# University of Toronto June 14, ECO 100Y INTRODUCTION TO ECONOMICS Midterm Test # 1

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1 Department of Economics Prof. Gustavo Indart University of Toronto June 14, 2007 SOLUTION ECO 100Y INTRODUCTION TO ECONOMICS Midterm Test # 1 A LAST NAME FIRST NAME STUDENT NUMBER SECTION ( Morning or Evening ): INSTRUCTIONS: 1. The total time for this test is 1 hour and 50 minutes. 2. This exam consists of three parts. 4. Aids allowed: a simple calculator. 5. Write with pen instead of pencil. DO NOT WRITE IN THIS SPACE Part I 1. /5 Part II 1. /6 2. /5 2. /8 3. /5 3. /16 4. /5 Part III /20 5. /5 6. /5 TOTAL /80 Page 1 of 15

3 2. When the price of apples is \$0.75 a piece, Yvonne doesn t buy any. However, when the price of apples drops to \$0.50 a piece she eats one apple a day, and when it drops to \$0.40 a piece she eats two apples a day. Statement: Natalia, an ECO100 student, concludes that Yvonne s consumer surplus is \$0.45 when the price of apples is \$0.40 a piece. Position: Do you agree with Natalia s conclusion? Indicate, with reasons, whether you agree or disagree with Natalia s view. [Note: Assume that Yvonne does not partially eat an apple, i.e., she only eats two whole apples, one whole apple, or none at all.] No, I disagree with Natalia s conclusion. When the price is \$0.75 Yvonne doesn t buy any apples. This means that the maximum price she is willing to pay for the first apple is less than \$0.75. However, when the price of apples drops to \$0.50 a piece she buys one apple a day. This means that the maximum price she is willing to pay for this first apple is exactly \$0.50, and thus the consumer surplus she gets by consuming this first apple is zero. Indeed, the maximum price she is willing to pay is equal to the actual price she is paying for the apple and thus the consumer surplus is zero. Now, when the price drops to \$0.40 she buys two apples a day. Again she will pay now the maximum price she is willing to pay for this second apple, but she will pay a price lower than the maximum price she was willing to pay for the first apple. The second apple does not generate any consumer surplus for Yvonne, but the first one generates a consumer surplus equal to the difference between the maximum price she was willing to pay for it (\$0.50) and the actual price she is paying (\$0.40) thus Yvonne s total consumer surplus is \$0.10 and not \$0.45 as Natalia indicates. P Consumer Surplus Q/day Page 3 of 15

4 3. Zijian spends all his disposable income on books [x-axis product] and CDs [y-axis product]. Zijian has negative income elasticity for books and his substitution effect for books is stronger than her income effect. Statement: Evangelos, Zijian s friend, believes that when the price of books rises Zijian will maximize his level of consumer satisfaction by purchasing more books and therefore Zijian s demand curve for books has a positive slope. Position: Do you agree with Evangelos s view? Use a proper diagram to analyze this situation and indicate, with reasons, whether you agree or disagree with Evangelos. No, I disagree with Evangelos s view. If Zijian has negative income elasticity for books, then books are an inferior good for him i.e., his quantity demanded of books decreases as income increases. Therefore, the substitution and the income effect move in opposite directions, but since the substitution effect is stronger than the income effect, the direction of the total effect will be determined by the substitution effect and Zijian s demand curve for books will have a negative slope. That is, books are an inferior non-giffen good for Zijian. This is illustrated in the following diagrams. Zijian is initially maximizing his utility consuming bundle A. As the price of books increases his budget line shifts from BL 1 to BL 2. He will now CD consume a different bundle on this new budget line and will reduce his level of satisfaction since B the highest indifference curve he will be able to reach is lower than indifference curve I 1. His real income has thus decreased. Let s examine the substitution and the income effect of this increase BL 2 A in the price of books. To measure the substitution effect we must I 1 consider the change in the quantity demanded as a result of the change in relative prices while C BL 1 assuming no change in real income (i.e., while assuming that Zijian remains on the same indifference curve). This is illustrated by the movement from point A to point B, and the quantity demanded decreases from B A to B B. I 2 Now we measure the income effect by allowing B B B C B A B real income to fall while keeping relative prices constant. In this way, Zijian moves to a lower indifference curve. Since books are an inferior P good for Zijian, as his income decreases his quantity demanded for books increases so he P 2 ends up consuming a quantity greater than B B. But the substitution effect is greater than the income effect, and thus although he ends up consuming P 1 more books than B B he will consume less than B A he will consume a quantity B C as shown in the diagram. D His demand curve for books thus has a negative slope as indicated in the diagram on the left. B C B A B Page 4 of 15

