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ECONOMICS A02Y - INTRODUCTORY ECONOMICS (A Mathematical Approach) End of term exam: December 10, 2002 – Answers MULTIPLE CHOICE ANSWERS 1. A record player is a complement in consumption to vinyl records. Therefore, a decrease in the price of a record player will increase the demand for vinyl records, shifting the demand curve to the right (as more people will purchase record players). A decrease in wages paid to labour in the production of vinyl records decreases the cost to produce vinyl records. As a result, supply of vinyl records will increase due to an increase in their production (shift supply curve to the right). Equilibrium quantity will rise, but it is uncertain whether the equilibrium price will rise or fall (it depends on the size of the shift in the supply curve and the size of the shift in the demand curve). The correct answer is (E). 2. The decreased demand for vinyl raincoats will decrease their price, if all other factors remain the same. Since vinyl raincoats are a substitute in production for the producers of vinyl records, a fall in the price of vinyl raincoats will encourage producers to decrease production of vinyl raincoats and increase production of vinyl records (shift supply curve to the right). At the same time, an increase in consumer incomes will cause a decrease in demand for vinyl records, which are an inferior good (shift demand curve to the left). Therefore, equilibrium price falls, but it is uncertain whether the equilibrium quantity will rise or fall (it depends on the size of the shift in the supply curve and the size of the shift in the demand curve). The correct answer is (H). 3. A tax on the producers of vinyl records will cause a decrease in supply of vinyl records (shift supply curve to the left) because it is now more expensive to produce vinyl records. Since CD’s are considered to be a good substitute for vinyl records, a decrease in their price will cause demand for vinyl records to fall (shift demand curve to the left). Therefore, equilibrium quantity falls, but it is uncertain whether the equilibrium price will rise or fall (it depends on the size of the shift in the supply curve and the size of the shift in the demand curve). The correct answer is (F). 4. Substituting X = 4 into the PPF, we can calculate that Y = 228 – 2(4) – 6(4)2 = 124. This tells us that the point (X=4, Y=124) is on the PPF, rather than inside it or outside it. The formula for the opportunity cost of X for points on the PPF is –dY/dX = -(-2 – 12X). When X = 4, this is equal to 50. We are instead, interested in the opportunity cost of Y, which is just the inverse of the opportunity cost of X, or 1/50. The correct answer is (P). 5. The Optimal Hiring Rule requires that workers be hired up to the point that their marginal contribution to revenues of the firm just equals the marginal cost of hiring one more worker. In a competitive labour market, the marginal contribution to revenues is just the marginal product of labour times the price of one unit of the good (MPL x PX). This will be set equal to the price of hiring one more unit of labour – the worker’s wage (P L). Since the marginal product of labour 1 is dQ/dL = 50 – L, we can calculate (50 - L) x PX = 100 or (50 – 40) x PX = 100. In other words, 10PX = 100 or P X = 10. The correct answer is (K). 6. If a demand curve is inelastic, that means that the percentage change in price will be greater than the percentage change in quantity. When the price is raised, the quantity demanded will decrease, and the elasticity of the demand curve tells us that the price will rise by a greater percent than quantity falls. Since the price movement increases total revenue while the quantity movement reduces total revenue, we can conclude that total revenue will rise. The correct answer is (B). 7. We obtain the demand curve by setting P = MU. Therefore, demand is P = dU/dX = 128 – 0.16X. If P = 8, then 8 = 128 – 0.16X, so X = 750. The correct answer is (K). 8. Consumer surplus (CS) at X = 750 is the dollar value of the consumer’s utility at X = 750 (more exactly, it is the consumer’s utility at X = 750 minus the consumer’s utility at X = 0) minus the cost of purchasing the good. In this case U – PX = 128(750) – 0.08(750)2 - 8(750) = $45000. The correct answer is (J). 