Department of Economics Prof. Gustavo Indart University of Toronto November 28, 2008 SOLUTIONS ECO 100Y 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. 2. Aids allowed: a simple calculator. 3. Write with pen instead of pencil. DO NOT WRITE IN THIS SPACE Part I 1. /8 6. /8 2. /8 7. /8 3. /8 4. /12 Part II /45 5. /8 TOTAL /105 Page 1 of 12
PART I (60 marks) Instructions: Answer all questions in the space provided. 1. (8 marks) Avi likes to attend both rock concerts and basketball games. The cost of attending rock concerts or basketball games is the same. For his current monthly consumption of rock concerts and basketball games, Avi values one more concert twice as much as he values one more basketball game i.e., his marginal utility of rock concerts (MU RC ) is twice as much as his marginal utility of basketball games (MU BG ). Placing rock concert on the horizontal axis, use an indifference curve diagram to indicate Avi s current consumption bundle. Can Avi increase his present level of utility or satisfaction by changing his current consumption choice? Briefly explain your answer with the help of your diagram. Avi is not presently maximizing his utility since at his current consumption bundle his MRS is greater than the relative prices of the two goods he consumes, that is, presently the last dollar he spends on rock concerts increases (RC) his total utility by more than the last dollar he spends on basketball games (BG) does it. Indeed, the MRS = MU RC / MU BG = 2 and P RC /P BG = 1 and thus MU RC /P RC > MU BG /P BG. This can be seen graphically in the diagram below. At the present consumption bundle (point A), Avi s MRS (i.e., the absolute value of the slope of indifference curve I 1 ) is greater than the relative prices of the two goods (i.e., the absolute value of the slope of his budget line). Avi can increase his level of utility (i.e., reach a higher indifference curve) by increasing his consumption of RC and reducing his consumption of BG. And he will be maximizing his utility when the last dollar he spends on RC and the last dollar he spends on BG both increase his total utility by the same amount i.e., when MRS = P RC /P BG. This is shown graphically in the diagram below by increasing the quantity of RC and reducing the quantity of BG (i.e., moving down along his budget line), Avi increases his utility (i.e., reaches higher indifferences curves) until he maximizes his utility (i.e., reaches the highest possible indifference curve) at point B (where MRS = P RC /P BG ). BG A B I 2 I 1 RC Page 2 of 12
2. (8 marks) Audrey spends her income on only two goods video games [X-axis good] and books [Y-axis good]. The price of video games decreases but Audrey continues purchasing the same quantity of video games as before. Dawoon, an economics student, explains to Audrey that video games are an income-independent good for her. Do you agree with Dawoon s view? Draw a consumer indifference curve diagram to analyze this situation and indicate, with reasons, whether you agree or disagree with Dawoon s view. No, I don t agree with Dawoon s view. If Audrey continues buying the same quantity of video games (VG) when its price falls, then we must conclude that VG is an inferior good for Audrey and that the substitution and income effects of the decrease in price are of different sign but of equal absolute value. Let me explain this conclusion using the diagram below. Initially, Audrey is maximizing her utility consuming bundle A bundle A lies on Audrey s original budget line (i.e., it s a feasible consumption bundle) and also on the highest possible indifference curve. When the price of VG decreases, bundle A lies now below Audrey s new budget line and thus she will choose a different combination on the new budget line that will allow her to increase and maximize her utility. She will choose to consume at point B where the quantity of books is greater than before but the quantity of VG is the same. The total effect of the drop in the price on her quantity demanded of VGs is thus nil but this total effect is the combination of the substitution effect and the income effect triggered by the fall in the price of VGs. What are the substitution and the income effects? The substitution effect is the change in the quantity demanded as a result of the change in relative prices while keeping real income constant (i.e., while remaining on the same indifference curve I 1 ) and this is shown in the diagram below by the movement from point A to point C on the same indifference curve I 1. The income effect is the change in the quantity demanded as a result of the change in real income while keeping relative prices constant at the new level (i.e., moving to a different indifference curve) and this is shown in the diagram below by the movement from point C to point B on the higher indifference curve I 2. Since the quantity demanded of VGs decreases when her real income rises, then VGs is an inferior good (and not an income-independent good) for Audrey. And the fact that she ends up consuming the same quantity of VGs as before the drop in its price is explained by the different signs but equal absolute value of the changes in the quantities demanded as a result of the substitution and the income effects. B B I 2 A C s.e i.e. I 1 VG Page 3 of 12
