Econ 112 Assignment Solutions

True, False, or Uncertain [48 marks - 6 marks each] Explain why each of the following statements is True, False, or Uncertain according to economic principles. Use diagrams where appropriate. Unsupported answers will receive no marks. It is the explanation that is important. A5-1. Ian buys 100 shares of a hot cannabis stock for $1 each on the stock market and pays a brokerage commission of $9.99. The transaction adds $109.99 to GDP. A5-2. If the result of cannabis legalization in Canada is that the value added from the illegal transactions moves to a legal market, then GDP will increase and so will economic well-being. A5-3. Imagine that a country produces only two final goods: Cannabis (Cs) and Munchies (Ms). In Year 1 it produced 10 Cs at a price of $5 each and 50 Ms at a price of $1 each. In Year 2 it produced 15 Cs at a price of $6 and 50 Ms at a price of $2. If Year 1 is the base year, the inflation rate in the GDP deflator between Years 1 and 2 is 52%. A5-4. When aggregate consumption is $100 (billion) while disposable income is only $80 (billion), the marginal propensity to save from disposable income must be negative.

Unformatted text preview: ECONOMICS 110/112* Assignment #4/Assignment #1 – Suggested Solutions 2011/2012 Due Dates and Notes: • DUE: By Friday February 3, 2:00 PM. Completed assignments should be placed in the slot marked for your section in the white assignment collection box on the 2nd floor of Dunning Hall. Late assignments will not be accepted. • Use the Cover Page when submitting assignments. • Group Work: Maximum four per group, all students must be registered in the same section of the same course. Names must be in alphabetical order on the cover page. • • Graded work will be available for pick-up beginning on the afternoon of Friday February 17 in the Econ Distribution Center, Dunning Hall Room 334. You will require your student card. This assignment covers material from Chapters 16-19 of the text (Econ 110). • This assignment covers material from Chapters 1, 2, 33 (pp 802-13), 3, 19 of the text (Econ 112). True, False, or Uncertain [48 marks - 6 marks each] Explain why each of the following statements is True, False, or Uncertain according to economic principles. Use diagrams where appropriate. Unsupported answers will receive no marks. It is the explanation that is important. 110 assignment – first 5 questions – 112 first 5 follow A4-1. Suppose two cottagers share a lake. One likes to drive a motorboat at high speed around the lake (and values this activity at $100) while the other hates the noise (and values peace and quiet at $75). If they can negotiate without cost, then it does not matter who is given the right to decide lake use, the result will be efficient use of the lake. True. Because the boater values this activity more than the lover of peace and quiet values that peace and quiet, the efficient use of the lake would then be for boating to take place. If the boater gets to decide lake use, then no amount that the other user is willing-to-pay (up to $75) would compensate him/her for the lack of boating. So the boater will go ahead and drive the motorboat. If the other user gets to decide lake use, then the boater is willing-to-pay enough to compensate for the noise (up to $100), so again boating will take place. This logic (with different numbers) applies if the parties agree to a more complicated usage pattern (say no boating after 5 or on Sunday morning). A4-2. As long as the marginal cost of production is constant, private markets will provide the efficient amount of a pure public good. False. Suppose that (as in the diagram below) the public good G can be provided at constant marginal cost p. Since all consumers can enjoy the full quantity of G, then the marginal social benefit (MSB) of G is the vertical summation of all individual marginal private benefits (MPBi). In the diagram below, this is shown as MSB, the vertical summation of the MPBs of our two consumers A and B. Efficiency in G requires the production (or purchase) of G* where MSB equals MSC. However, if purchases are left to private markets, the most that will be provided is Gb. If A purchased first, he/she would choose Ga (where MPBa = MSC), then B would purchase the only the balance, Gb – Ga, because at Gb MPBb = MSC). B is therefore free-riding on A’s purchases. If B purchased first, he/she would choose Gb while A would purchase no additional units, free-riding on the purchases made by B. This is an inefficient outcome because at Gb, MSB > MSC leading to a deadweight loss on all units between Gb and G*. This