University of Toronto June 22, 2004 ECO 100Y L0201 INTRODUCTION TO ECONOMICS. Midterm Test #1

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1 Department of Economics Prof. Gustavo Indart University of Toronto June 22, 2004 SOLUTIONS ECO 100Y L0201 INTRODUCTION TO ECONOMICS Midterm Test #1 LAST NAME FIRST NAME STUDENT NUMBER INSTRUCTIONS: 1. The total time for this test is 1 hour and 45 minutes. 2. This exam consists of three parts. 3. This question booklet has 16 (sixteen) pages. 4. Aids allowed: a simple calculator. DO NOT WRITE IN THIS SPACE Part I /40 Part II 1. /5 2. /5 3. /5 Part III 1. /10 2. /10 3. /10 4. /10 4. /5 TOTAL /100 Page 1 of 16

2 PART I (40 marks) Instructions: The multiple choice questions are to be answered using a black pencil or a black or blue ball-point pen on the separate (SCANTRON) sheet being supplied. Be sure to fill in your name and student number on the SCANTRON sheet! When you finish your examination, place the SCANTRON sheet inside the question booklet. Each question is worth 2 (two) marks. No deductions will be made for incorrect answers. You may use the question booklet as a worksheet to answer questions, and then transfer your answers onto the SCANTRON sheet. Make sure that all your answers are transferred onto the SCANTRON sheet. In case of a disagreement, the answer to be marked is the one in the SCANTRON sheet. 1. A society can increase its production possibilities curve through a) investment = depreciation b) positive net investment c) emigration of the labour force d) technological improvement with no change in resources e) both b) and d) are correct 2. Sean has received a $2,000 scholarship to attend university as a full time student this year. Sean therefore had to give up his full time job in which he earned $20,000 per year. In addition, Sean must pay tuition of $5,000; buy text books for $500 and enrol in a university residence which costs $10,000 per year. The opportunity cost for Sean to become a full-time university student thus becomes: a) $20,000 b) $25,000 c) $33,500 d) $15,500 e) $35, Assume that apples and oranges are substitute goods in consumption. Given the initial supply and demand curves for apples, a reduction in the price of oranges will tend to a) increase the price of apples b) increase the demand for apples c) increase the demand for oranges d) decrease the demand for oranges e) decrease the price of apples 4. With a given supply curve for sirloin steak, a normal good, a rise in household income will cause a) the equilibrium price to increase and the equilibrium quantity of sirloin steak to decrease b) both the equilibrium price and the equilibrium quantity of sirloin steak to increase c) both the equilibrium price and the equilibrium quantity of sirloin steak to decrease d) the equilibrium price to decrease and the equilibrium quantity of sirloin steak to increase e) none of the above 5. If demand is inelastic, a very good harvest will cause farm receipts to a) increase because of the increase in quantity that farmers can sell b) remain unchanged, because the increase in the quantity that can be sold will be matched by an equal decrease in price c) increase because of the downward movement along the supply curve, encouraging an increase in demand d) decrease because the percentage fall in price is greater than the percentage increase in quantity sold e) decrease because the percentage fall in price is less than the percentage increase in quantity sold Page 2 of 16

3 6. The price of apples at a local market rises from $2.95 to $3.05 per kilo, and as a result the quantity of oranges that households purchase increases from 3,950 to 4,050 kilos/week. The cross-price elasticity is a) b) c) 0.75 d) 1.33 e) insufficient information to know 7. Suppose fixed costs are $100 and average variable costs are constant regardless 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 increases c) marginal cost will be less than average variable cost d) average total cost will be constant e) none of the above 8. For a certain firm, total cost is $10 at 5 units of output and $13 for 6 units. In that range of output, marginal cost is a) decreasing b) less than average variable cost c) greater than average total cost d) equal to average variable total cost e) less than average total cost 9. Which one of the following statements is correct relating to the imposition of a specific commodity tax on a perfectly competitive industry in the short run: a) the more inelastic the demand curve, the smaller the tax burden of the tax on consumers b) the more elastic the demand curve, the smaller the reduction in industry output c) the more inelastic the demand curve, the smaller the tax revenue received by the government d) the more elastic the demand curve, the greater the price increase for consumers e) none of the above are correct 10. Suppose all farmers grow both wheat and oats for sale. If the price of oats increases, we would predict that farmers would react in such a way that, ceteris paribus, a) the supply of wheat would increase causing the price of wheat to fall b) the supply of wheat would decrease causing the price of wheat to rise c) the price of wheat would not be affected d) the price of wheat might rise or fall but the supply of wheat would definitely fall. e) the price of wheat would fall 11. Which one of the following statements is correct: a) marginal product is at a maximum when marginal product equals average product b) average product is at a maximum when average product equals marginal product c) marginal product is at a maximum when a ray from the origin is tangent to the total physical product curve d) marginal product will reach a maximum when total product reaches a maximum e) none of the above 12. If the total cost of producing one unit of output is $1,000 and marginal cost of that unit is $250, the average fixed cost of producing two units of output is a) $375 b) $500 c) $750 d) $1,250 e) none of the above Page 3 of 16

