Final answer:
Without the quantity produced, we can't calculate the exact profit for the firm with a cost curve of C=3q³−4q²+20q+25 and a market price of $100. Total profit is found by subtracting total costs from total revenues, which is determined by the quantity produced and the market price. In perfect competition, a firm makes a profit when market price is above average cost.
Step-by-step explanation:
To determine the profit for a firm in a perfectly competitive market, we need to calculate the firm's total revenue and subtract the total cost from it. The firm's total cost curve is given as C=3q³−4q²+20q+25, and the market price (p) is $100. Since the firm is a price taker in a perfectly competitive market, it can sell its product at the market price.
First, we need to calculate the quantity (q) that the firm will produce to maximize profit. This quantity is the one where marginal cost equals the market price, as firms in perfect competition maximize profit at this point. However, since the marginal cost is not provided here, and without more information about the market demand or the firm's production capacity, we cannot determine the exact quantity.
Assuming that quantity is known, the total revenue (TR) would be TR = p × q. Once we have the quantity, we can plug it into the cost curve equation to get the total cost (TC), and then calculate profit as Profit = TR - TC. The process described is similar to the one shown in the reference where a firm with the total revenue of $640 and total cost of $580 makes a profit of $60.
In this scenario, without the quantity, we cannot provide the exact profit number. It's important to note that in a perfectly competitive market, if the firm's price (p) is above average cost, the firm will make an economic profit, similar to the provided example where a price of $16 lies above the average cost curve resulting in profit.