is shown as the area “xyz”. $ MSB = MPBa + MSBb y x Ga z MSC MPBb MPBa Gb G* G A4-3. Suppose three voters on a committee (A, B, and C) are trying to decide which of 3 projects to approve (X, Y, or Z). A’s valuations of the projects are (in order) 20, 10, and 0. B’s valuations are 0, 20, and 10. C’s valuations are 10, 0, and 20. If they vote on the programs in pairs, they will never decide anything. True. Consider first voting for X or Y. X wins because both A and C prefer it over Y. Now consider voting for X or Z. Z wins because both B and C prefer it over X Finally consider voting for Z or Y. Y wins because both A and B prefer it over Z. But X is preferred to Y, etc.. So there is no stable voting equilibrium. A4-4. Ian makes $25,000, pays $2,500 in income tax and $2,500 in sales tax. Lorne makes $50,000, pays $11,000 in income tax and $4,000 in sales tax. The sales tax is regressive, but the overall tax system is progressive. True. Sales Tax: Average Tax Rate (atr) = Sales Tax/Income Ian’s atr = 2,500/25,000 = .10 = 10% Lorne’s atr = 4,000/50,000 = .08 = 8% Therefore the average tax rate is decreasing with income so the sales tax is regressive. Total Taxes Average Tax Rate (atr) = Total Taxes/Income Ian’s atr = (2,500 + 2,500)/25,000 = 5,000/25,000 = .20 = 20% Lorne’s atr = (11,000 + 4,000)/50,000 = 15,000/50,000 = .30 = 30%. Therefore the overall tax system is progressive since the average tax rate is increasing with income. A4-5. Suppose the government funds the provision of a pure public good from tax revenue. The cost to the economy of providing the good exceeds the amount spent on the good. True. The revenue required to purchase the public good is raised through taxation. This taxation causes deadweight loss. Thus, the public good costs society more than the amount required to purchase it. To see the deadweight loss from taxation, examine the figure below. The tax shifts the supply curve up by the amount of the tax, from S to ST. Quantity falls to QT. The tax raises revenue of tQT (shown on the diagram as area “acde”). However, producers and consumers lose the area “abcde” of total surplus. The tax revenue goes to the government to purchase the public good but the area “abc” is lost. It is this area that is the deadweight loss from taxation. p e d ST t a S b D c QT Q Q 112 assignment – first 5 – common ones follow 112-A1-1. It is often argued that developing countries should not bother installing old fashioned wired communication networks, because the cost of installing wired systems is high relative to using wireless systems. By this logic, a country like Canada should switch to wireless as well. False/Uncertain. The opportunity cost of having a wired system in a country that does not currently possess one must include the cost of installation. This may tilt the decision against a wired system versus a wireless system. However, in Canada (which has already borne the installation costs), the opportunity cost of having a wired system is simply the cost of maintenance for the system. Therefore it may (and likely does) make sense for Canada to continue with its wired system (in addition to any wireless elements it wishes to add), while it may not make sense for a developing country to bear the additional cost of installation. 112-A1-2. In an economy that produces only guns and butter, if the economy is currently producing only butter, then the opportunity cost of guns is zero. False/Uncertain. Consider the Production Possibilities Curve shown in the figure below. The economy is currently operating at point A. If the country is going to produce some guns, it will use those resources best at producing guns first. By "best" we mean those resources that are relatively best at producing guns as opposed to butter. We give up the least butter possible to get more guns, that is, the opportunity cost of guns is at its lowest. The opportunity cost at a point on the PPF is the slope of the PPC at that point. However, unless those resources were actually useless in butter production, we will give up some butter. Therefore the opportunity cost of guns is at its lowest, but will not be zero. butter A guns 112-A1-3. Suppose that Ontario can produce 1 ton of wheat or 3 tons of corn per unit of resources and Manitoba can produce 4 tons of wheat or 4 tons of corn per unit of resources. Manitoba has an absolute advantage in the production of wheat, but Ontario has a comparative advantage in wheat production. False. It is true that Manitoba has an absolute advantage in the production of wheat. Manitoba can produce more wheat (4 vs 1 ton) with a unit of resources, that is, productivity in Manitoba is higher in wheat. To determine comparative advantage we must look at opportunity costs: Opp Cost of Wheat: If Ontario moves a unit of resources from corn to wheat production it gains 1 units of wheat but loses 3 units of corn. Therefore the opp cost of a unit of wheat in Canada is 3 (=3/1) tons of corn. If Manitoba moves a unit of resources from corn to wheat production it gains 4 tons of wheat but loses 4 tons of corn. Therefore the opp cost of a unit of wheat in Manitoba is 1 (=4/4) tons of corn. Therefore it is Manitoba that has a comparative advantage in wheat production (lower opp cost). 