Suppose a firm has the following total cost function: TC = 50 + 2q².What is the minimum price necessary for the firm to earn profit? A) p = $20 B) p = $30 C) p = $35 D) p = $40

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Quizplus · Accepted Answer

The firm's total cost function is TC = 50 + 2q. To earn a profit, the firm's revenue must exceed its total costs. The break-even point occurs when revenue equals total costs. Assuming q represents the quantity of goods sold and p represents the price per unit, the revenue function is R = pq. At the break-even point, R = TC, so pq = 50 + 2q. To find the minimum price necessary to earn a profit, solve for p when q is greater than 0. Dividing both sides by q gives p = (50/q) + 2. As q increases, (50/q) decreases, making the minimum value of p greater than 2 for any positive quantity of q. Since the options are discrete, the closest value to just above 2 is $20, indicating that any price above $20 would cover the variable costs and contribute to covering the fixed costs of $50, eventually leading to profit.

Suppose a Firm Has the Following Total Cost Function: TC