5 4. Oranges are produced with a fixed factor (land) and a variable factor (labour). Statement: Ronaldo a former ECO100 student states with authority that when the average product of labour is increasing, the marginal product of labour must also be increasing in the orange industry. Position: Do you agree with Ronaldo s statement? Use a proper diagram to analyze this situation and indicate, with reasons, whether you agree or disagree with Ronaldo. I don t agree with Ronaldo s statement. The average product of labour is increasing as long as the marginal product of labour is greater than the average product. Let s look at an example. Suppose that the average product of labour is 10 when 5 units of labour are used in production and that the marginal product of the 6 th unit of labour is 16 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 had, on average, increased total product, the average product of labour rises. In our example, total product increases from 50 units to 66 units and thus the average product of labour increase from 10 units to 11 units. Therefore, the correct statement should be that when the average product of labour is increasing, the marginal product of labour must be greater than the average product in the orange industry. But note that the marginal product of labour might be increasing or decreasing when it s greater than the average product. This is illustrated in the following diagram. AP MP A B MP AP L A L B L Page 5 of 15

6 5. Consider that the government wished to reduce the quantity of consumer purchases for a product and imposed a specific commodity (per-unit tax) in the industry to be paid by producers. Statement: Cristóbal believes that the intended impact of the tax would be more successful if the product had a relatively inelastic demand curve. Position: Do you agree with Cristóbal s position? Use a proper diagram to analyze this situation and indicate, with reasons, whether you agree or disagree with Cristóbal. I disagree with Cristóbal s position. The imposition of the per-unit tax will increase the cost of production of this commodity and shift the supply curve up to the left (i.e., it will cause a decrease in supply). Therefore, the market price (i.e., the price paid by consumers) increases and the quantity bought and sold in the market decreases as the government intended. This is shown in the diagram below. The initial equilibrium before the imposition of the unittax is at point A price P 1 and quantity bought and sold Q 1. The imposition of the unit-tax causes the supply curve to shift up exactly by the size of the tax (t). As a result, consumers end up paying a price P 2 in the new equilibrium and buying a quantity Q 2. Note that producers now receive a price P 3 equal to P 2 t. P S t S P 2 P 1 P 3 D Q 2 Q 1 Q Now let s examine whether the reduction in the quantity consumed will be greater if this product has a relatively inelastic demand curve or a relatively elastic one. That is, what we want to determine is in which case relatively inelastic or relatively elastic demand curve the reduction in the quantity consumed will be greater after the imposition of this unit-tax. The price elasticity of demand is defined as the ratio between the percentage change in quantity demanded and the percentage change in price. If (in absolute value) this ratio is greater than one, then at that point or segment the demand for this product is elastic; if the ratio is less than one, then at that point or segment the demand for this product is inelastic. A relatively elastic demand curve means that the % Q > % P and, therefore, for a given % P the quantity demanded decreases by more in this case. Cristóbal is thus not correct. Page 6 of 15

