Department of Economics Prof. Gustavo Indart University of Toronto July 27, 2006 SOLUTION ECO 100Y L0201 INTRODUCTION TO ECONOMICS Midterm Test # 2 LAST NAME FIRST NAME STUDENT NUMBER INSTRUCTIONS: 1. The total time for this test is 1 hour and 50 minutes. 4. Aids allowed: a simple calculator. 5. Write with pen instead of pencil. DO NOT WRITE IN THIS SPACE Part I /30 Part II 1. /5 2. /5 3. /5 Part III 1. /30 2. /25 TOTAL /100 Page 1 of 11
PART I (30 marks) Instructions: Enter your answer to each question in the table. Only the answer recorded in the table will be marked. Table cells left blank will receive a zero mark for that question. Each question is worth 3 (three) marks. No deductions will be made for incorrect answers. 1 2 3 4 5 6 7 8 9 10 B E B D C A E C B B 1. Consider a perfectly competitive firm in the following position: output = 4000 units, market price = $2, fixed costs = $10,000, variable costs = $1000, and marginal cost = $1.10. To maximize profits in the short-run, the firm should A) reduce output B) expand output C) shut down D) increase the market price E) not change output 2. In the short-run, a decrease in a perfectly competitive firm s fixed costs should lead to A) a decrease in output B) a decrease in the number of sellers C) an increase in price D) lower variable costs E) none of the above 3. Suppose a typical competitive firm has the following data in the short-run: price = $10; output = 100 units; ATC = $12; AVC = $7. A) in the long-run the industry will expand because of economic profits B) in the long-run the industry will contract because firms are suffering losses C) the size of the industry will remain the same in the long-run D) price will fall in the long-run E) there is not enough information to formulate an answer 4. Assume that a perfectly competitive industry has a perfectly inelastic supply curve. The government introduces a specific commodity tax of $2.50 per unit of output. As a result, which one of the following statements would be correct? A) the consumer price would increase by $2.50 B) the consumer price would fall by $2.50 C) the burden of the tax would fall completely on consumers D) the price received by the producer would decrease by $2.50 E) none of the above Page 2 of 11
5. Suppose all of the firms in a perfectly competitive industry form a cartel and agree to restrict output, thereby raising the price of the product. Individual firm A will gain the most from the existence of the cartel if A) all firms, including A, cooperate and restrict output B) firm A restricts output, while the other firms do not C) all firms, except A, cooperate and restrict output D) no firms restrict output E) all firms revert back to their competitive outputs 6. A perfectly competitive industry is in long run equilibrium. Under these conditions, which one of the following statements is correct? A) marginal revenue, marginal cost, average revenue and average cost are equal B) marginal revenue equal marginal cost but not average revenue and average cost C) marginal revenue equals average revenue but marginal cost and average total cost D) marginal revenue equals average total but not marginal cost and average revenue E) none of the above 7. An unregulated monopolist is in short-run equilibrium with economic profits. Which one of the following statements is correct? A) an increase in rent will cause an increase in the monopoly price and a decrease in the monopolist s output B) an increase in rent will cause an increase in the monopoly price and an increase in the monopolist s output C) the monopolist s price will equal its marginal cost at the equilibrium output D) the monopolist s marginal revenue will equal its average revenue at the equilibrium output E) none of the above 8. A monopolist is currently producing an output level where P = $4, AVC = $2, ATC = $8, and MC = $4. In order to maximize profits, this monopolist should A) shut down B) increase production C) decrease production D) not change the level of output, because the monopolist is maximizing profits E) not enough information to answer 9. Suppose we compare two monopolists with identical cost and demand conditions. Monopolist A charges a single price. Monopolist B engages in price discrimination. Which one of the following statements is correct? A) B will produce less than A, resulting in a deadweight loss B) B will produce more than A, resulting in less deadweight loss C) A will produce less than B, resulting in smaller deadweight loss D) A will produce more than B, resulting in larger deadweight loss E) A and B will both produce the same amount 10. Which of the following is included in the calculations of current GDP? A) the purchase of a second hand automobile B) pizza purchased by college students for dinner C) volunteer work undertaken by Mary Smith D) the purchase of a 1939 painting E) welfare payments Page 3 of 11
