Workbook for the New I.B. Economics (2 nd edition)

Transcription

1 1 SOLD TO THE FINE HL Paper 3 Quantitative Exercises and Worked Solutions taken from Workbook for the New I.B. Economics (2 nd edition) by Bryce McBride Copyright 2013, Croecko Publishing All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior written permission of the publisher. Croecko Publishing 650 Lacroix Bay Road, R.R. #1 Westmeath, Ontario Canada K0J 2L0 For ordering and other information, please go to and or send an to bryce@brycemcbride.com ISBN

2 2 Author s Introduction Since the fall I have been working on a new and improved edition of Workbook for the New I.B. Economics featuring improved lessons and additional exercises presented with the aid of attractive graphic design. I expect to complete the entire revision later this spring (most likely in April, 2013) but have decided to release these exercises and worked solutions earlier (without the benefit of graphic design) in order to assist teachers and students facing the first examinations under the new syllabus coming up in May. The questions are arranged in the order that the expectations they refer to appear in the syllabus. Section one features questions arising from syllabus sections 1.1 and 1.3 (Markets and Government Intervention), section two features questions arising from syllabus section 1.5 (Theory of the Firm), section 3 features questions arising from syllabus section 2 (Macroeconomics) while section 4 features questions arising from syllabus section 3 (International Economics). I would like to thank Kathryn Peyton for her help in reviewing some of the questions and answers and would encourage anyone finding anything questionable to me with their concerns. Thank you for your consideration and best wishes in the upcoming exams. Bryce McBride bryce@brycemcbride.com Table of Contents Additional HL Paper 3 Exercises Section 1 Page 3 Additional HL Paper 3 Exercises Section 2 Page 11 Additional HL Paper 3 Exercises Section 3 Page 16 Additional HL Paper 3 Exercises Section 4 Page 20 Section 1 Solutions Page 30 Section 2 Solutions Page 41 Section 3 Solutions Page 46 Section 4 Solutions Page 48

3 3 Additional HL Paper 3 Exercises Section 1 1. Given the demand function Qd = 100 2P and the supply function Qs = P: a) Plot the functions on the grid below and label them. You may first like to calculate the ordered pairs using a table of values as indicated below. Price Qd = 100 2P Qs = P b) Using algebra, find the equilibrium price and quantity implied by the intersection of the two functions. Check that it agrees with what is suggested by your graph from part a.

4 4 c) Using geometry (and remembering that the area of a triangle is calculated according to the formula A = ½ b * h) calculate the consumer and producer surplus enjoyed at this equilibrium point. d) Using algebra, calculate the quantity demanded and the quantity supplied at a price of $20. Would there be excess demand or excess supply at this price and of how many units? e) Just by looking at the functions expressed algebraically, how can you tell how many units people would want to buy at a price of zero? How can you tell at which price sellers will begin to bring the good to market? f) If buyers suddenly began buying many more additional units every time the price dropped by $1, how would you expect the demand function to change? Conversely, if sellers suddenly began supplying many more additional units every time the price rose by $1, how would you expect the supply function to change? Explain your answers.

5 5 2. Given the same linear demand and supply functions as were used in question 1: a) Apply a $5 per unit specific indirect tax to the good and plot the resultant supply and demand curves on the grid below: b) Looking at the diagram, what has been the impact of the tax on the equilibrium market price and quantity sold as compared to the situation without the tax looked at in question 1? Estimate the new equilibrium price and quantity to the nearest whole unit. c) Calculate the consumer and producer surplus associated with this new post-tax equilibrium point as well as the revenue gained by the government through the imposition of the tax. Comparing the sum of these three amounts to the sum of the consumer and producer surplus associated with the equilibrium point in question 1 c above, which is greater? What then has been the impact of the tax on overall welfare?

6 6 d) Calculate and compare consumer expenditure and producer revenue before the tax was applied to consumer expenditure and producer revenue after the tax was applied. What was the impact of the tax on each? e) Comparing the initial equilibrium price from Q1 with the post-tax equilibrium price from part b above, how much of the $5 tax has been borne by consumers? What portion therefore has been borne by producers? Explain why the incidence of the tax is different for consumers and producers (or, in other words, why the burden of the tax has been borne unevenly). 3. Given the same linear demand and supply functions as were used in question 1: a) Apply a $5 per unit specific indirect subsidy to the good and plot the resultant supply and demand curves on the grid below:

7 7 b) Looking at the diagram, what has been the impact of the subsidy on the equilibrium market price and quantity sold as compared to the initial situation looked at in question 1? c) Calculate the consumer and producer surplus associated with this new post-subsidy equilibrium point as well as the money spent by the government to pay for the subsidy. Compare the sum of the consumer and producer surplus to the total welfare associated with the equilibrium point in question 1 c. What has been the impact of the subsidy on overall welfare? d) After making the necessary calculations, compare consumer expenditures and producer revenues before the subsidy was applied to consumer expenditures and producer revenues after the subsidy was applied. What is the impact of the subsidy on each? e) Comparing the initial equilibrium price from Q1 with the post-subsidy equilibrium price from part b above, how much of the $5 subsidy has been transferred to consumers? What portion therefore has been transferred to producers? Explain why the incidence of the subsidy is different for consumers and producers (or, in other words, why the benefits of the subsidy have been distributed unevenly).