4 13. An increase in household income and a technological change that improves production will cause which of the following scenarios in the market for a normal good? a) price and quantity would both be higher b) price and quantity would both be lower c) price might be higher or lower but the new equilibrium quantity would be higher d) price would be lower but the new equilibrium quantity would be higher e) price and quantity could be lower or higher 14. Diminishing returns in the short-run begin immediately after a) total product is at a maximum b) average product is at a maximum c) marginal product is at a maximum d) average variable costs are at a minimum e) average costs are at a minimum 15. If the demand for sugar decreases when the price of honey falls, then sugar a) is a normal good b) is an inferior good c) is a substitute for honey in consumption d) is a complement of honey in consumption e) is a complement of honey in production 16. If potatoes are a Giffen good, then an increase in the price of potatoes will cause a) an increase in the demand for potatoes b) a decrease in the quantity demanded of potatoes c) a decrease in the demand for potatoes d) an increase in the quantity demanded of potatoes e) a decrease in money income 17. The demand for shrimp would decrease if a) the price of shrimps increases b) disposable incomes increase and shrimp was a normal good c) disposable incomes decrease and shrimp was an inferior good d) the price of white wine (a complementary good) decreases e) the price of salmon (a substitute good) decreases 18. If the price elasticity of demand for tape decks is -0.5, then a 20% increase in price will a) reduce quantity demanded by 40% b) reduce quantity demanded by 5% c) increase total expenditure d) increase quantity demanded by 40% e) increase quantity demanded by 10% 19. If the price elasticity of demand for opera was inelastic, then total receipts from opera a) increase with a rise in price of opera b) decrease with a rise in price of opera c) increase with a fall in price of opera d) increase with a fall in price of ballet e) increase with an increase in income 20. When marginal product is at a maximum a) average product is falling b) marginal product equals average product c) total product is at a maximum d) marginal cost is at a maximum e) marginal cost is at a minimum Page 4 of 16

5 Solutions to Multiple Choice Questions e c e b d c b c e b b a c c c d e c a e PART II (20 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. 1. Rachel consumes only Good A (x-axis good) and Good B (y-axis good). If Rachel income decreases, the utility-maximizing model will predict that she will buy fewer units of Good A and fewer units of Good B. False The statement would be correct if both Good A and Good B were normal goods (Figure 1 ICC with a positive slope). If one of the goods were an inferior good, say Good A, then Rachel would decrease her consumption of Good B but increase her consumption of Good A (Figure 2 ICC with a negative slope). And if one of the goods were an income-independent good, say Good A again, then Rachel would decrease her consumption of Good B but leave her consumption of Good A unchanged (Figure 3 ICC vertical). Note that in the last two cases Good B must be necessarily a normal good. Figure 1: Figure 2: A and B are A is inferior and A both normal A B is normal A Figure 3: A is income-indep. and B is normal ICC ICC ICC B B B Page 5 of 16