PART II (15 marks) Instructions: Answer true or false to the following statements and explain your answers in the space provided (if space is not sufficient, continue on the back of the previous page). Draw the appropriate diagram or diagrams to assist your answer. Each question is worth 5 (five) marks. Marks will be given entirely for the explanation. 1. Scooters are produced in a constant cost industry with two factors of production: capital [K] and labour [L]. If the price of labour [the wage rate] increases by 5% and, at the same time, the price of capital [rental fee] increases by 2%, then both the marginal product of labour and the marginal product of capital will increase in this industry in the long-run. False Although the prices of both K and L have increased, the price of L has increased relatively more, which means that the relative price of labour has increased. Therefore, in the long-run a profit maximizing firm will produce any given output using more of the relatively less expensive factor of production and less of the relatively more expensive factor of production. In this case, therefore, the firm will substitute capital for labour (i.e., it will adopt a more capital-intensive method of production). This is represented by a movement up along the isoquant representing the level of output being produced. K K 2 K 1 Q 1 L 2 L 1 L Given the assumption of diminishing marginal productivity of factors of production, as the quantity of K increases, the MP K decreases; in turn, as the quantity of L decreases, the MP L increases. [Note that this outcome is reinforced by the fact the MP of a factor of production also increases when the quantity of another factor of production increases.] The firm will minimize the cost of producing any particular level of output by choosing a combination of K and L given by the point of tangency between the isoquant and an isocost line. At this point the slopes of the isoquant and the slope of the isocost are equal, i.e., the MRTS is equal to the relative price of labour (w/r). Initially, MRTS = w/r where MRTS = MP L /MP K. This equilibrium is altered when w/r increases to w /r. Indeed, now MP L /MP K < w /r. To restore equilibrium, then, MP L must increase (through a decrease in L) and MP K must decrease (through an increase in K). Page 4 of 11
2. A constant cost, perfectly competitive industry is initially in long-run equilibrium with n 1 identical firms. A technological innovation causes the average variable cost curve for each firm to decrease by exactly $2.50 per unit of output. In the new long-run equilibrium, the industry price will decrease by exactly $2.50; industry output will increase; each firm will produce a larger output, and more firms will enter the industry. False If the industry is in long-run equilibrium, then each firm is making zero economic profits and producing at the minimum of the LRAC curve. Since this is a constant cost industry, the LRS is horizontal at the level of the minimum of the LRAC curve. Therefore, as the diagram below shows, the initial long-run equilibrium price is P 1, each firm is producing an output q 1, and the total output of the industry is Q 1 (where Q 1 = n*q 1 ). The decrease in AVC of $2.50 per unit of output will reduce LRAC by exactly $2.50 at each level of output; most particularly, it will reduce the minimum of the LRAC curve by exactly $2.50. Therefore, the level of output at which each firm reaches the minimum efficient scale of production will remain unchanged, and thus each firm will continue producing the same level of output (q 1 ) in the new long-run equilibrium. Therefore, the LRS curve will shift down by exactly $2.50, and thus the new equilibrium price will be P 2 = P 1 $2.50. However, the new total industry output will be larger than before (i.e., Q 2 > Q 1 ). This is so because as variable cost decreases, existing firms make economic profits, which prompts new firms to enter the industry in the long-run. Therefore, the number of firms in the new long-run equilibrium is greater than before (i.e., n 2 > n 1 ). Note that Q 2 = n 2 *q 1 >. Therefore, the statement is false. It is correct that the industry price will decrease by exactly $2.50, industry output will increase, and more firms will enter the industry; but each firm will produce the same output as before and not a larger output. $ Industry $ Representative Firm LRAC LRAC P 1 P2 P = $2.50 LRS LRS P 1 P 2 $2.50 D Q 1 Q 2 q 1 q Q Page 5 of 11