7 6. Pawel only purchases product X and product Y. Pawel s demand curve for product X is downward-sloping. Statement: Evangeline, a friend of Pawel s, concludes that product X must be a normal good for Pawel. Position: Do you agree with Evangeline s conclusion? Use a proper diagram to analyze this situation and indicate, with reasons, whether you agree or disagree with Evangeline s view. No, I don t agree with Evangeline s conclusion since income-independent goods and inferior non-giffen goods also have negatively-sloped demand curves. Let s consider the case of an inferior non-giffen good for Pawel. Initially Pawel is maximizing his utility consuming bundle A. As the price of good X increases his budget line shifts from BL 1 to Y BL 2. He will now consume a different bundle on this new budget line and will reduce his B level of satisfaction since the highest indifference curve he will be able to reach is lower than indifference curve I 1. His real BL 2 income has thus decreased. Let s examine the A substitution and the income effect of this increase in the price of books. I 1 To measure the substitution effect we must consider the change in the quantity demanded C as a result of the change in relative prices while assuming no change in real income (i.e., BL 1 while assuming that Pawel remains on the I same indifference curve). This is illustrated by 2 the movement from point A to point B, and the X B X C X A X quantity demanded decreases from X A to X B. Now we measure the income effect by allowing real income to fall while keeping relative prices constant. In this way, Pawel moves to a lower P indifference curve. Since good X is an inferior good for Pawel, as his income decreases his quantity demanded of good X increases so he will end up consuming a quantity greater than X B. But good X is an inferior non-giffen P 1 good for Pawel and thus the substitution effect is greater than the income effect and he will end up consuming more than X B but less than D X A he will consume a quantity X C as shown in X C X A X the diagram. His demand curve for good X thus has a negative slope as indicated in the diagram on the left. P 2 Page 7 of 15

8 PART II (30 marks) Instructions: Answer all questions in the space provided (if space is not sufficient, continue on the back of the previous page). 1. Elasticity (6 marks) a) What is the arc elasticity of demand for loaves of bread if 5.8 million loaves of bread are sold at \$0.95 and 6.2 million loaves are sold at \$0.85? (2 marks) The arc elasticity of demand is equal to the percentage change in quantity over the percentage change in price taking as the point of reference the average quantity and the average price within the arc. The change in quantity is 0.4 million from 5.8 million to 6.2 million and the average quantity is 6.0 million. Therefore, the percentage change in quantity is 0.4 / 6.0 x 100. The change in price is -\$0.10 from \$0.95 to \$0.85 and the average price is \$0.90. Therefore, the percentage change in price is / 0.90 x 100. And the arc elasticity of demand is: 0.4 / 6.0 x 100 1/15 η = = = 9/15 = 3/5 = / 0.90 x 100 1/9 b) What is the point elasticity of demand for CDs at Q = 7,500 if the equation for the CD demand curve is P = Q? (2 marks) When Q = 7500, P = (7500) = 10. The point elasticity of demand is equal to P 1 /Q 1 divided by slope of the demand curve at the point (Q 1, P 1 ). Therefore, η = (10/7500) / ( 0.004) = 1 / (750 x 0.004) = 1 / 3 = c) Suppose that the arc elasticity of water coolers is at a quantity demanded between 7,200 and 8,800 units. What is the percentage change in the price of water coolers if the quantity demanded increases from 7,200 to 8,800 units? (2 marks) The change in quantity demanded is 1600 units and the average quantity is 8000 units. Therefore, the percentage change in quantity demanded is 1600 / 8000 x 100 = 20%. Since the elasticity is equal to the ratio between the percentage change in quantity demanded over the percentage change in price, the percentage change in price is: % P = 20% / 1.25 = 16%. Page 8 of 15

9 2. Production Possibilities Curve (8 marks) A country has 100,000 units of a single homogeneous resource with which it can produce the following output combination (in units) in any year. A B C D E F Wheat 65,000 60,000 50,000 35,000 15,000 0 Tractors 0 8,000 20,000 30,000 40,000 45,000 75,000 A A B Wheat (bushels/year) 50,000 B C C D D 25,000 E E 15,000 30,000 45,000 Tractors (units/year) F F a) In the diagram above, draw the production possibility curve for this economy and clearly indicate all the relevant points (i.e., points A, B, etc.). (1 mark) b) What is the opportunity cost per unit of increasing tractor output from 20,000 to 30,000 units? (2 marks) The opportunity cost of increasing tractor production from 20,000 to 30,000 units/year is 15,000 bushels of wheat per year. The per unit opportunity cost is 15,000/10,000 = 1.5 bushels of wheat per year. Page 9 of 15