6 2. The benefit of a per unit subsidy will accrue entirely to producers if the demand for a commodity is perfectly elastic and the supply curve is upward sloping. True If demand is perfectly elastic (horizontal line), then the price that consumers will pay will be the same before and after the introduction of the subsidy. That is, consumer will not benefit from the subsidy other than being able to purchase now a larger amount at the same price. Therefore, the subsidy will accrue entirely to producers as the diagram below shows. The introduction of the subsidy causes the supply curve to shift down from S to S (exactly by the size of the subsidy) because now producers are able to request a lower minimum price from consumers for each unit being supplied of the commodity. Of course, the net price producers will receive is equal to the price consumers will pay (P C ) plus the subsidy they receive from the government (s) for a total of P P. P S P P S s s P C D Q 1 Q 2 Q Page 6 of 16

7 3. Julian purchases only Good A [x-axis good] and Good B [y-axis good]. The income consumption curve for Good A is perfectly inelastic. As a result of a price increase in Good A, it can be shown that Julian s demand curve for Good A is also perfectly inelastic. False If the income consumption curve for Good A is perfectly inelastic (vertical line), then Good A is an income-independent good. The change in the quantity demanded of Good A as a result of an increase in its own price will be the summation of the substitution effect and the income effect. Since Good A is an income-independent good, the income effect is nil. But the substitution effect will move counter to the change in price, that is, the substitution effect will imply a decrease in the quantity demanded of Good A. This is shown in the left diagram below. Therefore, as the price of Good A increases the quantity demanded of Good A decreases (as a result only of the substitution effect), and the demand curve for Good A has then a negative slope. This is shown in the right diagram below. B P A P A 2 P A A 2 A 1 A A 2 A 1 A Page 7 of 16

8 4. Bananas are produced with a fixed factor land [T] and a variable factor labour [L]. At the level of labour input where total product is at a maximum, the average product of labour will be equal to the marginal product of labour. False Marginal product will be equal to average product at the level of labour input where average product (and not total product) is at a maximum. This can be observed in the diagram below. TP TP Assume a TP curve with the general shape, that is, a TP depicting first increasing marginal productivity and then decreasing marginal productivity of labour (that is, an increasing positive slope first and then a decreasing positive slope). A B Average product (AP) is equal to total product (TP) divided by the quantity of labour input (L), that is, AP = TP/L. Therefore, at any quantity of L, AP is equal to the slope of a ray through the origin to a point on the TP curve. The graph on the right shows that the slope of such a ray increases as L increases, reaches a maximum at L B, and then decreases. AP MP L A L B L Marginal product (MP), in turn, is equal to the change in TP given a change in L, that is, MP is equal to the slope of the TP curve ( TP/ L). In the graph on the right we can observe that the slope of TP first increases as L increases, reaches a maximum at L A, and then decreases. The graph also shows that the slope of the TP curve is equal to the slope of a ray through the origin to the TP curve at L B. That is, MP = AP at L B, the point where AP reaches a maximum. At the same time, it shows that MP > AP for L < L B and that MP < AP for L > L B. These results are depicted in the bottom diagram. MP AP L A L B L Page 8 of 16

9 PART III (40 marks) Instructions: Answer all questions in the space provided (if space is not sufficient, continue on the back of the previous page). Each question is worth 10 (ten) marks. 1. Suppose that the demand curve for tomatoes is linear and has a slope of a) What is the point price elasticity of demand at equilibrium if the supply curve intersects the demand curve at P = 1,500 and Q = 5,000 tons, where P is price in dollars of one ton of tomatoes and Q is tons of tomatoes per week? (2 marks) η = ( Q / P) (P 0 / Q 0 ) = [1 / ( P / Q)] / (P 0 / Q 0 ) = (1 / 0.2) (1500 / 5000) = 5 (3 / 10) = 1.5 (or 1.5 in absolute value) b) Suppose that a tomato disease causes a shift in supply that results in a new equilibrium at P = 2,000 and Q = 2,500 tons. What is the arc price elasticity of demand between the pre-disease equilibrium of part a) and this new equilibrium? (2 marks) η = ( Q / P) (P AVE / Q AVE ) = ( 2500 / 500) (1750 / 3750) = 5 (7 / 15) = 7 / 3 = 2⅓ (or 2⅓ in absolute value) Page 9 of 16