3. In the short-run, a firm generates the following information at its current level of output: the industry price is $15; the marginal revenue is $9; the average total cost is $18; the marginal cost is $9 and average fixed cost is $5. Therefore, the firm is not in perfect competition and should shut down to minimize its economic losses. False Independently of the nature of the market structure, any profit maximizing firm should produce a level of out where MR = MC. This firm is indeed maximizing profits since its producing at the level where MR = MC = $9. But at this profit-maximizing level of output, price is greater than MR. This indicates that this market structure is not perfect competition, but rather a monopoly market. Indeed in an unregulated monopoly market, P is always greater than MR. The information also indicates that P = $15 < ATC = $18, and thus the firm is making economic losses in the short-run. However, the firm should not shut down since it s covering AVC = $13 (since ATC = AVC + AFC). Therefore, the losses that the firm is making are less than the losses it would make if it were to shut down. In the latter case, economic losses would be equal to TFC. Continuing producing the firm minimizes losses (i.e., maximizes profits). This is shown in the diagram below. The statement is, therefore, false although the firm is certainly not in perfect competition, it should not shut down in the short-run since variable costs are covered in excess (and thus losses are being minimized). $ MC ATC 18 AVC 15 13 9 MR D Q 1 Q Page 6 of 11
PART III (55 marks) Instructions: Answer all questions in the space provided (if space is not sufficient, continue on the back of the previous page). Question 1 (30 marks) Gadgets are produced in a constant cost, perfectly competitive industry by firms with traditional U-shaped LRAC. Minimum LRAC is $50 and the efficient scale of production (where LRAC reaches a minimum) is 25 gadgets per day. The demand for gadgets is given by the equation: P = 125 0.1 Q, where P is price and Q is quantity per day. a) Fill in the following table describing the initial long-run equilibrium. (6 marks) [Note: Show all your work in the space below. If space is not sufficient, continue on the back of the previous page.] Firm Item Value Industry Item Value Firm s quantity 25 Price 50 Firm s profits 0 Quantity 750 Number of firms 30 Consumer Surplus 28,125 In a constant cost industry, the long-run equilibrium price is equal to the minimum of the LRAC, i.e., $50. At this price, the total quantity transacted in the market is: P = 125 0.1 Q 50 = 125 0.1 Q 0.1 Q = 125 50 0.1 Q = 75 Q* = 750 Since each firms is producing at the minimum of the LRAC curve (i.e., 25 gadgets per day), the total number of firms is n = 750/25 = 30. Since the industry is in long-run equilibrium, each firm is making zero economic profits (i.e., they are producing at the minimum of the LRAC). The consumer surplus is equal to the area below the demand curve and above the price line. That is, the consumer surplus is equal to the area of the triangle with a height of 75 (i.e., 125 50) and base of 750: (75 x 750)/2 = 58,125. Page 7 of 11
b) Show the initial long-run equilibrium for a representative firm and for the industry on the diagram below. Include both short-run and long-run cost curves, and clearly show the consumer surplus. (3 marks) $ $ Industry Representative Firm 200 200 150 125 100 60 50 C.S. LRS LRS D D 150 100 60 50 SRMC SRAC LRAC LRAC 650 750 1000 1250 1500 25 50 Quantity Quantity c) Suppose that the demand for gadgets increases and is now given by the equation: P = 150 0.1 Q. Fill in the following table describing the new long-run equilibrium. (6 marks) Show the new long-run equilibrium for a representative firm and for the industry on the diagram above, but do not show changes in short-run cost curves. (3 marks) [Note: Show all your work in the space below. If space is not sufficient, continue on the back of the previous page.] Firm Item Value Industry Item Value Firm s quantity 25 Price 50 Firm s profits 0 Quantity 1,000 Number of firms 40 Consumer Surplus 50,000 In a constant cost industry, the long-run equilibrium price is equal to the minimum of the LRAC. Since there has been no change in LRAC, then P remains unchanged at $50. At this price, the total quantity transacted in the market is now: P = 150 0.1 Q 50 = 150 0.1 Q 0.1 Q = 150 50 0.1 Q = 100 Q* = 1,000 Since each firms is producing at the minimum of the LRAC curve (i.e., 25 gadgets per day), the total number of firms is now n = 1,000/25 = 40. Since the industry is in long-run equilibrium, each firm is making zero economic profits (i.e., they are producing at the minimum of the LRAC). The consumer surplus is equal to the area below the demand curve and above the price line. That is, the consumer surplus is equal to the area of the triangle with a height of 100 (i.e., 150 50) and base of 1,000: (100 x 1000)/2 = 50,000. Page 8 of 11
