Final answer:
To calculate equilibrium price, quantity, and profit for each firm, set the industry demand function equal to marginal cost for each firm. Calculate total cost using each firm's cost curve, and use the profit equation considering that firms are price takers in a perfectly competitive market. Equilibrium is reached where industry supply equals demand, and profit is the difference between total revenue and total cost at equilibrium.
Step-by-step explanation:
To find the equilibrium price, quantity, and profit for each firm in a perfectly competitive market, we need to use the industry demand function and the cost curves for each firm. Given the industry demand function P = 100 – 0.20Q, we can set this equal to the marginal cost for each firm to find the quantity supplied by each firm at equilibrium. Since the market is perfectly competitive, we assume that all firms have the same price in equilibrium.
Now, total cost (∑Ci) for each firm is given by their cost curves: C1 = 10Q, C2 = 20Q, C3 = 15Q, C4 = 12Q, and C5 = 18Q. The profit equation is (Price)(Quantity produced) – (Average cost)(Quantity produced), and the perfectly competitive firm is a price taker, which means it will accept the market price determined by the intersection of industry supply and demand.
Equilibrium is found where the sum of quantities provided by each firm equals the quantity demanded by consumers. Firms will produce up to the point where P = MC (marginal cost), and total profits for each firm are calculated by taking the difference between total revenue and total cost at the equilibrium quantity and price.