112-A1-4. The data in 112A1-3 tells us that trading wheat from Manitoba to Ontario at a price of 2 tons of corn per ton of wheat will make both provinces better off. True. If Manitoba increases its production of wheat, each ton costs a ton of lost corn production. If it can trade the extra wheat for 2 tons of corn it is better off. If Ontario decreases its production of wheat then for each lost ton of wheat it gains 3 tons of corn. If it can then purchase the lost ton of wheat production for only 2 tons of corn, it is better off. 112-A1-5. An increase in consumer incomes will result in an increase in the price of any consumer good. False/Uncertain. For most consumer goods, those that are considered to be “normal”, an increase in consumer incomes means that consumers want to buy more of the good at any price. This is a shift to the right of the demand curve (an increase in demand). In the diagram below this is represented by the shift from D to D’. Therefore there is an increase in both the equilibrium price and quantity. For those consumer goods considered to be “inferior”, an increase in consumer incomes leads to a decrease in demand. The demand curve would shift from D’ to D and equilibrium price and quantity would both fall. p S D' D Q Common Ones A4-6. A decrease in posted (nominal) interest rates necessarily means a decrease in real interest rates. False The real interest rate (r) is the nominal interest rate (i) less the inflation (π) that is expected over the lifetime of the financial contract. So, viewed another way, i = r + π. So a decrease in a nominal interest rate can be the result of a decrease in the real interest rate and/or a decrease in the expected rate of inflation over the life of the contract. A4-7. On June 3, 2011 the Canadian dollar exchange rate with the Euro was 1.4316, while on January 20, 2012, the rate was 1.3105. The Canadian dollar appreciated between June 2011 and January 2012. True. Since it takes fewer Canadian dollars to purchase a Euro in January 2012 than it did in June 2011 the Canadian dollar has increased its value. This is referred to as an appreciation of the currency. A4-8. Suppose an economy has a labour force of 10 and 2 unemployed workers. If one of the unemployed workers becomes discouraged and leaves the labour force, the unemployment rate decreases and the unemployment problem is reduced. False/Uncertain. The unemployment rate is defined as u = U/L = U/(U+E) where u is the unemployment rate, U is the number of unemployed, and L is the labour force defined as the number of unemployed plus the number employed (E). So, when one of the unemployed becomes discouraged and leaves the labour force, the unemployment rate falls from 20% (=2/10) to 11% (=1/9). This part of the statement is true. But it is difficult to argue that the unemployment problem has been reduced since just because a discouraged worker leaves the labour force. Problems [52 marks - marks for each part as shown] 1st Problem for 110 A4-9. Suppose the marginal costs of emissions abatement (MCAs) for firms 1 and 2 and the marginal benefit of emissions abatement (MBA) are given by: MCA1 = 20 + A1 MCA2 = 10 + 2A2 MBA = 50 where Ai is firm i’s abatement and the benefits and costs are measured in dollars. (a) In the absence of any pollution control program, how much pollution will be abated? What is the efficient level of abatement for each firm? Illustrate in a diagram. [5] Since abatement is costly for firm, then, in the absence of any control program, the firms will choose to abate zero units. Efficiency requires that firms abate until the marginal cost of doing so is equal to the marginal benefit of doing so, since MCAi represents the marginal social cost of abatement by firm i, and MBA (the reduction in external emissions costs) represents the marginal social benefit of abatement. Therefore the efficient levels of abatement are given by: 20 + A1 = 50 10 + 2A2 = 50 A1* = 30 A2*= 20 P 50 MCA2 B C D 20 30 MCA1 MBA 40 30 20 10 