10 c) Write the expression for the demand curve for tomatoes. (2 marks) At what price/quantity combination would the total expenditure on tomatoes be maximized? (2 marks) We know that the slope of the demand curve is P / Q = 0.2. We also know that points (5000, 1500) and (2500, 2000) are on the demand curve. Let s consider point (5000, 1500) and the vertical intercept of the demand curve where Q = 0. The vertical intercept point is (0, P 0 ). As we move from point (5000, 1500) to the vertical intercept, the change in quantity demanded is Q = 5000 and the change in price is P = P Therefore, since P / Q = 0.2 (P ) / 5000 = 0.2 P = 0.2 ( 5000) P 0 = 2500 Therefore, the expression for the demand curve is P = Q. d) Go back to the initial equilibrium of part a) above. Suppose now that the demand for lettuce a complement of tomatoes increases and the price of lettuce rises by 10%. If the cross-price elasticity of demand between lettuce and tomatoes is equal to 2, what will the new equilibrium quantity of tomatoes sold in the market be? (2 marks) η = % Q T / % P L = % Q T / 10% = 2 % Q T / 10% = 2 % Q T = 2(10%) = 20% Q T = 0.8(5000) = 4000 The cross-price elasticity between complements is negative, but in the question it was indicated as positive. Since this might have been a source of confusion, the following answer will also be accepted as correct. η = % Q T / % P L = % Q T / 10% = 2 % Q T / 10% = 2 % Q T = 2(10%) = 20% Q T = 1.2(5000) = 6000 Page 10 of 16

11 2. The market demand and supply curves for meat are given by the following equations. Demand: Q = 8 P Supply: Q = 0.5P 1 where P is the money price of one ton of meat (in thousands) and Q is tons of meat per day (in thousands). Gain in Consumer Surplus P S Loss in Consumer Surplus The total change in Consumer Surplus is equal to the area representing a gain in Consumer Surplus minus the area representing a loss in Consumer Surplus D Q a) If the market for meat is a free market, what are the equilibrium price and the equilibrium quantity of meat? (2 marks) Sketch the demand and supply curves in the diagram above, and show the equilibrium price and quantity you found in part a). Label the graph and indicate all relevant points. (1 mark) D = S 8 P = 0.5P 1 1.5P = 9 P* = 6 Q* = 8 P* = 8 6 = 2 Page 11 of 16

12 b) Suppose that the government imposes an effective price ceiling of $4 on a ton of meat (that is, a price ceiling of $4,000 per ton). How many tons are now sold? (1 mark) Is there an excess supply or excess demand? If so, how much is this excess supply or demand? (1 mark) Neatly show in your diagram the change in consumer surplus as a result of the imposition of this price ceiling. (2 marks) At P = 4, Q S = 1 and Q D = 4. Therefore, there is an excess demand equal to 3 tons of meat per day. Since only 1 ton of meat will be supplied at this price, the amount sold in the market will be 1 ton per day. The total change in Consumer Surplus is equal to the area representing a gain in Consumer Surplus minus the area representing a loss in Consumer Surplus (see diagram). c) If a black market arises in this situation, what would the black market price for meat be? (1 mark) What is the total expenditure by consumers at this price? (1 mark) How does it compare to the total expenditure in part a) above? Is the demand for meat elastic or inelastic in this range? (1 mark) At Q = 1, some consumers will be willing to pay a price equal to 7. The total expenditure at this price would be $7,000 times 1 ton = $7,000. When P was $6,000 and Q was 2 tons, total expenditure was $12,000. Since total expenditure decreased as P increased, we can conclude that the demand curve was elastic in this range. Page 12 of 16