3. (8 marks) Nerissa spends her income on gas for her car and food. Both gas and food are normal goods for Nerissa. The government raises the tax on gas, thereby raising the price of gas. But the government also lowers the income tax, thereby increasing Nerissa s money income, and this rise in her money income is just enough to leave Nerissa with the same real income as she had before the price of gas increased. With the help of an indifference curve diagram, explain whether Nerissa will buy now more, less, or the same amount of gas as before these changes. In your diagram, place food on the vertical axis and gas on the horizontal axis. The rise in the gas tax increases the price of gas, and thus it has an impact on Nerissa s quantity demanded of gas. The total effect of the price increase on the quantity demanded of gas can be split into the substitution effect and the income effect. On the one hand, the substitution effect measures the change in the quantity demanded as a result of the change in relative prices while keeping real income constant (i.e., while remaining on the same original indifference curve). On the other hand, the income effect measures the change in the quantity demanded due to the change in real income while keeping relative prices constant at the new level (i.e., moving to a different indifference curve). All else equal, Nerissa s quantity demanded of gas decreases because of both the substitution and the income effect since gas is a normal good for her. However, the decrease in income tax allows Nerissa s money income to increase enough to offset the income effect of the increase in the price of oil. Therefore, this increase in money income allows Nerissa to remain on the original indifference curve (i.e., to continue achieving the same level of satisfaction as before). Therefore, since the reduction in income tax eliminates the income effect of the increase in the price of oil, the change in the quantity demanded of gas will only be due to the substitution effect. The new quantity demanded will be at the point on the original indifference curve where the MRS is equal to the new relative prices. This can be observed in the diagram below. Nerissa is initially maximizing utility by consuming bundle A. Point A is the point on Nerissa s budget line (BL 1 ) that reaches the highest indifference curve (I 1 ), i.e., at this point the MRS is equal to the relative prices of the two goods. As the price of gas increases, Nerissa s budget line becomes steeper (BL 2 ) and she cannot enjoy the same level of satisfaction as before (i.e., she cannot consume at a point on the original indifference curve). In turn, the reduction in income tax increases her money income and her budget line shifts up to BL 3, just enough for her to reach once again indifference curve I 1 at consumption bundle B. Therefore, as a result of all these changes, Nerissa ends up buying less gas than before while enjoying the same level of satisfaction than before. Books B A I 1 BL 3 BL 2 BL 1 Gas Page 4 of 12
4. (12 marks) Alexine consumes only two goods: CDs and books. The graph below depicts four of Alexine s indifference curves. 12 Books per month 8 4 C B A 4 BL 2 8 12 CDs per month BL 1 16 4.1 (3 marks) Suppose the price of one CD is $5 and the price of one book is $10 and Alexine s monthly income is $80. What is the expression for Alexine s budget line? Draw her budget line in the diagram above. How many CDs and books will she purchase every month? Briefly explain. (Note: Use whole units, not fractions of units of CDs and books.) Alexine s budget line is given by the expression 80 = 5 CD + 10 B or B = 8 0.5 CD. Her budget line is shown as line BL 1 in the diagram above. As shown in the diagram, she will maximize her utility when purchasing 4 books and 8 CDs per month (point A). Indeed, given her budget constraint she will maximize utility (i.e., reach the highest possible indifference curve) at the point on her budget line where the budget line is just tangent to an indifference curve (i.e., to the highest possible indifference curve). 4.2 (3 marks) What is the marginal rate of substitution (MRS) of CDs for books at Alexine s equilibrium of part 4.1 above? Briefly explain. If the marginal utility of the last book purchased by Alexine is 8, what is the marginal utility of the last CD she purchases? Show all your work. At her equilibrium of part 4.1, the slope of the indifference curve is equal to the slope of the budget line, i.e., the MRS is equal to P CD /P B = 0.5. The MRS is equal to the ratio of the marginal utilities of the two goods, i.e., MRS = MU CD /MU B. Therefore, since MRS = 0.5 and MU B = 8, then MU CD = MRS * MU B = 0.5 * 8 = 4. Page 5 of 12