8 8 4. Given the demand function Qd = P and the supply function Qs = P: a) Plot the functions on the grid below and label them. You may like to first calculate the ordered pairs using a table of values as indicated below. Price Qd = P Qs = P b) Using algebra, find the equilibrium price and quantity implied by the intersection of the two functions. Check that it agrees with what is suggested by your graph from part a.

9 9 c) Using geometry (and remembering that the area of a triangle is calculated according to the formula A = ½ b * h) calculate the consumer and producer surplus enjoyed at this equilibrium point. d) If the government were to impose a floor price of $6, would there be a shortage or surplus in response and of how many units? e) Compare producer revenue and consumer expenditure in this situation (the $6 price floor) with producer revenue and consumer expenditure in the initial situation without the price floor. Consider only the units that are actually sold by producers to consumers. f) If the government were to commit to buying the surplus production at the price they have mandated, how much would they have to spend? g) If instead the government were to impose a price ceiling of $4, would there be a shortage or a surplus in response and of how many units?

10 10 h) Compare the producer revenue and consumer expenditure in this situation (the $4 price ceiling) with the producer revenue and consumer expenditure in the initial situation without the price ceiling. Consider only the units that are actually sold by producers to consumers. i) Calculate the consumer and producer surplus enjoyed under the $4 price ceiling and compare it to the consumer and producer surplus enjoyed in the initial situation set out in part c. Has the price ceiling transferred some surplus from producers to consumers and if so, how much? Has some welfare simply been lost? If so, explain your answer and calculate the extent of the welfare loss. You may wish to use the grid below to draw the demand and supply functions and the price ceiling to help you answer the question.

11 11 Additional HL Paper 3 Exercises Section 2 1. A monopolist can supply a product for $3 per unit (which is both his marginal and average cost) while the demand curve for the product is Qd = 10 P. a) Complete the table below: Price $10 $9 $8 $7 $6 $5 $4 $3 $2 Qd = 10 P Total Revenue Marginal Revenue Average Revenue b) On the grid below, graph the monopolist s marginal and average cost curves along with their marginal and average revenue curves c) Were the firm not a monopolist, the equilibrium point would be where the marginal cost curve met the demand curve. Identify this point and label the resulting price and quantity Pc and Qc.

12 12 d) Calculate, using geometry, the producer and consumer surplus at this equilibrium point. e) Now find the price and output that a profit-maximizing monopolist would choose and mark them Pm and Cm (remember the profit maximizing rule produce until MR = MC). f) Calculate, using geometry, the producer and consumer surplus at the monopolist s preferred equilibrium point. g) From using the calculations and from looking at the diagram, how much surplus was transferred from consumers to the monopolist and how much was simply lost? h) In order to limit the welfare loss due to monopoly, the government decides to regulate the monopolist and mandates a fixed price of $4/unit for the product. Calculate the producer and consumer surplus at this new price and calculate the extent of the welfare loss to determine whether or not the fixed price would achieve the government s aim.

13 13 2. A farmer has a fixed amount of land and workers. However, he can vary the number of tractors he uses. He finds that his total production of corn varies with the number of tractors he uses as described by the table below: Number of Tractors Output of Corn (tonnes) Marginal Product Average Product a) Calculate the marginal product of each additional tractor and record it in the table above. At what point does the farmer begin suffering diminishing returns from using additional tractors? b) Calculate the average product attributable to each tractor for each quantity of tractors and record it in the table above. c) If corn prices are $100/tonne and if tractors cost $2000 per season to own and operate, how many tractors should the farmer use to maximize his returns? Explain your answer. 3. An entrepreneur s business exhibits the following total costs and total revenues: Output Total Costs Marginal Costs Average Costs Total Revenue Marginal Revenue Average Revenue a) From looking at the table, what are the entrepreneur s fixed costs? Explain your answer

14 14 b) Thus, what would be the entrepreneur s total variable costs where output is 6? Explain your answer. c) Calculate and record in the table the entrepreneur s marginal and average cost and marginal and average revenue at each level of output. d) Calculate the entrepreneur s profits at each level of output. At which level of output are profits highest? e) From the evidence provided by the table, is the entrepreneur operating in a competitive environment or is he operating as a monopolist? Explain your answer. f) What would be the entrepreneur s revenue-maximizing output? g) At what output levels does the entrepreneur roughly break even? h) On the grid that follows, record the entrepreneur s marginal and average costs and revenues. Mark in the profit-maximizing, revenue-maximizing and break-even points on the graph.

15 15 4. A firm is operating in a competitive market and exhibits the following total costs: Quantity Fixed Cost Variable Cost Total Cost Marginal Cost Avg. Var. Cost Avg. Total Cost a) Complete the table above after calculating the relevant costs. b) At which level of output are average total costs at a minimum? What is happening if the market price of the firm s output is exactly this amount? What is happening if the market price of the firm s output is greater than this amount? c) At which level of output are average variable costs at a minimum? What is likely to happen if the selling price of the firm s output is below this minimum amount? What is likely to happen if the selling price of the firm s output is above the minimum of average variable cost but below the minimum of average total cost?

