Department of Economics Prof. Gustavo Indart University of Toronto December 3, 2004 SOLUTIONS ECO 100Y L0101 INTRODUCTION TO ECONOMICS Midterm Test #2 LAST NAME FIRST NAME STUDENT NUMBER INSTRUCTIONS: 1. The total time for this test is 50 minutes. 2. This exam consists of two parts. 3. This question booklet has 7 (seven) pages. 4. Aids allowed: a simple calculator. 5. Use pen instead of pencil. DO NOT WRITE IN THIS SPACE Part I /15 Part II 1. /15 2. /20 TOTAL /50 /100 Page 1 of 7
PART I (15 marks) Instructions: Circle the best answers to each question. Each question is worth 3 (three) marks. No deductions will be made for incorrect answers. 1. A profit-maximizer firm will shut down production if price is A. below minimum total average cost but above minimum average variable cost B. below minimum average variable cost C. above minimum average fixed cost D. below minimum average revenue E. below minimum total average cost 2. If the average product curve is rising, then the marginal product curve A. must lie above the average product curve and must also be rising B. must be above the average product curve C. can be either above or below the average product curve although it must be rising over the entire range D. must lie below the average product curve E. none of the above 3. A perfectly competitive industry is in short run equilibrium. Each firm is initially making economic profits of $100,000 per year. Now, each firm faces an increase in property taxes of $40,000 per year. As a result of this shock, which one of the following statements is correct; A. each firm would shut down B. each firm would produce an unchanged output and make economic profits of $60,000 C. each firm would produce an increased output and make economic profits of more than $100,000 D. each firm would produce a lower output and make economic profits of less than $100,000 E. none of the above are correct 4. Assume a firm is now employing 100 units of labour and 50 units of capital to produce 200 units of "fax" machines. The price of labour is $10 per unit and the price of capital is $5 per unit. The MP L equals 2 and MP K equals 5. In this circumstance A. the firm is profit maximizing and cost minimizing B. the firm should increase the use of both inputs C. the firm could lower its production costs by decreasing labour inputs and increasing capital input D. the firm could increase output at no extra cost by increasing capital input and decreasing labour input E. none of the above 5. Which of the following would occur if a single farm in pure competition lowered its price below the equilibrium market price? A. all other farms would lower their prices too B. this single farm would not be maximizing profits C. this single farm would get a larger share of the market, and this would be profitable for it D. other farms would be driven out of the industry E. none of the above Page 2 of 7
PART II (35 marks) Question 1 (15 marks) Peter consumes only two goods, Good X and Good Y, where Good X is an income-independent good. His income is $1,000 per month, the price of Good X is $2.00 and the price of Good Y is $2.50. Peter maximizes his utility when he spends half of his income in the consumption of Good X. Y 400 300 C The substitution effect is shown by the movement from point A to point C. The income effect is shown by the movement from point C to point B. 200 B A I 1 100 s.e. I 2 125 100 200 250 300 400 500 X a) In the diagram above, sketch Peter s budget line (clearly indicate the values of the vertical and horizontal intercepts). Without drawing any indifference curve, indicate Peter s utilitymaximizing combination of Good X and Good Y (and label it point A ). (2 marks) b) Suppose now that the price of Good X increases to $4.00. In the same diagram, draw Peter s new budget line clearly indicating the values of the vertical and horizontal intercepts. Suppose that Peter still maximizes his utility when he spends half of his income in the consumption of Good X. Without drawing any indifference curve yet, indicate Peter s utility-maximizing combination of Good X and Good Y (and label it point B ). (2 marks) c) Assuming smooth and convex indifference curves, clearly show in your diagram the substitution and the income effects keeping in mind that Good X is an income-independent good. [Now you can and must draw the appropriate indifference curves.] (Note: draw the indifference curves with pencil; do not worry too much about the beauty of your smooth and convex curves.) (4 marks) Page 3 of 7
d) Define the substitution effect and the income effect. (3 marks) The substitution effect is the change in the quantity demanded of a commodity as a result of a change in relative prices, while keeping real income constant. The income effect is the change in the quantity demanded of a commodity as a result of a change in real income, while keeping relative prices constant. e) Measured in units of Good X, how much is the substitution effect in part c) above? How much is the income effect? (2 marks) The substitution effect is equal to a decrease of 125 units of X, that is, equal to -125 units of X. The income effect is equal to 0 units of X, since X is an income independent good. f) Given the information in parts a) and b) above, draw Peter s demand curve for Good X in the diagram below. Clearly indicate all relevant points. (2 marks) P X 4 3 2 1 D 125 250 X Page 4 of 7
