consider leaving the industry in the long run.
So, the correct answer is: The firm is charging $10 and will remain in the industry in the short-run; but it is not covering its total costs and will consider leaving the industry in the long run.
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