0 F E 10 40 50 Ai (b) What is the deadweight loss (if any) of being at the unregulated solution? [Hint: Remember that there are two firms here.] [5] When firm i abates zero, society loses the difference between MCAi and MBA on each unit between 0 and Ai*. So, for firm 1, this is area BDF and for firm 2, it is the area BCE. We can calculate the dollar values of these areas as follows: DWL(1) = area BDF DWL(2) = area BCE = ½(50 – 20)(30 – 0) = ½(50 – 10)(20 – 0) = ½(30)(30) = 450 = ½(40)(20) = 400 Therefore the total deadweight loss in the unregulated case is BDF + BCE = $850. (c) If the government wants to restore efficiency in this market, what level of tax should it levy on pollution emissions? What is the gain to society? Illustrate and explain. [5] Firms respond to an emissions tax by abating those units of emissions such that the cost of abatement is less than or equal to the tax, and paying the tax on those units of emissions for which paying the tax is cheaper than bearing the cost of abatement. So the level of abatement for a given level of tax is defined by MACi(Ai) = t. So it is clear that to obtain the efficient level of abatement, the government should set the tax, t* = 50. Society “regains” the deadweight loss associated with producing emissions at Ai = 0. As shown above in part (b) this deadweight loss is equal to area BDF + BCE = $850. (d) Suppose that the government observes a decrease in the tax revenue received under the program. What does this tell the government about the technology of abatement? [5] Since firms pay tax on each unit of emissions that they choose not to abate, then a decrease in tax revenue signals that firms are abating more units of emissions. Given that firms abate until MACi(Ai) = t, then the only reason for a firm to increase its abatement is because there has been a decrease in its cost of abatement. This implies an improvement in the technology of abatement. 1st Problem for 112 112-A1-9. Using supply and demand diagrams, separately analyze the effects that each of the following events would have on the North American market for natural gas (a major heating and power generation fuel). Note the direction of any change in price and/or quantity traded (equilibrium quantity). p S' X S Y W Z D' D Q (a) Ontario and several other jurisdictions switch their coal-fired power plants to more clean burning natural gas power plants. [3] Begin at Z. Demand shifts right from D to D’ since more gas is required for power at any price. This leads to a new equilibrium at Y with a higher price and quantity. (b) A major hurricane in the Gulf of Mexico shuts down gas production there for several weeks. [3] Begin at Z. Supply shifts left from S to S’ since less gas is supplied at any price due to the shutdowns. This leads to a new equilibrium at W with an increase in price, and a decrease in quantity. (c) A technological change allows drillers to extract previously unavailable gas from shale deposits. [3] Begin at X. Supply shifts right from S’ to S since the technological change means that more gas will be supplied at any price. This leads to a new equilibrium at Y with a lower price and higher quantity. (d) A sudden and expected to be protracted January thaw causes both buyers and sellers of natural gas to expect the price to decline in the future. [3] Begin at X. Demand shifts from D’ to D because if consumers expect lower prices in the future, they will reduce purchases as much as possible now. In addition, supply shifts from S’ to S because if suppliers expect prices to fall in future they will try to sell as much as possible now. This leads to a new equilibrium at Z with a lower price but an uncertain or ambiguous effect on quantity. (e) Both event (a) and event (c) take place simultaneously. [4] Begin at W. As shown above in parts (a) and (c), demand shifts to the right from D to D’, and supply shift to the right from S to S’. This leads to a new equilibrium at Y with an increase in quantity but an ambiguous effect on price. (f) Two of the events above result in an increase in the price of gas. Suppose that you observed an increase in the price, but were unsure which of the events had taken place. What additional market information would you need to be sure? [4] Both events (a) and (b) lead to higher gas prices. However, with (a) part of the adjustment to a new equilibrium comes about through an increase in quantity, while with (b) there is a decrease in quantity. Therefore if you could observe the direction of the quantity, you could be sure whether (a) or (b) occurred. A4-10. Below are data describing the Canadian economy