Final answer:
The profit-maximizing level of output for the firm is at a quantity of 40, where marginal revenue and marginal cost intersect. This results in a price of $16, total revenue of $640, total cost of $580, and profits of $60, indicating economic profitability for the firm.
Step-by-step explanation:
To find the profit-maximizing level of output q* for the firm, we must understand how marginal revenue (MR) and marginal cost (MC) interact. The profit-maximization condition in economics states that a firm should produce at the level where MR equals MC. Given the demand function Q(p)=3−p, we can derive the MR function by evaluating the change in total revenue for a change in quantity. To calculate MC, we differentiate the total cost function C(q)=40q³−917q²+q+300 with respect to q.
In this example, it is stated that MR and MC intersect at a quantity of 40, which suggests that the quantity of 40 is the profit-maximizing output level. Once the firm has chosen this quantity, it can calculate total revenue and total cost to determine profits. We're provided information that indicates that at a quantity of 40, the firm's price is $16, its total revenue is $640, its total cost is $580, and therefore its profits are $60. This means that for quantity 40, the firm is above its average cost curve and making economic profits.