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时间：2022-06-09
ECON10004
Introductory Microeconomics
Semester 2, 2020
Solution Guide
SECTION A 1] C 2] A 3] C 4] B 5] D 6] B 7] A 8] B 9] D 10] C
SECTION B
Question B1 Recently a Pablo Picasso painting, ‘Women of Algiers’, sold for $(AUS)180 million. Alan Accountant and Edwina Economist have been discussing why the painting sold for such a high price. They agree that demand for Picasso’s art has increased in the past 10 years. Alan says: “There are just no close substitutes for Picasso’s art. Hence demand for Picasso’s paintings is price-inelastic, and therefore any increase in demand will cause a large price increase”. Edwina disagrees. She replies: “But the real problem is that since Pablo Picasso is deceased, there will never be any addition to the existing stock of Picassos. Therefore, supply is relatively price-inelastic. This is why prices are increasing so much as demand grows.” Solution Alan is incorrect and Edwina is correct. First, the size of increase in price caused by an increase in demand will depend on the own-price elasticity of supply; not the own-price elasticity of demand. That is, when there is an increase in demand, the new equilibrium will shift up the supply curve; and therefore, the extent to which the increase in demand
translates into changes in the equilibrium price and quantity traded depends on the own-elasticity of demand. Second, it is when the own-price elasticity of supply is relatively inelastic that the increase in demand will cause the largest size of increase in the equilibrium price. Third, Edwina’s logic that the number of Picasso paintings being fixed implies that the own-price elasticity of supply will be relatively inelastic seems correct.
Question B2 Alan Accountant and Edwina Economist are discussing whether the two suppliers of air flights within Ozland, Cheap Flights and Qanwings, should be allowed to merge to become a single supplier. Alan says: ‘A single supplier will mean that the average cost of supply is lower due to economies of scale in the supply of air flights. Hence allowing the merger will definitely increase total surplus in the market for flights within Australia’. Edwina Economist disagrees. She says: ‘I agree about the potential benefits from a merger coming from lower costs. But we cannot say that total surplus will definitely increase. It is also necessary to take into account how the merger affects market power’. Solution Alan is incorrect and Edwina is correct. Alan’s point that a single supplier will cause a lower average cost of production where long-run costs exhibit economies of scale is valid. That is, if there are economies of scale, it implies that average total cost decreases with the total quantity a firm supplies. Hence, the average total cost of having a single firm supply the whole output in a market will be lower than if there are (for example) two firms which each supply one-half of the market’s output. Alan is also correct that a lower cost of production will increase total surplus – that is, lower cost implies the same amount of output is being produced at lower opportunity cost. However, Alan is not correct that the lower cost of production will definitely imply an increase in total surplus. The reason that Alan is wrong is the reason provided by Edwina. The merger will mean that there is now a single supplier in the market for air flights in Australia. A monopoly supplier will have more market power than the two separate suppliers. The monopoly supplier is likely to use that power to restrict output compared to if there were two suppliers (in order to increase the price and hence profits). Where that happens, then the merger would also cause a decrease in total surplus. If the effect of higher market power outweighs the effect of decreased costs, then total surplus would be decreased due to the merger.