16 16 Additional HL Paper 3 Exercises Section 3 1. The following are the accounts of national expenditure for 2012: Consumption spending by households: Total investment spending by firms: Depreciation of firms existing capital stock: (ie spending needed to replace worn out machinery and equipment) Government spending on goods and services Spending on Imports Receipts from Exports $100 billion $15 billion $3 billion $20 billion $30 billion $31 billion a) Calculate nominal GDP from the expenditure side for b) If the nation s population was 40 million, what is the nation s nominal GDP per capita? c) If the nation s GDP deflator was set at 100 in 2011 and was estimated to be 105 in 2012, what was the nation s real GDP in 2012, measured in constant 2011 dollars? d) If the nation s GDP in 2011, measured in 2011 dollars, was 126 billion, what was the rate of real economic growth between 2011 and 2012? What was the nominal rate of economic growth between the two years? e) If the nation s workers and firms operating abroad produced (and earned) $10 billion while the workers and firms of other countries operating within the nation produced (and earned) $5 billion in 2012, what would be the nation s nominal GNP/GNI for that year?

17 17 2. As there are often unmet basic needs in poorer countries, their marginal propensity to consume is often much higher than in richer countries. If we assume that the MPC in the nation of Povertia is 0.96 while the MPC in the nation of Largesse is 0.7: a) Calculate the Keynesian multiplier for both nations. b) Using the multipliers from part a, calculate the effect on GDP of an additional $1000 of government spending in each country. How much would GDP increase as a result of the increase in government spending? 3. In Australia there were people working and people actively looking for work in What was Australia s unemployment rate that year? 4. Statisticians from the small island nation of Paradiso calculate that the average household in the country spends one quarter of its income on housing, another quarter on food, and an eighth on each of clothing, utilities, transportation and entertainment. The statisticians then decided to select representative goods from each category and then tracked the prices year by year, as shown in the table below: Good Price in 2010 Price in 2011 Price in BR House Rent, per month $500 $515 $520 2 BR Apartment Rent, per month $350 $375 $385 Bread, one loaf $2 $2 $2 Bananas, kg $1 $0.8 $1 Milk, litre $1 $1.25 $1.25 Leather shoes, one pair $30 $25 $25 Woman s cotton dress $30 $33 $35 Electricity, per kwh $0.10 $0.12 $0.13 Bus ticket $1 $1 $1.10 Gasoline, per litre $1.5 $1.35 $1.40 Cinema ticket $7 $7.50 $7.50 Dance hall admission $7 $7 $7 a) Construct a weighted price index for Paradiso using the data above. Give the index the value 100 for the prices given for It is suggested that you follow certain steps when constructing your index, such as:

18 18 i) Determining which items go under which category ii) Determining how to weight the different items in each category. As a default it is acceptable to weight each item the same within each category. For instance, it would be fine to give bread, bananas and milk equal weight in the food category (suggesting that I eat a loaf of bread about as often as I eat a kg of bananas or drink a litre of milk). However, make sure that food overall is one quarter of your overall index. iii) Figuring out the adjustment numbers to make your prices fit the category weights. For instance, for the food items, if I decide to give each item equal weight, I would want each of the three items to count for 8.3 % of the index (as 8.33 * 3 = 25), as 25% is the weight of the food category in the overall index. To get the $2 price of bread to 8.3, you would need to multiply it by To get the $1 price of bananas or milk to 8.3, you would just need to multiply it by 8.3, as below: (Price of Bread*adjustment #) + (Price of Bananas*adjustment #) + (Price of Milk*adjustment #) = ($2 * 4.15) + ($1 * 8.3) + ($1 * 8.3) = 25 Feel free to use the guide below to calculate your index. At the end of it, you should have something that looks like this: (3 BR House Rent) * + (2 BR Apartment Rent) * + {should = 25} (Bread Price) * + (Banana Price) * + (Milk Price) * + {should =25} (Price of Shoes) * + (Price of Cotton Dress) * + {should = 12.5} (Electricity Price) * + {should = 12.5} (Bus Ticket Price) * + (Price of a litre of gasoline) * + {should = 12.5} (Cinema Ticket Price ) * + (Dance Hall Ticket Price) * = 100 {should = 12.5} The blanks (ie ) are the weights given to each item in your index. Keeping these weights the same you will then be able to calculate new index numbers easily for 2011 and 2012 by simply plugging in the changed prices for each item.

19 19 b) Keeping the weights the same, what is the value of the price index for 2011 and 2012? c) What then was the rate of inflation between 2011 and 2012? 5. Gillian has two job offers to work in neighboring states. The stated salary for both positions is $ However, the income tax regimes are very different in each state, as described in the table below: State A State B Income Level Tax Rate Income Level Tax Rate Below $ Below Above Above a) What would be Gillian s marginal rate of income tax in each state? b) How many dollars of tax would Gillian pay in each state? c) What then is Gillian s average rate of tax in each state? d) Gillian s brother Jake faces a similar choice to Gillian, except that he has been offered a salary of $ What would be his marginal rate of tax in each state? What would be his tax burden and average rate of tax in each state?

20 20 Additional HL Paper 3 Exercises Section 4 1. Australia and Indonesia each produce 2 goods fruit and minerals. At the moment, Indonesia can produce one unit of minerals at an opportunity cost of two units of fruit while Australia can produce one unit of minerals at an opportunity cost of just one unit of fruit. If Indonesia were to devote a certain quantity of productive resources to the production of fruit it would be able to produce 1200 units per year, while if Australia were to devote the same quantity of productive resources to the production of fruit, they would only be able to produce 500 units per year. a) On the grid below, draw the PPCs for Indonesia and Australia for fruit and minerals. Minerals Fruit b) Which country enjoys an absolute advantage in the production of fruit and of minerals? Explain your answer with reference to resource costs. c) For which good does Indonesia enjoy a comparative advantage and for which good does Australia enjoy a comparative advantage? Explain your answer with reference to opportunity costs.

