Economics 101Summer 2009Answers to Homework #4Due Tuesday, June 16, 2009Directions: The homework will be collected in a box before the lecture. Make sure youwrite your name as it appears on your ID so that you can receive the correct grade. Late homework will not be accepted so make plans ahead of time. IMPORTANT! YOU WILL WANT TO USE A CALCULATOR FOR THIS HOMEWORK!!!!!1. Consider a perfectly competitive market with a market demand curve that is given by the equation P = 2000 - Q. A representative firm in this market has a total cost curve given by the equation TC = 121 + 64q + q2 and a marginal cost curve given by MC = 64 + 2q. Q is the market quantity and q is the firm quantity. Let's start in the short-run with this market. Suppose the short-run price in this market is $100. a. What is the market quantity in this market given this short-run price?To find the short-run market quantity you need to plug in the market price into the marketdemand curve. This gives us 100 = 2000 - Q or Q = 1900.b. What is the representative firm's level of production given this short-run price?To find the short-run level of production recognize first that the market price is the price the firm takes as a price-taking firm. Therefore the firm's Marginal Revenue curve is given by MR = 100. To find the firm's level of production you need to equate the firm's MR to the firm's MC. Thus, MR = 64 + 2q or 100 = 64 + 2q and therefore q = 18. c. What is the representative firm's level of profits in the short-run given this market price?To find the firm's profits you need to calculate both total revenue (TR) and total cost (TC)for the firm when it produces 18 units at a price of $100 per unit. The firm's TR = ($100 per unit)(18 units) = $1800. The firm's TC = 121 + 64(18) + (18)2. Or, the firm's TC = $1597. The firm's profits are therefore equal to $203.d. Can this short-run equilibrium also represent a long-run equilibrium for this firm? Explain your answer. What do you anticipate will happen as this market adjusts to the long-run?No, this cannot be a long-run equilibrium. In the long run the perfectly competitive firm must earn zero economic profits and this firm is currently earning positive economic 1profits. This implies that there will be entry of firms in the long-run which will cause the equilibrium price to fall in this market and thereby eliminate the positive economic profits. e. Rounding to the nearest whole number, how many firms are operating in the short-run in this market given a market price of 100 firms?To find the number of firms in the market, you need to know the total amount being produced (1900) and the amount a representative firm is producing (18). Dividing 1900/18 gives us the number of firms in the market or 106 firms.Now, let's go to the long-run in this market. Let's assume that nothing happens to the market demand curve, but that the market has adjusted and is now at a long-run equilibrium. f. Intuitively thinking, what do you expect to happen to the following in the long-run? Your answers should be "increase", "decrease", or "remain unaffected".i. Market quantityii. Market priceiii. Firm quantityiv. Firm pricev. Number of firms in the industryvi. Level of profits for the firmAnswers:i. Increaseii. Decreaseiii. Decreaseiv. Decreasev. Increasevi. Decrease until they are equal to $0g. What is the break-even price in the long-run for a representative firm in this industry?To find the break-even price in the long-run you need to first set MC equal to ATC for thefirm. Thus, 64 + 2q = (121 + 64q + q2)/q or q = 11. Then, use this quantity to figure out the break-even price using the MC curve: thus, MC = 64 + 2q or MC = 64 + 2(11) = 86 = break-even price. h. Assuming no change in the market demand for this product, what will be the long-run market quantity in this market?To find this quantity use the market demand curve and the break-even price you have justcalculated. Thus, P = 2000 - Q or 86 = 2000 - Q or Q = 1914. 2i. How many firms will be in this industry in the long-run?Since each representative firm produces 11 units of output and total market output is 1914, then the number of firms in the industry must equal 1914/11 or 174 firms. j. What happen to the number of firms in the industry in the long-run compared to the number of firms in the industry in the short-run?The number of firms in the industry in the short-run was approximately 106 firms and in the long-run the number of firms in the industry is 174 firms: there was entry of firms in the long-run.k. What is the level of profit in the long-run for the representative firm?In the long-run the level of profit for the representative firm in a perfectly competitive industry must be $0. You can verify this by calculating the firm's TR and TC. The firm's TR = 11(86) = $946; the firm's TC = 121 + 704 + 121 or $946. The firm's profit is therefore equal to $0. l. Calculate the value of consumer surplus (CS), producer surplus (PS) and deadweight loss (DWL) in the long run. Hint: you will need to find the market supply curve for this one! And, that means you will need to do the horizontal summation of the individual supply curves in order to find the equation for the market supply curve. From answer (j) you know that there are 174 firms in the industry and each firm has the same MC curve. So, when output is equal to 0 each firm’s MC curve intersects the vertical axis at 64. Then, pick another MC value to get a second point on the individual firm’s supply curve. I actually started by selecting an output of 100 units and asked the question, what price must the representative firm receive in order to be willing to supply 100 units? I got $264 as the price they must get. Thus, each of the firms will supply 100 units at a price of $264 per unit. So, now you need to think about 100 units multiplied by the number of firms and this gives you a second point on the market supply curve. The market supply curve is thus P = 64 + (1/87)Q.With this supply curve in hand, you can now calculate CS and PS. CS = (1/2)($2000 per unit - $86 per unit)(1914 units) = $1,831,698. PS = (1/2)($86 per unit - $64 per unit)(1914 units) = $21,054. DWL = $0 since there is no DWL in a perfectly competitive industry provided that the costs and benefits are accurately reflected in the cost curves forthe firms and in the market demand curve. m. Fill in the following table based upon this market being in long-run equilibrium. Price in the marketTotal Quantity (Q)
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