Microeconomics Problem Set 10 PDF

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Microeconomics Problem Set 10
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Problems and Applications 1. Many small boats are made of fiberglass and a resin derived from crude oil. Suppose that the price of oil rises. a. Using diagrams, show what happens to the cost curves of an individual boatmaking firm and to the market supply curve.

If the price of oil rises, the average total cost curve and marginal cost curve would rise because oil is part of input. As for industry, the supply curve would shift left because at any given price, sellers would produce less and even some firms would exit the market. b. What happens to the profits of boat makers in the short run? What happens to the number of boat makers in the long run?

In the short run, the profit is negative because the price is smaller than the average total cost. The negative profit leads some firms to exit the market and at the same time the supply curve shifts left until the price rises to meet the minimum point on the firm’s average total cost curve. That is the new equilibrium price P3. At that price, profits are zero again and firms stop exiting. Therefore, in the long run, the number of boat makers decreases.

4. Ball Bearings, Inc., faces costs of production as follows: a. Calculate the company’s average fixed cost, average variable cost, average total cost, and marginal cost at each level of production.

b. The price of a case of ball bearings is $50. Seeing that he can’t make a profit, the chief executive officer (CEO) decides to shut down operations. What is the firm’s profit/loss? Is shutting down a wise decision? Explain. There are losses at every level of output. If the firm shut down, the loss is equal to the fixed cost which is $100. It is not a wise decision. When MC=MR=Price= $50, the price is higher than the AVC but lower than the ATC. It means the firm could cover all the variable cost and some of the fixed cost, minimizing the losses to $40. Under this situation, the firm should better continue operating for less losses in the short run and exiting in the long run. c. It is better to produce 1 case of ball bearings because marginal revenue equals marginal cost at that quantity. What is the firm’s profit/loss at that level of production? Is producing 1 case the best decision? Explain. Producing 1 case is not the best decision because it leads to a loss of $100. Producing 4 cases is the best decision because it minimizes the loss to $40. 5. Suppose the book-printing industry is competitive and begins in a long-run equilibrium. a. Draw a diagram showing the average total cost, marginal cost, marginal revenue, and supply curve of the typical firm in the industry.

As the diagram shows, ATC1 represents average total cost, MC1 represents marginal cost, P1 represents marginal revenue. The supply curve is the marginal curve MC1

above the minimum point of AVC1. b. Hi-Tech Printing Company invents a new process that sharply reduces the cost of printing books. What happens to Hi-Tech’s profits and to the price of books in the short run when Hi-Tech’s patent prevents other firms from using the new technology?

The reduction in cost of printing books leads to a decrease of marginal cost and average total coat. Therefore, these two curves shift downward to ATC2 and MC2 while the price remains P1 because of the insulation of the new technology. Thus HiTech produces Q2 units at price P1 and earn positive profits. c. What happens in the long run when the patent expires, and other firms are free to use the technology? When the patent expires, all firms’ average total cost corves shift down to the ATC2 and the price would decrease to P2 to reach the status earning zero profits. 10. An industry currently has 100 firms, each of which has fixed cost of $16 and average variable cost as follows. a. Compute a firm’s marginal cost and average total cost for each quantity from 1-6.

b. The equilibrium price is currently $10. How much does each firm produce? What is the total quantity supplied in the market?

When the price is $10, each firm produces 5 units to earn the most profits. The total quantity supplied in the market is 500 units. c. As this market makes the transition to its long-run equilibrium, will the price rise or fall? Will the quantity demanded rise or fall? Will the quantity supplied by each firm rise or fall? Explain your answers. When the price is $10 and each firm produces 5 units. The profit is $10 so more firms would enter, shifting the supply curve to the right. Thus, the price would fall and the quantity demanded would increase. The quantity supplied by each firm would fall because of the lower price. d. Graph the long-run supply curve for this market, with specific numbers on the axes as relevant.

The long-run equilibrium price would be nearly $8 and each firm would produce 4 units. 11. Suppose that each firm in a competitive industry has the following costs, where q is an individual firm’s quantity produced. The market demand curve for this product is. where P is the price and Q is the total quantity of the good. Currently, there are 9 firms in the market. a. What is each firm’s fixed cost? What is its variable cost? Give the equation for average total cost. When q=0, total cost is $50 which is equal to the fixed cost. Thus, the variable cost 50 q q2 ATC = + VC= . The equation for average total cost is: is: q 2 . 2 b. Graph the average-total-cost curve and the marginal-cost curve for q from 5 to 15. At what quantity is the average-total-cost curve at its minimum? What is marginal cost and average total cost at that quantity?

The ATC is minimum at the 10 units of output where the MC = $10 and the ATC = $10. c. Give the equation for each firm’s supply curve. The supply curve of each firm is the same as the marginal cost curve above the minimum point of average variable cost. Thus, the equation is: Supply=q (q>=10). d. Give the equation for the market supply curve for the short run in which the number of firms is fixed. In the short run, if the number of firms is fixed, it means that firms earn zero profit. Therefore, the market price is equal to the minimum point of ATC and the quantity supplied by each firm. Total supply= 9×q=9PQ (S)=9P. e. What is the equilibrium price and quantity for this market in the short run? Q (S)=9P, Q (D)= 120-P. When the market meets the equilibrium point, total supply would be equal to total demand. Therefore, P=12 and Q (D)= 108. f. In this equilibrium, how much does each firm produce? Calculate each firm’s profit or loss. Do firms have an incentive to enter or exit? q2 Each firm produces=108/9=12. Each firm’s profit= P×q-50- 2 =12×12-5012×12÷2=$22. Firms have an incentive to enter the market because of the positive profits. g. In the long run with free entry and exit, what is the equilibrium price and quantity in this market? In the long run, the equilibrium price is equal to the minimum point of ATC, which is $ 10. Therefore, total quantity produced = 120 - 10 = 110 units. h. In this long-run equilibrium, how much does each firm produce? How many firms are in the market?

In the long-run equilibrium, the price is also equal to q, so each firm produces 10 units. 110/10=11. So there are 11 firms in the market....