10 c) Suppose that the stock of tractors at the beginning of the year is 150,000 and the depreciation of tractors is 10,000 units a year. What is the stock of tractors at the end of the year if the economy produces the output of option D? [Note: Depreciation of tractors of 10,000 units a year means that, as a result of the normal wear and tear, 10,000 tractors are taken out of circulation over the year.] (1 mark) Stock of tractors at the end of the year = stock of tractors at the beginning of the year + year s production year depreciation = 150, ,000 10,000 = 170,000 d) Suppose that technological change increases the output of wheat by 10% per unit of resource but does not affect the output of tractors per unit of resource. In your diagram in part a), sketch the production possibilities curve that results from this technological change, clearly identifying all the relevant points as in part a) above. (2 marks) A B C D E F Wheat 71,500 66,000 55,000 38, ,500 0 Tractors 0 8,000 20,000 30,000 40,000 45,000 e) What is the opportunity cost of increasing tractor production from 30,000 to 40,000 units given that technological change increased wheat output by 10% per unit of resource without changing tractor output per unit of resource? (2 marks) The opportunity cost of increasing tractor production from 30,000 to 40,000 units/year is 22,000 bushels of wheat per year. Page 10 of 15

11 3. Price Ceilings vs. Per-Unit Subsidy (16 marks) The supply and demand for a new medical product are given by the following expressions: Q = 2P 100 and Q = 200 2P respectively. Government health analysts are concerned that under equilibrium conditions the product will be too expensive for poorer Canadians. To this end, they are considering two policy alternatives. Under the first policy, the government would legislate a price ceiling for this good at \$60. Under the second policy, the government agrees to pay a per-unit subsidy to firms so that the price paid by consumers is \$ S Price (in dollars) D Quantity (in 1000 units/year) a) Compute the equilibrium price and quantity in the absence of government intervention. (2 marks) Sketch the demand and supply curves in the diagram above, clearly indicating all the relevant points (e.g., intercepts, equilibrium price, etc.). (1 mark) S = D 2 P 100 = P 4 P = 300 P* = 75 And Q* = 2 P* = 2 (75) 100 = 50 To facilitate sketching the curves, let s write their expressions in the following way: D: Q = P 2 P = 200 Q P = Q S: Q = 2 P P = Q P = Q Page 11 of 15

12 b) What quantity will be sold and bought in the market when a \$60 price-ceiling is imposed? (1 marks) Use your diagram to asses the impact of the imposition of this price-ceiling in terms of consumer and producer surplus. Clearly identify any loss or gain in consumer and producer surplus. (4 marks) Given the demand curve Q = 2P 100, the when P = 60, Q = 2(60) 100 = 20 thousand. The change in consumer surplus is equal to the increase in area 1 minus the decrease in area 2. The change in producer surplus is equal to the decrease in areas 1 plus 3. The welfare change to society is thus the summation of the changes in consumer and producer surplus, equivalent to a net loss represented by the summation of the areas 2 and 3. c) Reproduce in the diagram below the equilibrium situation in the absence of any government intervention (i.e., the situation determined in part a) above). Price (in dollars) S S D Quantity (in 1000 units/year) Page 12 of 15