Question 2 (20 marks) Suppose that the ice cream industry is a perfectly competitive, constant cost industry with demand defined by P = 50 0.003Q, where P is the price of ice cream and Q is the quantity of ice cream per week measured in gallons. Suppose that there are 100 identical firms in the industry and that the short-run Marginal Cost equation for each firm is MC = 10 + 0.2q. The minimum of the AVC of each firm is reached at 40 units of output, and the minimum of the ATC of each firm is reached at 80 units of output. The industry is initially in long-run equilibrium. P Firm P Industry 60 60 40 S 40 S 26 20 ATC LRAC 2 AVC D 29 26 LRAC 1 20 MC D 40 50 80 100 q 50 100 70 80 Q (100 s) a) What is the expression for the supply curve of an individual firm? (3 marks) Draw the firm s supply curve in the left-hand side diagram above. Label the curve and indicate all the relevant points. (Note: draw the supply curve even if you cannot derive its mathematical expression.) (1 mark) The supply curve of an individual firm has two segments: 1) for prices below the minimum of the AVC curve, the quantity supplied will be zero; and 2) for prices above the minimum of the AVC curve, the supply curve will be equal to the MC curve. If the price equal to the minimum of the AVC curve, then the firm will be indifferent between shutting down production and producing a minimum positive output as determined by the MC curve. Since the minimum of the AVC curve is reached at q = 40, this minimum is: MC = 10 + 0.2 (40) = 10 + 8 = 18. The expression for the firm s supply curve is therefore: 1) q = 0 if P < 18; and 2) P = 10 + 0.2q or q = 5P 50 if P > 18 Page 5 of 7
b) What is the expression for the short-run market supply curve? (3 marks) Draw the short-run industry s supply curve in the right-hand side diagram above. Label the curve and indicate all the relevant points. (Note: draw the supply curve even if you cannot derive its mathematical expression.) (1 mark) The industry supply curve has three segments: 1) for prices below the minimum of the firms AVC curve, the quantity supplied will be zero; 2) for prices above the minimum of the AVC curves of the firms, the supply curve will be equal to the horizontal summation of the firms MC curves; and 3) for the price equal to the minimum of the AVC curve, the supply curve will be horizontal up to its intersection with the segment determined by the firms MC curves. Since the minimum of the firms AVC curve is reached at q = 40, the horizontal segment of the industry supply curve will be up to the level of output Q = 40 (100) = 4,000. The expression for the industry s supply curve is therefore: 1) 2) 3) Q = 0 if P < 18; and Q = 100q = 500 P 5000 or P = 10 + 0.002 Q if P > 18 P = 18 if 0 < Q < 4,000 c) Draw the market demand curve in the above diagram and clearly show the market equilibrium price and quantity. (1 mark) Calculate algebraically the short-run competitive equilibrium price and quantity in this market? (3 marks) What is the short-run equilibrium output of the individual firm in this market? (1 mark) D = S 50 0.003 Q = 10 + 0.002 Q 0.005 Q = 40 Q* = 8,000 P* = 50 0.003 (8,000) = 50 24 = 26 Since Q = 100 q q* = Q*/100 = 8,000/100 = 80 Page 6 of 7
d) In the industry diagram above, draw the industry s long-run supply curve (and label it LRS 1 ). (2 marks) Since this industry is a constant cost industry, the LRS curve will be horizontal at the level of the minimum LRAC curve. Since the industry is in long-run equilibrium, each firm is producing at the minimum LRAC and making zero profit. Therefore, the LRS curve will be horizontal at P = 26. e) Suppose now that the government introduces a permanent $3 tax per unit of ice cream to be paid by the producers. In the industry diagram above, draw the industry s new long-run supply curve (and label it LRS 2 ). (Hint: You don t need to draw the new short-run supply curves of the firm and the industry in order to answer this question). (1 mark) The new long-run supply curve will be horizontal at P = 29 since LRAC will increase by $3 at all levels of output (and the minimum of the LRAC will now be 29, and firms will reach this minimum at the same level of output as before, i.e., at q = 80 since LRAC has increase by $3 at each level of output). f) What is the new long-run equilibrium price and quantity for the industry? (2 marks) The new long-run equilibrium price will be P = 29 (as determined by the LRS curve). To find the long-run equilibrium quantity, we must equate D and S. Therefore, P* = 50 0.003 Q* 0.003 Q* = 50 P* 0.003 Q* = 50 29 = 21 Q* = 21/0.003 = 70 g) What is the new long-run equilibrium output of each firm? (1 mark) Since the minimum optimum scale of production has not changed, firms will continue maximizing profits at q = 80. (See answer to part e) above.) h) What is the number of firms in the new long-run equilibrium? (1 mark) Since Q* = n.q* n = Q*/q* = 7,000 / 80 = 87.5 (or, if you wish, either 87 or 88). Page 7 of 7