Question

Industry demand is given by: QD = 1000 - P All firms in the industry have identical and constant marginal and average costs of $50 per unit. If the industry is perfectly competitive, what will industry output be? What will be the equilibrium price? What profit will each firm earn? Now, suppose that there are five firms in the industry and they collude to set the price. What price will they set? What will be the output of each firm? What will be the profit of each firm?

Answer 1

As given, industry demand curve is , and all firms are identical and have marginal cost (MC) and average cost (AC) equals $50, in a market which is perfectly competitive. All we need is to derive the supply schedule of the market. The MC above the average variable cost (AVC) is the supply curve of a particualr firm.

let us first derive the total cost (TC). As we know, , we have hence . As can be seen in this cost function, there is no constant term, and hence no fixed cost. Thus, the average variable cost is itself equal to the average total cost. So, since AVC and MC, being equal, overlaps, the supply curve of a firm is , ie the firm has an infinite supply at the price $50. Hence, the industry supply curve is .

The equilibrium output will be where the demand price will be equal to the supply price. The inverse demand function is , and equating with the supply function, we have , or . Putting this equilibrium output in inverse demand, , we have the equilibrium price in the market. Profit of each firm will be equilibrium quantity supplied multiplied by the difference between equilibrium price and the average cost, , since price minus the average cost is the profit earned by each firm for supplying one unit. Thus, profit by each firm is hence

Supposing there are five firms in the industry, and the collude, forming a cartel in the market to set the price. A cartel is a group created by all firms in the industry to act as a single firm in the market and set the price as a monopoly firm. The monopoly firm sets peice and produce quantity where the marginal revenue (MR) is equal to the marginal cost. The total revenue (TR) is quantity multiplied by the inverse of given industry demand, ie . It is the schedule of the total reciept that can be earned by a firm for a given market demand. The . Equating the MR to MC, we have , or . Hence, all the firm, acting as a single firm would supply a quantity of 475, to maximize the profit. The price will be set at where the demand is equal to 475, ie , and hence, price will be set at $525. As there are 5 firms, and total output is 475, each firm would supply a quantity of units. The profit of each firm can be calculated same as before, ie , where is the output supplied by each firm, and is the equilibrium price, while AC is same as before equal to $50. Thus, profit by each firm is hence, . Hence, each firm would gain $45125 if acted with the design of cartel.