Final answer:
The profits for each firm competing in quantities can be calculated by subtracting total cost from total revenue; the formulas involve the market demand function P = 10 - Q, where Q is the sum of quantities produced by both firms.
Step-by-step explanation:
The student's question about the profits of two firms competing in quantities involves economic principles related to cost, revenue, and profit calculation in a market. Given that the total costs (TC) for each firm are equal to their respective quantities (q1 for firm 1 and q2 for firm 2), and that the market demand function is given as P = 10 - Q where Q is the sum of q1 and q2, the firms' profits can be calculated by identifying the price each firm can command for their goods, their total revenue (TR), and then subtracting total costs from total revenue.
Profit for firm 1 would be calculated as Profit1 = TR1 - TC1, where TR1 = P * q1 and TC1 = q1; similarly, Profit2 = TR2 - TC2, where TR2 = P * q2 and TC2 = q2. By plugging in the demand function P = 10 - Q and the expressions for total revenue, we can solve for the profits of each firm. Without specific quantities, we cannot provide exact profit figures, but the formula for calculating profits is clear.