9. The consumer has the option of paying $4 per unit or a flat fee of $3100. At a price of $4 per unit, the consumer will set P = MU or 4 = 128 -.16X. The optimum consumption of X will be 775 units. The consumer surplus would be 128(800) – 0.08(775)2 – 4(775) = $48,050. If the consumer pays the flat fee, he/she will consume the maximum of 800 units. In this case, consumer surplus will be128(800) – 0.08(800)2 – 3100 = $48,100. The consumer does better by choosing the flat fee. The correct answer is (A). 10. Since P = MR, this is a perfectly competitive producer. Since P = MR = MC, this firm is producing the profit maximizing output. Since AC = MC, we must be at the minimum point on the average cost curve. Since MC > AVC, the marginal cost is pulling the average variable cost up. In other words, the AVC is rising at the current level of output. The correct answer is (F). 11. If MC = 0, then profit maximization will occur when MR = 0. If we take a general linear form for the demand curve (P = a – bQ), then the MR will be given by MR = a – 2bQ. At profit max, MR = 0 or a-2bQ = 0 or Q = a/2b. Find the price by substituting this into the demand function to get P = a/2. The elasticity of demand can be calculated as –(1/[-b] x [a/2]/[a/2b]) = 1. This problem can also be done graphically. The correct answer is (A). 12. The long-run equilibrium price is the minimum point on the average cost (AC) curve. AC = TC/q = 432/q + 12 + 3q and dAC/dq = 3 – 432q-2 . We can set this derivative = 0 to find the output level at which AC reaches its minimum. So, 3 – 432q-2 = 0, or q = 12. Substituting this value into the AC function gives us 432/12 + 12 + 3(12) = $84. The correct answer is (U). 13. The firm will be indifferent between continuing in operation and shutting down when it faces a price which only just covers its average variable costs. Find this minimum point on the average variable cost curve. AVC = 192/q + 12 + 3q and dAVC/dq = 3 – 192q-2. We can set this derivative = 0 to find the output level at which AVC reaches its minimum. So, 3 – 192q-2 = 0, or 2 q = 8. Substituting this value into the AVC function gives us 192/8 + 12 + 3(8)= $60. The correct answer is (R). 14. At this price, we need to find out how much the firm will be producing. To do so, we set P = MC. MC is the derivative of TC. TC = 432 + 12q + 3q2 . dTC/dq = 12 + 6q. Setting P = MC we get $156 = 12 + 6q or q = 24. The firm therefore earns revenue of 156 * 24 = $3744. Total costs can be found with the total cost function as 432 + 12(24) + 3(24)2 = $2448. The firm therefore makes a profit of $1296. The correct answer is (M). 15. Let “W” stand for the number of units of wheat and “C” stand for the number of units of cloth. In Canada, each unit of wheat requires 1 worker and each unit of cloth requires ¼ of a worker, so we can represent Canada’s production possibilities by W + 1/4C = 100, or W = 100 – 1/4C. In Mexico, each unit of wheat requires 4 workers and each unit of cloth requires 2 workers. We can represent Mexico’s production possibilities by 4W + 2C = 1000, or W = 250 – 1/2C. Then the opportunity cost of cloth in Canada is -dW/dC = 1/4, while the opportunity cost of wheat is the inverse of this, which is 4. The opportunity cost of cloth in Mexico is -dW/dC = 1/2, while the opportunity cost of wheat is the inverse of this, which is 2. Mexico therefore has the opportunity cost advantage, or comparative advantage, in wheat, while Canada has the comparative advantage in cloth. Since Canada uses fewer resources (units of labour) than Mexico to produce either wheat or cloth, Canada has the absolute advantage in both wheat and cloth. The correct answer is (J). 16. In competitive markets, prices equal costs, so the ratio of wheat price to cloth price in each country before trade should be equal to the opportunity cost of wheat (measured in units of cloth). In Canada, Pw/Pc would be 4 and in Mexico, Pw/Pc = 2. If both countries are to gain from trade, then the relative price ratio of wheat to cloth would have to be between 2 & 4. The correct answer is (I). 17. First, we need to calculate current equilibrium price and quantity. 100 - .1Q = 40 + .05Q, so .15Q = 60 or Q* = 400. Substituting into the demand function, we find that P* = 100 – 40 = 60. Elasticity of supply at this equilibrium point is 1/(dP/dQ) x P/Q = 1/0.05 x 60/400 = 3 and elasticity of demand at this equilibrium point is -(1/(dP/dQ) x P/Q) = 1/.1 x 60/400 = 1.5. The correct answer is (L). 