Suppose the total cost to produce quantity q is TC(q)= 10 + q²/10. If this firm is a price- taker and the market price is p = 10, then the firm's profits will be: A)250. B)260. C)0. D)240.

Question

Quizplus · Accepted Answer

The total cost (TC) function is TC(q) = 10 + q^2. To find the firm's profit, we first need to determine its revenue, which is price (p) times quantity (q), or R = pq. Given that p = 10, the revenue function is R(q) = 10q. The profit (π) function is the revenue function minus the total cost function, so π(q) = R(q) - TC(q) = 10q - (10 + q^2). To maximize profit, we set the derivative of the profit function with respect to q equal to zero and solve for q. The derivative of π(q) with respect to q is dπ/dq = 10 - 2q. Setting this equal to zero gives 10 - 2q = 0, which solves to q = 5. Substituting q = 5 back into the profit function gives π(5) = 10(5) - (10 + 5^2) = 50 - (10 + 25) = 50 - 35 = 15. However, the correct calculation for profit at the optimal output level involves substituting q = 5 into the revenue and cost functions separately and then calculating profit as the difference. The correct profit calculation is π = R - TC = (10*5) - (10 + 5^2) = 50 - (10 + 25) = 50 - 35 = 15, indicating an error in the initial explanation. The correct profit should be calculated directly from the given price and the cost function, without the need for optimization steps, as the firm is a price-taker and will produce where price equals marginal cost. Given the error in the explanation process, the correct answer involves directly calculating profit based on the given market price and the total cost function for the specified quantity.

Suppose the Total Cost to Produce Quantity Q Is TC(q)=