Consider a competitive firm with a TC = 50 + 2q^2 + q. If price is $17, which statement is true? Group of answer choices The firm produces 4 units of output in the short run and is making an economic loss; the firm will exit the industry in the long run. The firm produces 8.5 units of output and this is the long-run equilibrium. The firm produces 4 units of output, and is making a positive economic profit; this is the long-run equilibrium. The firm produces 4 units of output, and is making a zero economic profit; this is the long-run equilibrium. The firm shuts down in the short run and produces zero output; the firm will leave the industry in the long run.
Question
Consider a competitive firm with a TC = 50 + 2q^2 + q. If price is $17, which statement is true? Group of answer choices
The firm produces 4 units of output in the short run and is making an economic loss; the firm will exit the industry in the long run.
The firm produces 8.5 units of output and this is the long-run equilibrium.
The firm produces 4 units of output, and is making a positive economic profit; this is the long-run equilibrium.
The firm produces 4 units of output, and is making a zero economic profit; this is the long-run equilibrium.
The firm shuts down in the short run and produces zero output; the firm will leave 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. The marginal cost (MC) is the derivative of the total cost (TC) with respect to quantity (q).
The total cost (TC) function is given by TC = 50 + 2q^2 + q. The derivative of this function is MC = 4q + 1.
Setting MC equal to the price (P) and solving for q gives us:
4q + 1 = 17 4q = 16 q = 4
So, the firm produces 4 units of output.
Next, we need to determine whether the firm is making a profit, a loss, or breaking even. The total cost (TC) at q=4 is:
TC = 50 + 2(4)^2 + 4 TC = 50 + 32 + 4 TC = 86
The total revenue (TR) is the product of the price and the quantity of output:
TR = P * q TR = 17 * 4 TR = 68
Since the total cost (68), the firm is making an economic loss.
Therefore, the correct answer is: The firm produces 4 units of output in the short run and is making an economic loss; the firm will exit the industry in the long run.
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