21 21 c) If Indonesia and Australia did not trade, but instead simply devoted half of their productive resources to the production of fruit and the other half to the production of minerals, how much of each good could each produce? Minerals Fruit Indonesia Australia Total d) Now, if Australia were to devote all of its resources to producing minerals, and if Indonesia were to devote enough of its resources to producing minerals to keep the total mineral production the same for the two countries as in part c, how much fruit could Indonesia produce? Is this amount greater than the total fruit produced in part c? What does this answer suggest about the gains to be had from trade based on comparative advantage? 2. The following diagram shows the French market for berets: Price (dollars) Domestic Supply 16 (Qs = P) Demand (Qd = P) Quantity ( 000s)

22 22 a) What is the equilibrium price and quantity in the absence of trade? b) If France were to throw open the doors to free trade in berets, manufacturers in Vietnam and other countries know they can supply an unlimited quantity of berets at a price of $6. What would be the new equilibrium price and quantity sold of berets in France when foreign-made berets are made available for sale? Change the diagram above to reflect the entry of foreign manufacturers. c) How have the revenues of French beret makers been affected by the entry of the imported berets? Using the diagram, compare their revenues before and after the event. How much revenue are the foreign manufacturers earning from French beret buyers? d) How has consumer surplus been affected by the entry of the imports? Calculate the consumer surplus enjoyed in the initial situation with the surplus enjoyed when $6 berets are made available. e) In order to stem the tide of foreign berets, the French government imposes a $2 tariff on imported berets. i) Show the impact of the tariff on the diagram above ii) What is the new equilibrium price and quantity? iii) How much revenue is the French government collecting from the tariff? iv) How much additional revenue is being earned by French beret makers? v) How much less revenue is being earned by foreign beret makers in the French market?

23 23 vi) What has been the impact of the tariff on consumer surplus as compared to the freetrade case described in part d above? f) Faced with complaints from the public that the tariff is a government tax on berets, the government eliminates the tariff in favour of an import quota of 7000 berets. Price (dollars) i) Show the impact of such a quota on the diagram below: 18 Supply Demand Quantity ( 000s) ii) What would be the new equilibrium price and quantity after the imposition of the import quota? iii) With the quota in place, how many berets would French beret-makers be able to sell? What has been the impact of the quota on their sales revenue as compared to the free-trade case described in part c above?

24 24 iv) What has been the impact of the quota on the French revenues of foreign beret makers? Why have their revenues not been reduced as much as was the case when the tariff was imposed in part e above? v) What has been the quota s impact on consumer surplus as compared to the free trade case described in part d above? g) Rather improbably, consumer complaints about rising beret prices cause the government to eliminate the quota and instead give a $2 per beret subsidy to French beret makers. As in part b, foreign manufacturers are once again welcome to sell as many berets in France as they wish. i) Show the impact of such a subsidy on the diagram below: Price ($) 18 Supply Demand Quantity ( 000s) ii) What is the new equilibrium price and quantity after the subsidy is granted to French beret makers?

25 25 iii) With the subsidy in place, how many berets are French manufacturers able to sell? What is their total revenue in this situation? Be sure to include both the revenue earned from consumers and the revenue earned from the government in the form of the subsidy. iv) Why would consumers be happier with the subsidy than either the quota or the tariff? Why would foreign producers prefer to face quotas than tariffs or subsidies? Use revenue and surplus calculations to justify your answers. 3. After travelling to France from Morocco, Majid received his credit card bill and noticed that the restaurant meal that had cost him 30 Euros was listed on his statement as costing 340 Dirham. What does this suggest is the currency exchange rate of Euros in terms of Dirhams? 4. It has always been Julia s dream to buy a Ural motorcycle from Russia. Searching online one day, she noticed a recent model for sale for Russian rubles. If the exchange rate of US dollars in terms of rubles is 32, how much would her dream motorcycle cost in terms of USD? 5. While on holiday in Thailand, Lee Hong from Singapore noticed that while he had gotten 2500 Thai Baht last week per $100 SGD note, on his most recent trip to the money changer he had received 2650 Baht per $100 SGD note. a) Calculate the initial exchange rate for Thai Baht in terms of Singapore dollars. b) Had the Thai Baht appreciated or depreciated during Lee Hong s holiday? By what percentage had it changed in value?