18. A $12 tax on buyers will shift the demand curve to the left. If the demand curve net of the tax is shifted down to P = 88 – 0.1Q, then the new equilibrium quantity will be at 88 – 0.1Q = 40 + 0.05Q, so 0.15Q = 48 or Q 1 * = 320. The new equilibrium price can be found by substituting into the original demand curve, so P1 * = 100 – 0.1(320) = $68. The new price received by sellers can be found by substituting into the new, net of tax, demand curve, so P S = 82 – 0.1(320) = $56. Therefore the buyers bear $68 - $60 = $8 (2/3) of the tax while sellers bear $60 - $56 = $4 (1/3) of the tax. The correct answer is (B). 19. Total tax revenue is $12 x 320 = $3840. The correct answer is (J). 20. The excess burden of the tax is [(400-320) x 12]/2 = $480. The correct answer is (A). 3 21. Demand is P = 93 - 0.05Q. Marginal revenue is MR = 93 - 0.1Q. Marginal cost is MC = 1. The unregulated monopolist will set 93 - 0.1Q = 1, or Q* = 920. Substituting into the demand curve, the equilibrium price will be P* = 93 - .05(920) = $47. The correct answer is (P). 22. Zero profit implies that price is equal to Average Cost. The Total Cost function is TC = 3600 + Q and the Average Cost function is AC = 3600/Q + 1. At P = AC, we will have 93 - 0.05Q = 3600/Q + 1, or 92 - 0.05Q – 3600/Q = 0. Multiply through by Q and rearrange terms to get - 0.05Q² + 92Q – 3600 = 0. We can solve this using the quadratic formula, to find two possible values of Q, which are Q = 1800 and Q = 40. Only the larger quantity makes sense as a form of regulation of monopoly. At this quantity, the relevant price will be P = 93 - 0.05(1800) = $3. The correct answer is (D). 23. The Gain to Society is composed of Consumer Surplus + Profit. In the unregulated monopoly position, the consumer surplus will be (93– 47) x 920/2 = $21,160. The profit is TR – TC = (47 x 920) – (3600 + 920) = $38,720. The total gain to society is $59,880. Under the regulated monopoly, the consumer surplus will be (93 – 3) x 1800/2 = $81,000. There is no profit when price = average cost, so total gain to society is $81,000. Therefore the extra gain to society due to regulation is $21,120. The correct answer is (E). 24. The most efficient allocation of resources, the one where Gain to Society will be maximized, will occur when P = MC, which is where P = $1. The correct answer is (B). 25. It will no longer make sense to build the bridge if the Gain to Society falls below zero. This is true even if the most efficient price, the one where P = MC is charged. When P = 1, the quantity of trips across the bridge will be 1 = 93 - 0.05Q, so Q = 1840. Consumer Surplus is [(93 – 1) x 1840]/2 = $84,640. Profit will be Total Revenue minus Total Cost. TR = (1 * 1840) and TC =(1 *1840) + fixed costs. By implication, if fixed costs are greater than $84,640 the Gain to Society will be less than zero. The correct answer is (Q). 26. A competitive market will produce where demand and long run supply are equal. In other words, 600 - .05Q = 120, or Q* = 9600. The correct answer is (L). 27. Adding private costs per unit of output of $120 plus the external costs of the pollution ($60), the marginal social cost is $180. The optimum output, the one that produces the socially efficient result, will be where the marginal benefits reflected by the demand curve equal the marginal social benefits. In other words, 600 - .05Q = 180, or Q = 8400. The correct answer is (J). 28. If there is no tax, the economy gains from consumer surplus of (600 - 120 ) x 9600/2 = $2,304,000. However, it suffers from pollution costs of 9600 x 60 = $576,000. The net benefit is $1,728,000. If there is a tax, output drops to 8400, so consumer surplus is (600 – 180) x 8400/2 = $1,764,000. There are tax revenues raised of $504,000 which will be used to provide benefits to society. And the pollution costs will have been reduced to 60 x 8400 = $504,000. 4 The gain to society under conditions of this tax are therefore $1,764,000. The increased benefits to society are $36,000. The correct answer is (J). 29. Elasticity of demand is 1.5 and there is a 2% increase in price. Since the elasticity of demand can be interpreted as the percentage change in quantity divided by the percentage change in price, this implies that quantity will change by about 3% (2 x 1.5). This change will, of course, be negative, since price and quantity are negatively related along the demand curve. Price has risen by 2% and quantity has fallen by 3%. If we imagine that the price was 100, it has risen to 102. If we imagine that quantity was 100, it is now 97. Multiplying 102 x 97, we get 9894, which is about 1.06% less than 100 x 100 = 10000. The correct answer is (A). 