13 3. Suppose that Laura s income is $100 and that she consumes only two goods, good X and good Y. The price of X is $4 and the price of Y is $2. Laura s marginal rate of substitution of X for Y is given by the expression MRS XY = X / Y. a) Write the expression for Laura s budget line. (1 mark) What is the opportunity cost of X for Laura? (1 mark) What is the opportunity cost of Y? (1 mark) Laura s budget constraint is given by 100 = 4X + 2Y, which could also be expressed as Y = 50 2X. Since the price of X is $4 and the price of Y is $2, Laura will have to give up 2 units of Y in order to consume an additional unit of X. That is, the opportunity cost of X is 2 units of Y. Similarly, Laura will have to give up 2 unit of X in order to consume an additional unit of Y. That is, the opportunity cost of Y is 2 unit of X. b) What are the two conditions for utility maximization? (2 marks) What are Laura s utilitymaximizing values of X and Y? (1 mark) Let (X*, Y*) be the utility-maximizing combination of X and Y. The two utility-maximizing conditions are: 1) (X*, Y*) must lie on the budget line, that is, Y* = 50 2X*. 2) An indifference curve must be tangent to the budget line at (X*, Y*), that is, the slope of the budget line and the slope of the indifference curve must be equal at this point: MRS (X*, Y*) = P X / P Y X* / Y* = 2 X* = 2Y* Substituting X* = 2Y* for X* in Y* = 50 2X*, we obtain Y* = 50 2(2Y*) = 50 4Y* 5Y* = 50 Y* = 10 X* = 2Y* = 2(10) = 20 Page 13 of 16

14 c) Suppose now that the price of X falls to $2. What are Laura s new utility-maximizing values of X and Y? (1 mark) The two utility-maximizing conditions are: 1) Y* = 50 X* 2) X* / Y* = 1 X* = Y* Y* = 50 Y* 2Y* = 50 Y* = 50/2 = 25 X* = Y* = 25 d) In the diagram below, sketch Laura s demand curve for good X assuming a constant slope. Label the graph and indicate all relevant points. (1 mark) What is the slope of her demand curve? (1 mark) What is the price elasticity of demand for X when its price is $4? (1 mark) P X 5 4 A 3 2 B 1 D Quantity of X As we move along the demand curve from point A to point B, P X = 2 and X = 5. Therefore, P X / X = 2 / 5 = 0.4. The price elasticity of demand at P X = 4 is: η = (4 / 20) / ( 0.4) = 0.5 Page 14 of 16

15 4. Suppose that John consumes only two goods, books (B) and video games (VG), where video games are income-independent goods for John. B 30 Income effect = no change in the quantity demanded of VG Substitution effect = a decrease of 10 units in the quantity demanded of VG 20 C 10 8 A B VG a) Write an expression of John's budget line when the price of books is $5 per unit, the price of video games is $2 per unit, and John's income is $100 per week. (1 mark) Sketch John s budget line in the diagram below. Place books on the vertical axis of your diagram. Clearly indicate all relevant points. (1 mark) John s budget constraint is given by: 100 = 5B + 2VG or Y = 5B + 2VG. Page 15 of 16

16 b) At the utility maximizing combination of books and video games, John consumes 25 video games. How many books does John consume when maximizing his utility? (1 mark) Show this utility-maximizing equilibrium in your diagram (label it point A). [Do not draw any indifference curve yet.] Given John s budget line and VG = 25, 100 = 5B + 2(25) 100 = 5B B = 50 B* = 10 c) Suppose now that the price of video games increases to $4 while income and the price of books do not change. Draw John's new budget line. (1 mark) At the new utility maximizing combination of books and video games, John consumes 8 books. How many video games does John consume now? Show this utility-maximizing equilibrium in your diagram (label it point B). [Do not draw any indifference curve yet.] (1 mark) New budget constraint: Y = 5B + 4VG. Therefore, 100 = 5(8) + 4VG 4VG = 60 VG* = 15 d) Assuming smooth and convex indifference curves, clearly show in your diagram the substitution and the income effects keeping in mind that video games are incomeindependent goods. [Now you can and must draw the appropriate indifference curves.] (4 marks) Measured in units of video games, how much is the substitution effect? How much is the income effect? Are books normal, inferior, or income-independent goods? (1 mark) The substitution effect is the change in quantity demanded as a result of a change in relative prices while holding real income constant. In the diagram above, this is represented by the movement from point A to point C. In terms of units of VG the substitution effect represents a reduction of 10 units (from 25 to 15). The income effect is the change in quantity demanded as a result of a change in real income while holding relative prices constant. In the diagram above, this is represented by the movement from point C to point B. In terms of units of VG the income effect is nil since VG is an income-independent good. Books are normal goods for John since as real income decreases the quantity demanded of books also decreases. Page 16 of 16