26 26 6. If the demand and supply functions for the Philippine Peso are defined as Qd = P and Qs = P, and where P is the price of the Philippines Peso in terms of US cents: a) What is the equilibrium exchange rate of the Philippine Peso in terms of US cents? Determine your answer through solving the system of equations. If you would like to check your answer by constructing a supply and demand diagram, feel free to do so. b) Given this exchange rate, what would be the exchange rate of US dollars in terms of Philippine Pesos? 7. An oil-producing nation in West Africa has just published its balance of payments accounts for 2012: Imports of Goods Exports of Goods Imports of Services Exports of Services Income from Foreign Sources Payments to Foreign Beneficiaries Current Transfers from Foreign Sources Current Transfers to Foreign Beneficiaries Debt Forgiveness and other Capital Transfers Direct Investment from Foreign Sources Direct Investment Abroad from Domestic Sources Portfolio Investment from Foreign Sources Portfolio Investment Abroad from Domestic Sources Change in Reserve Assets $50 billion $80 billion $15 billion $2 billion $1 billion $8 billion $1 billion $5 billion 0.5 billion $3 billion nil nil $6 billion $3.5 billion a) Calculate: i) The balance of trade in goods ii) The balance of trade in services, income and current transfers iii) The overall current account balance iv) The balance in the capital account v) The balance in the financial account

27 27 b) The presence of a large, multinational oil company (such as Shell or Exxon-Mobil) employing some expatriate technicians and managers would likely affect which entries in the accounts? Explain your answer. 8. A nation operating under a fixed exchange rate currency regime is suffering from a current account deficit of $100 (imports are $1000 and exports are $900) and wishes to try to reduce the deficit through devaluing its currency by 20%. Economists estimate that the PED for the country s imports is 0.6 while the PED for the country s exports is 0.3. a) Will the devaluation have its intended effect? Explain your answer with the help of a calculation using the numbers above. b) Again using calculations to support your answer, show you the devaluation would have a different effect if the PED of imports and the PED of exports were both The prices of a country s imports and exports are given in the table below: Good Price in 2011 Price in 2012 Price in 2013 Oil (import) $100/barrel $120 $90 Bananas (import) $1/kg $ Iron Ore (export) $100/tonne $90 $120 Machinery (export) $100/piece $100 $105

28 28 a) Taking the figures from 2011 as representing the base year (with a value of 100 ), and assuming that oil comprises 3/4 of the value of the country s imports (while bananas comprise just one quarter) and that iron ore and machinery both make up half of the value of the country s exports, calculate the country s terms of trade in 2012, by, in order: i) Calculating the index of export prices ii) Calculating the index of import prices iii) Using these two figures to arrive at the country s 2012 terms of trade b) Again using the figures from 2011 to represent the base year, using a similar method to part a calculate the country s terms of trade in i) Index of export prices ii) Index of import prices iii) 2013 terms of trade c) In what year did the country s terms of trade improve? In what year did they deteriorate?

29 29 d) Can you assume that the country s current account balance would have improved in the year in which its terms of trade improved? Explain your answer with reference to the price elasticity of demand for exports and imports and the following trade volume figures: Good Volume traded, Oil 75 barrels Bananas 2500 kg Iron Ore 50 tonnes Machinery 50 pieces (note that in 2011 there is a balance in the trade in goods, as imports are 75 barrels * $100/barrel plus 2500 kg * $1/kg = $ and exports are 50 tonnes * $100/tonne plus 50 pieces * $100/piece = $10 000)

30 30 Additional HL Paper 3 Exercises Section 1 Solutions 1. a) Price ($) Qd = 100 2P Qs = P Price ($) Supply Demand 0 Quantity b) Setting Qd = Qs and solving for P: 100 2P = P 150 = 6P 25 = P Then substituting 25 for P in either (or both) equations and solving for Q: Qd = 100 2P or Qs = P Qd = 100 2(25) Qs = Qd = 50 Qs = 50 Confirming that at the equilibrium price $25, the Qd and Qs are both 50 as suggested by the graph.

31 31 c) Looking at the graph, we are looking at a welfare triangle that looks like: P=50 (50, 25) P = 12.5 We can confirm the y-intercepts suggested by the graph algebraically as follows: To find the y-intercept of the demand curve, find the price when the quantity is set to 0. Qd = 100 2P 0 = 100 2P 2P = 100 P = 50 T o find the y-intercept of the supply curve, find the price when the quantity is set to 0. Qs = P 0 = P 50 = 4P 12.5 = P Thus, the consumer surplus is the area represented by the following triangle: P = 50 P = 25 (50, 25) A = ½ Base * Height A = ½ (50) * 25 A = 625, so the consumer surplus is $625 Meanwhile, the producer surplus is the area represented by the following triangle: P = 25 (50, 25) P = 12.5 A = ½ Base * Height A = ½ (50) * 12.5 A = 312.5, so the producer surplus is $312.50

32 32 d) Find the quantity demanded and the quantity supplied at P = 20 by plugging 20 into both equations and finding Q Qd = 100 2P Qd = (20) Qd = 60 Qs = P Qs = (20) Qs = 30 As quantity demanded is 60 while quantity supplied is 30, there is an excess demand of 30 units at a price of $20. e) I can easily tell how many units people will want to buy at a price of zero, as that is told to me by the fixed term in the demand function. For example, using the demand function Qd = 100 2P, I can easily see that at a price of zero, Qd = 100, as Qd = 100 2(0). While it is not so easy to find the price at which sellers will begin to bring the good to market, as that requires me to find the price when quantity is equal to zero, it is not difficult. Again using our supply function, just set Q = 0 and solve for P, as in 0 = P 50 = 4P 12.5 = P f) The demand function should get flatter, as the slope coefficient will have gotten larger. The quantity demanded has become more responsive to changes in price. For instance, looking at our demand function, if it were Qd = 100 4P, a drop in price of $1 would result in 4 more units being demanded, not 2. Similarly, the supply function would become flatter, as its slope coefficient would have also gotten larger as the quantity supplied is now more responsive to changes in price. For instance, looking at our supply function, if it were Qs = P, a price increase of $1 would bring 8 more units to market instead of just 4.