Question B3 A group of developed countries and a group of developing countries must decide whether to ‘Cut’ or ‘Keep at current levels’ emission of pollutants. If both groups of countries decide to ‘Cut’ there will be a significant improvement in the global environment, and hence in the well-being of both groups of countries. But if either or both groups of countries decide to
‘Keep at current levels’, then there will be no improvement in the global environment. Alan Accountant says: ‘Both groups of countries will know they are best off by both choosing ‘Cut’. Therefore, this will happen.’ Edwina Economist has a different view: ‘I agree that both countries choosing to ‘Cut’ is the most likely outcome. But I also think that a possible equilibrium would be for both countries to choose to ‘Keep at current levels’’. Solution The game table for this game is shown below (It is assumed that B > 0). Alan is correct to say that both groups of countries are made best off if they both choose ‘Cut’. As can be seen from the game table below, {‘Cut’, ‘Cut’} is a weak dominant strategy equilibrium, and hence we would generally consider this to be the best prediction of the outcome in the game. However, Alan may not be correct to say that this will definitely be the outcome in the game. In addition to {‘Cut’, ‘Cut’}, there is also another Nash equilibrium in the game, which is {‘Keep at current levels’, ‘Keep at current levels’}. That is, given that the other group of countries chooses to ‘Keep at current levels’, neither group of countries can do strictly better by switching from ‘Keep at current levels’. Hence Edwina’s judgement about the likely outcome is probably better than Ed’s – since she recognizes that {‘Cut’, ‘Cut’} is the most likely outcome, but that there is some possibility that both groups of countries might choose ‘Keep at current levels’ since this is also a Nash equilibrium. Developing countries Cut Keep at current levels Developed countries Cut B,B 0,0 Keep at current levels 0,0 0,0
SECTION C
Question C1 (15% of total marks)
a) (5 marks) ‘Jet fuel consumption remains the hardest hit section of the global oil market as passengers avoid air travel as a result of the pandemic and government travel restrictions. The specific problems of the jet market explain why prices for distillates such as diesel are being hit much harder than benchmark oil prices’ (John Kemp, ‘Oil market rebound hinges on return of international flights’, The Age, 22/9/2020, pp.24-25): i) Use the demand/supply model to explain how the larger decrease in the price of distillates than benchmark oil prices could be explained by different sizes of decrease in demand. Is your explanation consistent with information in the newspaper article excerpt above? ii) Can you think of another possible explanation – using the demand/supply model - for why there has been a larger decrease in the price of distillates than benchmark oil prices? Solution i) The larger decrease in price for the distillates than benchmark oil prices can be explained by there being a larger decrease in demand for distillates than benchmark oil. This is consistent with the newspaper article excerpt which describes how there has been a large decrease in demand for distillate products due to them being used in aviation transport – which has been one of the areas of economic activity most adversely affected by COVID-19. ii) Other possible explanations would be that: • The supply of distillates could be relatively own-price inelastic compared to the supply of benchmark oil. In that case, even if the decrease in demand was similar for the two products, there would be a larger decrease in the price of distillates than benchmark oil. • A price floor for benchmark oil might prevent its price decreasing by as much as for distillates.
b) (5 marks) ‘Consumers are being warned of price hikes for fresh food if farmers cannot secure more workers to pick their fruit and vegetables…National Farmers’ Federation chief executive Tony Mahar said…’We know that some farmers are planning to decrease the size of their next crop…’’ (David Crowe, ‘Farmers fear price hikes amid slavery attack’, The Age, 1/10/20, p.17): i) Use the demand/supply model to explain why a shortage of workers to pick agricultural crops could cause an increase in prices of fruit and vegetables? ii) Is there a type of government policy that could be used to increase the supply of workers to pick fruit and vegetables? Explain briefly how the policy would have that effect.
Solution i) First, a shortage of workers is likely to decrease the supply of fruit and vegetables. This could happen because the shortage of workers causes an increase in the price of workers used as an input to supply of fruit and vegetables – which then causes a decrease in supply. Or perhaps the number of workers implies an upper limit on the amount of fruit and vegetables than can be picked and hence supplied – similar to the effect of a quota. Second, the decrease in supply of fruit and vegetables would be predicted to increase the equilibrium price. ii) The main policy I had in mind is a subsidy; that is, some type of monetary payment intended to increase the incentive for labour supply to picking fruit and vegetables. The predicted effect of a subsidy is to increase the wage paid to workers doing fruit picking, and hence increase the equilibrium quantity of workers employed.