d) Suppose new evidence shows that the industry is not constant cost, but increasing cost. If the industry is increasing cost, the new long-run equilibrium after the increase in demand will have the following attributes, compared to when the industry is constant cost. Circle the correct answer. (3 marks) [Note: You don t need to show this equilibrium on the diagram above.] Item Price (P) Industry Quantity (Q) Each Firm s Profits Value Same / Higher / Lower Same / Higher / Lower Same / Higher / Lower e) Go back to the initial long-run equilibrium of a constant cost industry (i.e., before the increase in demand). Suppose now that the government introduces an excise tax (i.e., a tax per unit) of $10. Fill in the following table describing the new long-run equilibrium. (6 marks) Show the new long-run equilibrium for a representative firm and for the industry on the diagram above. (3 marks) [Note: Show all your work in the space below. If space is not sufficient, continue on the back of the previous page.] Firm Item Value Industry Item Value Firm s quantity 25 Price 60 Firm s profits 0 Quantity 650 Number of firms 26 Consumer Surplus 21,125 The imposition of the excise tax of $10 per unit will shift the LRAC curve up exactly by $10. Since the long-run equilibrium price is equal to the minimum of the LRAC, the new long-run equilibrium price will be now $60. At this price, the total quantity transacted in the market is now: P = 125 0.1 Q 60 = 125 0.1 Q 0.1 Q = 125 60 0.1 Q = 65 Q* = 650 Since each firms is producing at the minimum of the LRAC curve (i.e., 25 gadgets per day), the total number of firms is now n = 650/25 = 26. Since the industry is in long-run equilibrium, each firm is making zero economic profits (i.e., they are producing at the minimum of the LRAC). The consumer surplus is equal to the area below the demand curve and above the price line. That is, the consumer surplus is equal to the area of the triangle with a height of 65 (i.e., 125 60) and base of 650: (65 x 650)/2 = $21,125. Page 9 of 11
Question 2 (25 marks) The Red Farm is the sole source of supply of raspberries in Yorkland. The marginal cost of producing berries is constant at $20, and fixed costs are nil. The market demand schedule for berries is P = 100 0.01 Q, where P is price and Q is quantity measured in buckets of berries per day. a) What is the profit maximizing level of output? What price will this monopolist charge for a bucket of berries? What are the profits of the firm? (6 marks) We must equate MC and MR in order to find the profit maximizing level of output of the monopolist. The MR curve has the same intercept as the demand curve but it s twice as steep, i.e., the equation for the MR curve is MR = 100 0.02 Q. Therefore, MR = MC 100 0.02 Q = 20 0.02 Q = 100 20 0.02 Q = 80 Q* = 4,000 The price that the monopolist will charge is: P* = 100 0.01 Q* = 100 0.01 (4,000) = 100 40 = $60 Since marginal cost is constant at $20, then average variable cost is also constant at $20. And since there are no fixed costs, average total cost is also constant at $20. Therefore, the monopolist s profits are (P ATC) Q = ($60 $20) (4,000) = $160,000. b) Draw the profit maximizing solution in the diagram below. (2 marks) Clearly indicate the consumer surplus, the producer surplus, and the deadweight loss, if any. (3 marks) $ Consumer Surplus 80 Producer Surplus 60 40 Deadweight Loss 20 MC MR D 4 5 8 10 12 Buckets of berries per day (in thousands) Page 10 of 11
c) Suppose the owner of Red Farm has found a way (do not ask how!) to extract the highest price any consumer is willing to pay each day for every bucket of berries. Now complete the table below. (8 marks) [Note: Show all your work in the space below. If space is not sufficient, continue on the back of the previous page.] Item Value Item Value Price * 20 Total Profits 320,000 Quantity 8,000 Consumer Surplus 0 * of last unit sold If the monopolist can perfectly discriminate, it will produce an output where the MC curve intersects the demand curve, i.e., 8,000 gadgets per day. The last unit sold will have a price of $20 (i.e., equal to MC). The monopolist will appropriate the entire consumer surplus, so CS = $0. [Note that the producer surplus will be now equal to the total surplus, i.e., equal to the area below the demand curve and above the MC curve, so PC = $320,000.] Since there are no fixed costs, the monopolist s profits will be equal to the producer surplus, i.e., $320,000. d) Go back to monopoly market outcome when the monopolist did not price-discriminate. Suppose now that the government attempts to regulate this monopoly by implementing a marginal cost pricing policy. What price will the monopolist charge for a bucket of berries? What will the profit maximizing level of output be? What will the profits of the firm be? (6 marks) If the government implements a marginal cost pricing policy, then it will set a price ceiling at the level where the MC curve intersects the demand curve. Therefore, the price ceiling will be equal to $20. Since P = MR = MC = ATC = $20 for Q < 8,000, the monopolist will be making the same profits (i.e., zero economic profits) for any level of output up to 8,000 units. Therefore, there is no unique profit-maximizing level of output the monopolist will be indifferent producing any level of output less than 8,000 units (including Q = 0). Page 11 of 11