Final answer:
The firm's fixed cost is $20, the average cost formula is AC = (20/Q) + 5 + 0.5Q, the quantity sold at a price of $20 is 15 units, and the profit at that price is $25.
Step-by-step explanation:
Assuming a firm has a cost function of C=20+5Q+0.5Q² and sells its product in a competitive market at $20:
- a. Fixed costs of the firm are those costs that do not change with the level of output produced. Referring to the cost function (C=20+5Q+0.5Q²), the fixed cost is $20, since it is the cost when output Q is zero.
- b. Average costs (AC) are calculated by dividing the total cost (C) by the quantity (Q). The formula for average costs based on the given cost function would be AC = (20/Q) + 5 + 0.5Q.
- c. Quantity (Q) the firm will sell when the price is $20 is determined by setting marginal cost (MC) equal to the price, as this is the condition for profit maximization in competitive markets. The firm's marginal cost is the derivative of the cost function, which is MC = 5 + Q. Setting MC = 20 and solving for Q gives Q = 15.
- d. Profit is calculated as total revenue (TR) minus total cost (C). With a selling price of $20 and production of 15 units, total revenue would be TR = $20 × 15 = $300. The total cost is C = 20 + 5×15 + 0.5×15² = $275. Therefore, the firm's profit is $300 - $275 = $25.