13 d) Use the diagram in part c) to asses the impact of the introduction of the per-unit subsidy. Clearly identify in the diagram the impact of this policy in terms of any gain or loss in consumer and producer surplus and the cost of the subsidy to the government. (4 marks) The increase in consumer surplus is equal to the summation of the areas The increase in producer surplus is equal to the summation of the areas The cost of the subsidy to the government (i.e., to society) is equal to the summation of the areas The welfare change to society is thus the summation of the changes in consumer and producer surplus minus the cost of the subsidy, equivalent to a net cost represented by the summation of the areas 3 and 4. e) Indicate which of the two policies you feel it would be best for society. Would society be better off if the government did nothing? (4 marks) The analysis above suggests that society will be better off with the second policy the introduction of a per-unit subsidy. This policy achieves the government objective of facilitating an increase in consumers purchases of this new medical product. The policy of a price floor, however, contributed to the reduction of the quantity of this product available for consumption, thus defeating the intended objective of the government. Although the subsidy policy implies an explicit cost (areas 3 and 4 indicated above), this cost might be more than justified by the important benefit that the use of this new medical product might provide to society as a whole. f) Bonus question: What is the size of the per-unit subsidy that would establish a consumer price of \$60? (2 additional marks) If consumers pay a price of \$60, then given the expression for the demand curve the quantity bought and sold in the market will be: Q = P = 200 (2) 60 = 80. The price that producers must receive (as determined by the supply curve before the introduction of the subsidy) in order to produce 80 units of the product is: P = Q = (80) = 90. Therefore, since the subsidy is equal to the difference between the price producers receive and the price consumers pay, the subsidy is \$30 per unit. Page 13 of 15

14 PART III (20 marks) Instructions: Enter your answer to each question in the table below. 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 2.5 (two-and-one-half) marks. No deductions will be made for incorrect answers A B C B B C D B B 1. Because bagels and cream cheese are often eaten together, they are complements. We observe that both the equilibrium price of cream cheese and the equilibrium quantity of bagels have risen. What could be responsible for this pattern? A) A fall in the price of flour. B) A fall in the price of milk. C) An increase in the price of milk. D) An increase in the price of flour. E) A decrease in the price of muffins, a close substitute for bagels. 2. If the demand curve for good X is downward-sloping, a reduction in the price of an input used to produce good X will A) not affect consumer surplus. B) increase consumer surplus. C) increase the price of good X. D) reduce the quantity bought and sold of good X. E) shift the demand for good X to the right. 3. Which one of the following would cause the demand curve in an industry to increase? A) A decrease in the price of a substitute product. B) An increase in income and the good was an inferior good. C) A decrease in the price of a complementary product. D) Disposable income decreased and the good was a normal good. E) A decrease in the price of an important input used in this industry. 4. Suppose that the incomes of buyers in a market for a normal good decline and there is a reduction in input prices. What would you expect to occur in this market? A) Equilibrium price would increase, but the impact on the equilibrium quantity would be ambiguous. B) Equilibrium price would decrease, but the impact on the equilibrium quantity would be ambiguous. C) Both equilibrium price and equilibrium quantity would increase. D) Equilibrium quantity would increase, but the impact on the equilibrium price would be ambiguous. E) Equilibrium quantity would decrease, but the impact on the equilibrium price would be ambiguous. Page 14 of 15

15 5. If the increase in the price of good X causes the demand curve for good Y to shift to the left, then A) X and Y are substitutes. B) X and Y are complements. C) the price of X must be higher than the price of Y. D) Y must be a normal good. E) Consumer preferences for Y must have fallen. 6. If we know that capital is fixed and a basket-producing firm can produce 48 baskets per day with 4 workers and 55 baskets per day with 5 workers, then which of the following statements is not true: A) The marginal product of the fifth worker is 7. B) The average product of the fifth worker is 11. C) The firm has not passed yet the point of diminishing average productivity. D) The marginal product is below the average product. E) The firm has passed the point of diminishing marginal productivity. 7. The average product for six workers is 18. If the marginal product for the seventh worker is 16, A) marginal product is rising. B) marginal product is falling and average product is rising. C) both average and marginal product are rising. D) both average and marginal product are falling. E) marginal product is rising and average product is falling. 8. When one additional unit of labour is hired, total product increases from 100 to 110 units of output per unit of time. Marginal product must therefore be A) increasing. B) positive. C) decreasing. D) constant. E) zero. Bonus question (an additional 2.5 marks): 9. Consumers will bear a larger burden of a sales tax if A) demand is relatively elastic and supply is relatively inelastic. B) demand is relatively inelastic and supply is relatively elastic. C) both demand and supply are relatively inelastic. D) both demand and supply are relatively elastic. E) if the tax is collected by the firms rather than remitted directly to the government by consumers. Page 15 of 15