4.3 (3 marks) Suppose that the price of CDs increases to $10 (while her money income and the price of books remain as before), what is the expression for Alexine s new budget line? Draw in the diagram above her new budget line. How many CDs and books will she purchase now? Briefly explain. (Note: Use whole units, not fractions of CDs and books.) The expression for the new budget line is 80 = 10 CD + 10 B or B = 8 CD. Her budget line is shown as line BL 2 in the diagram above. As shown in the diagram, now she will maximize her utility when purchasing 4 books and 4 CDs per month (point B). Indeed, given her budget constraint she will maximize utility (i.e., reach the highest possible indifference curve) at the point on her new budget line where the budget line is just tangent to an indifference curve (i.e., to the highest possible indifference curve). 4.4 (3 marks) Measured in units of CDs, what are the substitution effect and the income effect of the increase in the price of CDs from $5 to $10? Briefly explain. Show the substitution and income effects in the diagram above. What type of goods are CDs for Alexine? The total effect of the increase in the price of CDs on Alexine s quantity demanded of CDs is a decrease from 8 to 4 units. This total effect is the summation of the substitution effect and the income effect. The substitution effect is the change in the quantity demanded as a result of the change in relative prices while keeping real income constant (i.e., while remaining on the same indifference curve) and this is shown in the diagram above by the movement from point A to point C on the original indifference curve. The change in the quantity demanded as a result of the substitution effect is thus a decrease of 4 CDs. The income effect is the change in the quantity demanded as a result of the change in real income while keeping relative prices constant at the new level (i.e., moving to a different indifference curve) and this is shown in the diagram above by the movement from point C to point B on a lower indifference curve. The change in the quantity demanded as a result of the income effect is thus zero, which means that CDs are an income-independent good for Alexine. Page 6 of 12
5. (8 marks) With the help of an appropriate diagram, explain whether the following statement is true or false: If the marginal product of labour (MP L ) is falling, then the average product of labour (AP L ) must also be falling. Use an example to illustrate your explanation. This statement is false. The AP L is increasing as long as the MP L is greater than the AP L. Therefore, if the MP L is falling but it s still greater than the AP L, then the AP L will be rising and not falling. Let s look at an example. Suppose that when 5 units of labour are used in production the AP L is 10 and the MP of the 5 th unit of labour is 16. Suppose further that the MP of the 6 th unit of labour is 14 (i.e., MP L is falling) what is the average product of labour when 6 units of labour are used in production? Well, since the additional unit of labour increases total product by more than each of the previous 5 units, the AP L rises. In our example, total product increases from 50 units to 66 units when the 6 th unit of labour is employed, and thus the AP L increases from 10 units to 11 units. Therefore, the correct statement should be that when the MP L is decreasing, the AP L might be increasing or decreasing depending on whether MP L is greater or smaller than AP L. This is illustrated in the following diagram. AP MP 16 14 11 10 MP AP 5 6 L Page 7 of 12