33 33 2. a) Price ($) Supply with $5 tax Supply Demand 0 Quantity b) The equilibrium market price appears to have risen to around $28 (from $25) while the quantity sold has fallen to around 43 units (from 50). To find the new equilibrium point algebraically, it would be necessary to first derive the new (post-tax) supply curve. If the tax has shifted the supply curve up $5, and if the slope of the supply curve is 4, then the translation of the curve $5 higher would suggest that the x-intercept of the new curve would be 20 units further to the left. Thus, the post-tax supply curve function would be Qs = P. To find the new equilibrium point, simply set Qd = Qs and solve for P P = 100 2P 6P = 170 P = 28.3 Which implies an equilibrium quantity of: Qd = 100 2P Qd = 100 2(28.3) Qd = 43.4 However, the answers that follow are calculated according to the equilibrium point (43, 28), as my reading of the syllabus suggests that students will not be expected to derive new supply curve functions resulting from the imposition of indirect, specific taxes. c) The government has earned $5 on each of the 43 units sold, so $215.

34 34 The consumer surplus is the area of the following triangle: P = 50 P = 28 (43, 28) So, as A = ½ Base * Height A = ½ (43) * 22 A = 473 so the consumer surplus is $473. The producer surplus is the area of the following triangle at right (remember that the $5 tax comes between the price consumers pay ($28) and what producers receive ($23): P = 23 (43, 23) P = 12.5 So, as A = ½ Base * Height A = ½ (43) * 10.5 A = so the producer surplus is $ Comparing the sum of these three figures ($215 + $473 + $ = $913.75) to the sum of producer and consumer surplus before the tax was imposed ($625 + $ = $937.50) we can see that the sum from part c is greater. Thus, we can conclude that the tax has led to a decrease in overall welfare of roughly $ d) Before the tax was applied, consumer expenditures and producer revenues were both (50 * $25) $1250. After the tax was applied, consumer expenditures were (43 * $28) $1204 while producer revenue was (43 * $23) $989. The difference between the two numbers ( ) was the tax collected by the government. In this case, the tax reduced both consumer expenditure (a little bit) and producer revenue (significantly). e) Well, as the initial price was $25, the fact that the price consumers pay rose to $28 while the price received by producers fell to $23 would suggest that consumers ended up paying $3 of the $5 tax while producers ended up paying the remaining $2. The reason the tax has been borne unevenly is that the price elasticity of demand is less than the price elasticity of supply around the old equilibrium price and quantity. To calculate: PED from (60, 20) to (40, 30) is: -(40 60)/60 = 0.33 = 0.66 (30-20)/ PES from (30, 20) to (70, 30) is (70-30)/30 = 1.33 = 2.66 (30-20)/20 0.5

35 35 The consumers end up paying more of the tax as their demand is less sensitive to price changes than is producer supply. Whoever is less likely to change their behavior in response to a price change will end up being hit with a greater price change whenever a tax is applied. Put more simply, whoever is less likely to duck is more likely to get hit. 3. a) Price ($) Supply Supply with $5 subsidy Demand 0 Quantity b) The subsidy has increased the equilibrium quantity from 50 to 56 while decreasing the equilibrium price from $25 to $22. c) The consumer surplus associated with the new post-subsidy equilibrium point can be calculated by finding the area of the triangle under the demand curve from Q = 0 to Q = 56 from P = $22 to P = $50: A = ½ Base * Height A = ½ (56) * 28 A = 784, so the consumer surplus is $784 The producer surplus associated with the same equilibrium point can be calculated by finding the area of the triangle above the supply curve from Q = 0 to Q = 56 from P = $7.5 to P = $22: A = ½ Base * Height A = ½ (56) * 14.5 A = 406, so the producer surplus is $408 The initial producer and consumer surplus in question 1 were $625 and $312.50, so the subsidy has clearly had a positive effect on both consumer and producer surplus, and hence overall welfare. However, the subsidy did cost the government money, to the tune of $5 per unit for each of the 56 units produced, or $280.

36 36 d) After the subsidy was granted, consumers spent (56 * $22) $1232, while producers would have received (56 * $27) $1512. Recall that while consumers only pay $22, the amount going to the producers is that amount plus the amount of the subsidy. The difference between these two numbers is the cost of the subsidy to government ($ = $280). Comparing these figures to the initial consumer expenditure/producer revenue of ($25 * 50) $1250, we can see that the subsidy has resulted in a slight reduction in consumer expenditure and a significant increase in producer revenue. e) Comparing the initial equilibrium price of $25 with the post-subsidy equilibrium price of $22, we can see that $3 of the $5 subsidy has been transferred to consumers, whereas producers are only gaining $2 (recall that while the price is $22, producers are receiving $22 + $5 = $27). Consumers are enjoying a greater portion of the subsidy than producers due to consumers and producers having different responses to a change in price, as measured by PED and PES. As we saw in our answer to question 2 e), the price elasticity of demand around the initial equilibrium point is only 0.66 while the price elasticity of supply is What this means is that producers are more likely to increase output in response to a price increase than consumers are likely to increase purchases in response to a price drop. So, when faced with a subsidy, which has the effect of increasing the price paid to producers even while reducing the price paid by consumers, producers are more likely to increase output than consumers are to increase purchases. This being the case, the subsidy in this instance lowers consumer prices more than it increases producer prices. 4. Price ($) Supply Demand Quantity