30. If demand is P = 100 - .1Q and P = 70, then industry output (Q) = 300. At a price of 70, each firm will set MC = P, so 10 + 3q = 70 or q = 20. There must be 300/20 = 15 firms in the industry. The correct answer is (G). 5 PART II - SHORT ANSWER PROBLEMS (total of 25 marks) 31. (9 marks) There are two labelled graphs below. The first shows the situation of one of a number of identical firms in an industry, the other shows the situation of the perfectly competitive industry as a whole. The industry shown is a constant cost industry, which is initially in short run and long run equilibrium. On both graphs, show the effects of a decrease in market demand, as follows. (a) On the diagram for the industry, show the new short-run equilibrium market price (P1) and quantity exchanged (Q1). (b) On the diagram for the firm, show the new short-run market price (P1) and the new short-run quantity produced (q1). Show (by shading in the appropriate area) the amount of profit/loss now earned by the firm in the short run. (c) Show any changes in the firm’s cost curves in the short run. (d) Show the new long run industry output (Q 2) and the output of each firm in the industry (q2 ). MC Loss AC SSR D1 AC 1 P0* P0* SLR * P1* P1 D q1* q0 =q*LR2 Q*LR Q1* Q0* Firm Industry A fall in demand will shift the demand curve down (left). Therefore, output in the firm and industry will drop in the short-run and losses are made (P1*,q1*) (P1*,Q1*). In the long-run, output in the firm returns to output at minimum AC, but output in the industry falls further as firms exit the industry. 6 32. (7 marks) The diagram below shows the situation faced by a natural monopoly producer. Draw on the diagram any additional lines you need and label them. (a) Show the quantity that the unregulated monopoly producer will produce (Q M) and its selling price (PM). (b) Show (by shading in) the profit that will be earned by the unregulated monopoly producer. (c) Show (using diagonal lines) the consumer surplus available under unregulated natural monopoly. (d) Show the quantity that would be produced (QMC) and the price (P MC) if the monopolist is regulated and compelled to follow marginal cost pricing. (e) Show the quantity that would be produced (Q AC) and the price P cs Unregulated Monopoly Profit M PM* PAC AC PMC MC D 0 QM* QAC QMC Q MR The unregulated monopolist will produce where MR=MC in order to maximize profit. At this point, we have (PM*,QM*). Profit under this pricing scheme is shown as the bold rectangle on the diagram. Consumer surplus is the area under the demand curve and above PM*. If the monopolist must use marginal cost pricing, it will produce where MC=D (quantity and price are show as P MC and Q MC on the diagram). Average cost pricing means the monopolist will produce where AC=D(quantity and price are shown as PAC and QAC on the diagram). 7 33.(9 marks) The diagram below shows the demand and supply for widgets in southern Ontario. Now, the government decides to levy a unit tax (or flat-rate excise tax) on sellers of widgets. (a) Label the initial equilibrium price (P0) and quantity exchanged (Q0). (b) Show any shifts in curves that occur. (c) Show the new price paid by buyers (P B) and received by sellers (PS) and the new quantity exchanged (Q T) after the tax. (d) Show on the diagram the buyers= share (BS) and sellers= share (SS) of the tax. (e) Show on the diagram the amount of excess burden of the tax, by labelling it EB. (f) Show also (by shading it in on the graph and labelling it TR) the amount of tax revenue raised. Label each of these changes clearly, for marking purposes. P S+T S TR PB EB B.S P0* S.S PS D 0 QT Q0* Q A tax on sellers will be added to the supply curve, therefore, the supply curve will shift upwards. The new equilibrium will occur where the new supply curve (S+T) intersects with the demand curve (P B,QT). The new equilibrium price is the price paid by buyers (P B). However, since there is a tax, the sellers receive a different price (P S). The tax revenue is the amount of the tax times the quantity sold at the new equilibrium price. The excess burden of the tax is the triangle shown on the diagram which is the area lost due to the imposition of the tax. Buyers share of the tax is the rectangle below PB and above P 0*. Sellers share is the rectangle above PS and below P 0*. 8