6. (8 marks) Scooters are produced using two factors of production: capital [K] and labour [L]. The price of labour [the wage rate] increases by 2% and, at the same time, the price of capital [rental fee] increases by 5%. Charmaine is of the view that the long-run impact of this change in the relative prices of the factors of production will be an increase in both the marginal product of labour and the marginal product of capital. Do you agree with Charmaine s view? Use an isoquant curve diagram to analyze this situation and indicate, with reasons, whether you agree or disagree with Charmaine s view. No, I don t agree with Charmaine s view. Although the prices of both K and L have increased, the price of K has increased relatively more, which means that the relative price of L has decreased. 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 labour for capital (i.e., it will adopt a more labour-intensive method of production). This is represented by a movement down along the isoquant representing the level of output being produced. K K 1 A K 2 B Q 1 L 1 L 2 L Given the assumption of diminishing marginal productivity of factors of production, as the quantity of L increases, the MP L decreases; in turn, as the quantity of K decreases, the MP K increases. Therefore, Charmaine s view is wrong. [Note that this outcome is reinforced by the fact the MP of a factor of production also increases when the 5quantity of another factor of production increases.] The statement can also be discussed as follows. 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, at point A the MRTS = w/r where MRTS = MP L /MP K, which means that the last dollar spent on capital and the last dollar spent on labour increase total output by the same amount. This equilibrium is altered when w/r increases to w /r. Indeed, at point A now MP L /MP K > w /r, which means that the last dollar spent on labour increases total output by more than the last dollar spent on capital does it. To restore equilibrium, then, MP L must decrease (through an increase in L) and MP K must increase (through a decrease in K), i.e., the firm will spend more on labour and less on capital since by doing so its total cost of producing the given level of output will decrease. Page 8 of 12
7. (8 marks) Greg owns a small business that produces apple pies for the local market. His total fixed cost (TFC) is the cost of his baking oven, while his total variable cost (TVC) is the cost of apples, flour and labour required for the production of pies. The table below shows Greg s cost of producing 100, 200 and 300 pies per day with different combination of his fixed and variable factors of production. Quantity of Total Variable Cost ovens Total Fixed Cost 100 pies 200 pies 300 pies 1 $400 $200 $500 $1,100 2 $600 $180 $280 $750 3 $800 $150 $160 $400 7.1 If Greg has only one oven at the present time, what is his short-run average total cost (ATC) of producing 100, 200, and 300 pies per day? Show all your work. (3 marks) TC(100) = TFC + TVC(100) = 400 + 200 = 600 ATC(100) = TC(100) / 100 = 600/100 = 6 TC(200) = TFC + TVC(200) = 400 + 500 = 900 ATC(200) = TC(200) / 200 = 900/100 = 4.5 TC(300) = TFC + TVC(300) = 400 + 1100 = 1500 ATC(300) = TC(300) / 300 = 1500/300 = 5 7.2 Greg is currently producing 200 pies per day and he believes the demand for his pies will not increase in the foreseeable future. Nonetheless, he is considering the possibility of buying one or two more ovens. Should he buy more ovens? If so, how many more? Briefly explain (marks will be given entirely for your explanation). (5 marks) Since all his factors of production are now variable, he would like to have the quantity of ovens that will allow him to produce 200 pies a day at the minimum cost. Let s compare the total cost of producing 200 pies a day with the three options of 1, 2, and 3 ovens: 1 oven TC(200) = TFC + TVC(200) = 400 + 500 = 900 (as in part 7.1 above) 2 ovens TC(200) = TFC + TVC(200) = 600 + 280 = 880 3 ovens TC(200) = TFC + TVC(200) = 800 + 160 = 960 Since the cost of producing 200 pies a day is minimized when having 2 ovens, Greg will buy one more oven. Page 9 of 12
PART II (45 marks) Instructions: Multiple choice questions are to be answered using a black pencil or a black or blue ballpoint pen on the separate SCANTRON sheet being supplied. Be sure to fill in your name and student number on the SCANTRON sheet! Each question is worth 3 marks. No deductions will be made for incorrect answers. Write your answers to the multiple choice questions ALSO in the table below. You may use this question booklet for rough work, and then transfer your answers to each multiple choice question onto the separate SCANTRON sheet. Your answers must be on the SCANTRON sheet. In case of a disagreement, the answer to be marked is the one on the SCANTRON sheet. 1 2 3 4 5 6 7 8 B D B D C E B A 9 10 11 12 13 14 15 A B E D C E E 1. Laraine consumes only books and CDs. Laraine s marginal utility of books measures A) the slope of her indifference curve. B) the additional satisfaction she gets from one more book while holding the quantity of CDs constant. C) the slope of her budget line. D) her marginal rate of substitution. E) none of the above. 