37 37 Price Qd = P Qs = P b) Setting Qd = Qs and then solving for P: P = P 250 = 50P 5 = P Substituting this value for P in either (or both) equations to find Q: Qd = P Qs = P Qd = (5) Qs = (5) Qd = 50 Qs = 50 Thus showing that at a price of $5, Qd = Qs at 50 units, which is in agreement with the graph. c) The consumer surplus can be described by the area of the triangle below the demand curve from its y-intercept to the equilibrium point. While I know the equilibrium point, I need to find the y-intercept, or the price at which the quantity demanded is zero. Qd = P 0 = P 30P = 200 P = 200/30 or 6.66 Thus, the consumer surplus can be calculated as the area of the following triangle: P = 6.66 P = 5 (50, 5)

38 38 A = ½ Base * Height A = ½ (50) * 1.66 A = so the consumer surplus is $41.66 The producer surplus can be described by the area of the triangle above the supply curve from its y-intercept to the equilibrium point. To find the y-intercept of the supply curve I need to find the price at which the quantity supplied is zero. Qs = P 0 = P 50 = 20P 50/20 = P, or in other words, P = $2.5 Thus, the producer surplus can be calculated as the area of the following triangle: P = 5 (50, 5) P = 2.5 A = ½ Base * Height A = ½ (50) * 2.5 A = 62.5 so the producer surplus is $62.50 d) If the government were to impose a price floor of $6, we can calculate the Qd and Qs as follows: Qd = P Qs = P Qd = (6) Qs = (6) Qd = 20 Qs = 70 Thus, as Qs is greater than Qd, there would be a surplus of 50 units. e) In the initial situation, producer revenue and consumer expenditure would both be (50 units at $5 each) $250. However, after the price floor has been put into place, while suppliers want to sell 70 units, only 20 will actually change hands. Thus, producer revenue/consumer expenditure will fall to (20 units at $6 each) $120. f) If the government were committed to buying the additional 50 units at the floor price, they would have to spend (50 units at $6 each) $300. g) if the government were to impose a price ceiling of $4, we can see from looking at the table of values in part a that there would be a shortage of 50 units as at that price the Qd is 80 units while the Qs is just 30 units.

39 39 h) With a $4 price ceiling, while consumers would like to buy 80 units, only 30 will be supplied by producers, so as a result total consumer expenditure and producer revenue will fall to (30 units at $4 each) $120. i) Price ($) 9 8 Supply Demand Quantity With a $4 price ceiling, the consumer surplus can be represented by the irregular area under the demand curve from the vertical axis until Q = 30. I will decompose it into two regular shapes as follows: A triangle: P = 6.66 P = 5.66 (30, 5.66) And the rectangle below: P = 5.66 (30, 5.66) P = 4 (30, 4) The areas of each shape are: A = ½ Base * Height and A = Length * Width A = ½ (30) * 1 A = 30 * 1.66 A = 15 A = 49.8 So the total consumer surplus is ( ) $64.8 The producer surplus is simpler to figure out, being just the area of the triangle above the supply curve from the vertical axis until Q = 30, as shown below: P = 4 (30, 4) P = 2.5

40 40 A = ½ Base * Height A = ½ (30) * (1.5) A = 22.5 so the producer surplus is $22.50 Thus, the overall welfare (producer and consumer surplus) in this situation is ( ) $87.3 Looking at the results from part c, where the consumer surplus was $41.66 and the producer surplus was $62.50 we can see that some producer surplus has been transferred to consumers as a result of the price ceiling. However, clearly some welfare has been lost as well, as total welfare before was $ before the price ceiling was put in place but just $87.30 afterwards. Looking at the graph we can try to measure the area of the welfare loss (the triangle from Q = 30 right towards the old equilibrium at (50,5) and see if it gives us a figure similar to the loss arrived at by subtracting $87.30 from $ (ie $16.86). The welfare loss can be represented by the triangle described below: (30, 5.66) (50, 5) (30, 4) Taking the vertical side as the base, we can calculate the area as follows: A = ½ Base * Height A = ½ (1.66) * 20 A = 16.6, or $16.60 which is quite close to the amount calculated above ($16.86)

41 41 Additional HL Paper 3 Exercises Section 2 - Solutions 1. a) Price $10 $9 $8 $7 $6 $5 $4 $3 $2 Qd = 10 P Total Revenue Marginal Revenue Average Revenue b) Price ($) Pm Pc 3 2 MC = AC 1 0 MR Qm Qc AR c) Pc = $3 and Qc = 7 units on the graph above d) There is no producer surplus as all output is at lowest average and marginal cost. Consumer surplus is the area of the triangle from $3 to $10 from output 0 to output 7, calculated as: A = ½ Base * Height A = ½ (7) * 7 A = 24.50, so the consumer surplus is $24.50