in 2006 and 2011 from the Statistics Canada website (www.statcan.gc.ca). In the table, nomY is nominal GDP in billions of that year’s dollars, Y is real GDP in billions of 2002 dollars, L is the labour force, E is employment, and Pop is the population, all in millions. (Express percentages to one decimal place and dollar figures to the nearest dollar.) Year 2006 2011 nomY 1,450 1,721 Y 1,283 1,360 L 17.6 18.7 E 16.5 17.3 Pop 32.6 34.6 (a) Calculate the five-year growth rate in both nominal and real GDP. What accounts for any difference? Explain [4] Growth rate (% change) in nominal GDP = (1721 – 1450)/1450 = 18.7% Growth rate (% change) in real GDP = (1360-1283)/1283 = 6.0% Since real GDP removes the effect of price changes, then the difference between the two numbers is accounted for by price changes between 2006 and 2011. We can calculate the average increase in prices as the difference between the growth rate in nominal and real GDP: 18.7% – 6.0 = 12.7% (b) Calculate the unemployment rate for each year. [4] To calculate unemployment we must first calculate the number of unemployed in each year. Since the labour force is the sum of the employed and unemployed this is easily done: U2006 = L2006 - E2006 = 17.6 – 16.5 = 1.1 U2011 = L2011 - E2011 = 18.7 – 17.3 = 1.4 The unemployment rate is the number of unemployed divided by the labour force, expressed as a percentage so: u2006 = U2006/L2006 = 1.1/17.6 = 6.3% u2011 = U2011/L2011 = 1.4/18.7 = 7.5% (c) Calculate real GDP per worker and real GDP per capita for both years. Real GDP per worker: Y2006/E2006 = $1283B/16.5M = $77,758 Y2011/E2011 = $1360B/17.3M = $78,613 Real GDP per capita: Y2006/Pop2006 = $1283B/32.6M = $39,356 Y2011/Pop2011 = $1360B/34.6M = $39,306 [4] (d) Calculate the growth rate in employment and in real GDP per worker. Can you see a simple relationship between these two numbers and the growth rate in real GDP? [4] Growth rate (% change) in employment = (17.3 – 16.5)/16.5 = 4.8% Growth rate (% change) in real GDP/worker = (78,613 – 77,758)/77,758 = 1.1% Comparing these numbers with the percentage change in real GDP it can be seen that the growth rate in real GDP is (almost) equal to the sum of growth rate in real GDP/worker plus the growth rate in employment. That is 6.0% ≈ 4.8% + 1.1% = 5.9%. The small difference is a result of rounding issues. A4-11. Suppose that average consumption baskets (bundles) for 2010 and 2011 are as shown in the table below: Number of iPads Pizza Slices 2010 {quantity, price} {2 iPads, $700/iPad} {200 slices, $3/slice} 2011 {quantity, price} {3 iPads, $600/iPad} {150 slices, $6/slice} (a) What is the percentage change in the price of each good? Calculate the consumer price index (CPI) for 2010 and 2011 using 2010 as the base year. What is the inflation rate in the CPI? [7] Growth rate of iPad price = [Price2011/Price2010 -1] = [600/700 – 1] = -14.3% Growth rate of pizza price = [Price2011/Price2010-1] = [6/3 –1] = 100.0% To calculate the CPI numbers, find the cost of the 2010 consumption bundle in each year: TC2010 = (2*700) + (200*3) = 1400 + 600 = 2000 TC2011 = (2*600) + (200*6) = 1200 + 1200 = 2400 The CPI in any year t is given by: CPIt = (TCt /TCb)*100. Therefore, with 2010 as the base year: CPI2010 = (2000/2000)*100 = 100 CPI2011 = (2400/2000)*100 = 120 So inflation in the overall price level (inflation in the CPI) is: Inflation rate = [(CPI2011 - CPI2010)/CPI2010]*100% = [(120-100)/100]*100% = 20% (b) Would all consumers be equally affected by the change in the reported cost of living? Explain. [5] Those people who consume more iPads and less pizza (than the standard bundle) may actually be better off in 2011 since the price of iPads has declined. They are certainly better off than those who consume more pizza and fewer iPads than the average consumer. This is because the cost of the bundle consumed by the first type has increased by less (or even declined) relative to the standard bundle, and the cost of the bundle consumed by the second type has increased by even more than the standard bundle. (c) What does the change in quantities in 2011 tell you about whether the CPI overstates or understates the effect of price changes on the cost of living? [4] The fact that consumers have responded to the change in relative prices by consuming more iPads and less pizza is significant. They have substituted towards the good that is relatively less expensive. Therefore, since the CPI is calculated using a fixed bundle, it is overstating the effect that the average price level increase has had on consumers. ...
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