2. Rachel consumes only books (Y-axis) and CDs (X-axis). Books and CDs are both normal goods for Rachel. If the price of CDs increases, which of the following statements is correct? A) Her budget line becomes flatter. B) Her quantity demanded of books increases as a result of the income effect. C) Her quantity demanded of books decreases as a result of the substitution effect. D) At her new equilibrium consumption bundle her MRS will be greater than before. E) None of the above is correct. 3. Matilda consumes only movies (Y-axis) and video games (X-axis). If Matilda s incomeconsumption line has a negative slope, which of the following statements might be correct? A) Both goods are normal for Matilda. B) One good is normal and the other is inferior for Matilda. C) Both goods are inferior for Matilda. D) One good is inferior and the other is income-independent for Matilda. E) Both B) and D) might be correct. Page 10 of 12
4. Sihang consumes only food and clothing, and the following table shows three of her possible consumption bundles: Bundle Food Clothing A 8 5 B 5 8 C 6 3 If preferences satisfy the three general assumptions stated in class, then Sihang A) is definitely indifferent between bundles A and B. B) is definitely indifferent between bundles B and C. C) prefers bundle A to bundle B. D) prefers bundle A to bundle C. E) prefers bundle B to bundle C. 5. A parallel shift in the consumer s budget line always indicates a change in A) the money price of at least one of the goods. B) money income. C) real income. D) the consumer s tastes. E) the prices of the two goods. 6. The average product for six workers is 15. If the marginal product for the seventh worker is 10, A) marginal product is rising. B) marginal product is falling. C) average product is rising. D) average product is falling. E) both marginal product and average product are falling. 7. Suppose total fixed cost is $100 and average variable cost is $5 at all levels of output. Which of the following is then true? A) Marginal cost will equal average total cost. B) Average total cost will decrease when output is increased. C) Marginal cost will be less than average variable cost. D) Average total cost will be constant. E) None of the above. 8. The total cost (TC) of producing donuts is given as TC = 100 + 2Q, where Q represents thousands of donuts per day. What is the total fixed cost (TFC)? A) 100. B) 2q. C) 2. D) 2 + 100/Q E) None of the above. 9. A local factory pays $100 per unit of labour and finds that the average product of labour is 10 units of output when 50 units of labour are employed. Therefore, when 50 units of labour are hired, average variable cost is A) $10. B) $5. C) $500. D) $100. E) None of the above. Page 11 of 12
10. Suppose fixed cost is $500 and average variable cost is constant at all positive levels of output. Which of the following is then true? A) Marginal cost is equal to average total cost. B) Average total cost continuously decreases when output is increased. C) Marginal cost is less than average variable cost. D) Average total costs is constant. E) None of the above is true. 11. For Eik s firm, total cost is $10 at 5 units of output and $13 for 6 units. In that range of output, his firm s marginal cost is A) greater than average total cost. B) equal to average total cost. C) less than average total cost. D) increasing. E) Both A) and D) are correct. 12. Suppose that the production function indicates that 200 units of labour and 400 units of capital can produce 1,000 units of output and that 600 units of labour and 1,200 units of capital can produce 4,000 units of output. On this basis, the firm is experiencing A) increasing marginal returns to labour. B) decreasing marginal returns to labour. C) constant returns to scale. D) increasing returns to scale. E) none of the above. 13. Arvind s firm produces 500 units of output per day. At this level of output, his marginal cost is $8.00, his average total cost is $7.50, and his average variable cost is $4.00. Therefore, his daily total fixed cost must be A) $7.50. B) $750. C) $1,750. D) $3,750. E) none of the above. 14. When a firm seeks to minimize the cost of producing a given output, it does NOT need to know A) the technically efficient input combinations. B) the economically efficient input combination. C) its production function. D) the prices of inputs. E) the maximum level of profits. 15. If capital costs $8 per unit and labour costs $4 per unit, and a firm s marginal product of capital is 4 and the marginal product of labour is 2, the firm should A) employ more capital and labour. B) employ less capital and labour. C) employ more capital and less labour. D) employ less capital and more labour. E) not change its current factor use. Page 12 of 12