42 42 e) The profit maximizing monopolist would choose to produce 4 units and charge $6, as shown on the graph. f) The producer surplus would be the rectangle from output 0 to 4 and from price $3 to $6, calculated as: A = l * w A = 4 *3 A = 12, so the producer surplus is $12 Consumer surplus can be calculated by taking the area of the triangle from output 0 to 4 and between the price $6 and $10, as follows: A = ½ Base * Height A = ½ (4) * 4 A = 8, so the consumer surplus is $8 g) $12 of surplus was transferred from consumers to producers and, as initially consumer surplus was $24.50, clearly $4.50 was simply lost. We can confirm this loss by calculating the area of the welfare loss triangle, which is the triangle beneath the AR curve between output 4 and 7 from $3 to $6 as follows: A = ½ Base * Height A = ½ (3) * 3 A = 4.5, so the welfare loss is confirmed as being $4.50 h) If the government mandates a price of $4 per unit, the new equilibrium price and quantity would be $4 and 6. The demand curve would still exist but the monopolist would no longer be aware of it or able to use it to calculate marginal revenue as under the fixed price, his marginal revenue (and hence average revenue) is $4 for every unit sold. So, taking this new equilibrium point, we can see that the consumer surplus is now represented by the triangle from Q = 0 to Q = 6 and from P = 4 to P = 10, which can be calculated as follows: A = ½ Base * Height A = ½ (6) * 6 A = 18, so the consumer surplus is now $18 Producer surplus is represented by the area of the rectangle from Q = 0 to Q = 6 between P = 3 and P = 4, and can be calculated as follows: A = l * w A = 6 * 1, so the producer surplus is now $6 Thus, total welfare is now $24, suggesting that the welfare loss has been reduced to $0.50. If you calculate the area of the welfare loss triangle you can confirm this result.

43 43 2. A farmer has a fixed amount of land and workers. However, he can vary the number of tractors he uses. He finds that his total production of corn varies with the number of tractors he uses as described by the table below: Number of Tractors Output of Corn (tonnes) Marginal Product Average Product a) See table above. He begins to suffer diminishing returns from the 3 rd tractor onwards, as his marginal product falls from 40 tonnes with the second tractor to just 30 tonnes with the third tractor. b) See table above. c) The farmer should use 4 tractors to maximize his returns. The marginal revenue from his 4 th tractor is equal to 20 tonnes * $100/tonne = $2000. The marginal cost of the 4 th tractor is also $2000. However, the 2 nd and 3 rd tractors yield more revenue than they cost. The 5 th and subsequent tractors, meanwhile, yield less revenue than they cost. 3. An entrepreneur s business exhibits the following total costs and total revenues: Output Total Costs Marginal Costs Average Costs Total Revenue Marginal Revenue Avg. Rev. Profit a) The entrepreneur s fixed costs are $10, as these are his costs when output is equal to zero, indicating that these costs do not vary according to output. b) Total variable costs when output is 6 are $17. Total costs are $27 at this output level. Subtracting fixed costs of $10 from $27 gives us $17. c) See table above. d) See table above. His profits are highest ($15) when output is 5 or 6.

44 44 e) The entrepreneur is operating as a monopolist, as he faces a downward sloping marginal revenue curve, which implies that he or she knows the demand curve for the product and is not therefore a price-taker. f) The entrepreneur s revenue-maximizing output is 6 or 7, where total revenue is $42. g) The entrepreneur roughly breaks even at two points the first point is at an output level between 1 (loss of $3) and 2 (profit of $2) and the second point is at an output level between 8 (profit of $6) and 9 (loss of $3). h) Price ($) Break-Even Points where AR = AC Marginal Cost 4 Average Cost Average Revenue Marginal Revenue -6 Quantity Revenue Maximizing Point where MR = 0; (Q = 7) Profit Maximizing Point where MR = MC; (Q = 6, P = $7) Note that the profit maximizing point is where MR = MC, and that the break-even points occur where AR = AC. The revenue maximizing point is where MR = 0, as so long as MR is positive, producing more units will increase total revenue.

45 45 4. a) Quantity Fixed Cost Variable Cost Total Cost Marginal Cost Avg. Var. Cost Avg. Total Cost b) Average total costs are at a minimum of $5.25 at an output of 8 units. If the market price of the firm s output is also $5.25 and if the firm produces 8 units the firm will be breaking even (neither earning profits nor incurring losses). As well, what is suggested by a situation where the market price of a good is equal to the minimum average cost to produce the good is that the firm is operating in a perfectly competitive industry, as firms operating in perfectly competitive industries are productively efficient and produce at lowest average cost. If the market price is above $5.25 the firm will potentially be making profits, so long as they produce where the market price is above average revenue. In a perfectly competitive market, a price above $5.25 would only be a short-term phenomenon as the profits earned at higher prices would attract new entrants to the industry which would in turn depress prices back towards $5.25. If the price remains above $5.25 consistently, the firm is not operating in a perfectly competitive industry. c) Average variable costs are at a minimum of $3.83 at an output of 6. If the selling price of the firm s output is below $3.83 the firm is likely to shut down as every unit produced will result in additional losses. If the selling price of the firm s output is between $3.83 and $5.25 the firm will likely stay in business but operate at a loss, as while the firm will lose money at such a price, if it shut down and had to pay its fixed costs without any revenue its losses would be even greater. For instance, if the price were $5, and if the firm were to sell 7 units, the firm would earn $35. This suggests a loss of $2 as the total cost to produce 7 units is $37. This loss of $2 is less than the loss that would be incurred if the firm were to shut down and still be responsible for its fixed costs of $10. Even if the price were $4, the same situation would apply. The revenues earned of $28 from 7 units are only $9 less than the $37 it cost to produce the goods, again less than the $10 loss that would be incurred were the firm to shut down and cease production.