c) (5 marks) ‘Coca-Cola Amatil fears its secret bottled water source in the NSW Southern Highlands is under threat from a major sand mine proposed for neighbouring land. The beverages giant – which manufactures popular brands Mount Franklin and Pump – is alarmed at the quarry’s potential to pollute its pristine water source…’ (Carrie Fellner, ‘Coca-Cola fears mine to spoil water source’, The Age, 28/9/20, p.14): i) What is market failure? ii) What type of market failure is described in the excerpt from the article above? iii) What would be the consequences of that market failure? iv) Can you suggest a policy that government could use to remedy the market failure? Briefly explain how the policy would work. Solution i) Market failure exists where the equilibrium market quantity traded (outcome) is not efficient. Possible sources are external effects; public goods; and imperfect competition. ii) The type of market failure is a negative external effect. First, the sand mine is going to take an action (mining sand) that affects the well-being (profitability) of Coca-Cola. Second, the sand mine would not take into account the impact on the profitability of Coca-Cola of its decision about whether and how much sand to mine. iii) The consequences of there being a negative external effect would be that the quantity of sand mined would be above the socially optimal quantity – because the sand mining company does not take into account the negative consequences of its actions on Coca-Cola. iv) A variety of policies could remedy the market failure – by shifting the quantity of output towards the socially optimal quantity: (i) A tax on the output of the sand mining company – This would increase the opportunity cost to the sand mining company and
hence cause it to reduce its quantity of output; (ii) Direct regulation of the quantity of output supplied by the sand mining company to the social optimal level; or (iii) Assigning property rights over the water in a way that would – for example – allow Coca-Cola to require a payment from the sand mine if it affects water quality. By being required to make a payment, the opportunity cost to the sand mining company would increase, causing it to reduce its quantity of output.
Question C2 (20% of total marks) Phil’s Car Wash Inc. has alternative production methods it can use. Some details of the costs of using these methods are described in the table below:
Production
Method 1
Production
Method 2
Number of
cars washed
per hour
Fixed cost ($) Marginal
Cost ($)
Fixed cost ($) Marginal
Cost ($) 0 2 10 1 2 1 10 1 2 2 2 10 1 3 2 3 10 1 4 2 4 10 1 5 2 5 10 1 6 2 6 10 1 a) (5 marks) What is the ATC of washing from one to six cars per hour using production method 1 and production method 2? Draw a graph of the Long-run Average total cost of washing from one to six cars per hour. How many cars would Phil need to expect to wash per hour for it to be optimal for his business to use production method 2?
Phil’s business operates in a monopolistically competitive market. Demand for car washes from his firm is: Price Quantity demanded 11 0 10 1 9 2 8 3 7 4 6 5 5 6 b) (5 marks) Suppose Phil is using production method 1. Assume that his business must set the same price for each car wash. What will be the profit-maximising price for him to choose? Will Phil be willing to operate his business in the short-run? Suppose that there are two types of customers for car washes – Owners of 4 Wheel Drives (4WDs) and owners of other cars, and that total demand for car washes at Phil’s is made up of demand by each type of owner as follows: Price Quantity demanded Quantity demanded by 4WD owners Quantity demanded by other car owners 12 0 11 1 1 10 2 2 9 3 2 1 8 4 2 2 7 5 2 3 6 6 2 4 c) (5 marks) Suppose Phil is using production method 2. Assume that his business can set a different price for car washes for 4WDs and other cars. What will be the profit-maximising price for him to choose for each type of car? Will Phil be willing to operate his business in the short-run? d) (3 marks) Does Phil earn higher profits in part (b) or (c)? Explain this result. Can you suggest an approach to pricing for Phil that would earn his business even higher profits? e) (2 marks) Why would it be profit-maximising for Phil to use production method 1 in part (b), and to switch to production method 2 in part (c)?
Solution Part (a): In order to use production method 2, Phil would need to wash at least 5 cars (ATC is lower for 5 cars or more).
Production
Method 1
Number of
cars
washed per
hour
FC ($) MC ($) VC ($) TC ($) ATC($)
0 2 1 2 1 1 3 3 2 2 2 3 5 2 ½ 3 2 3 6 8 2 2/3 4 2 4 10 12 3 5 2 5 15 17 3 2/5 6 2 6 21 23 3 5/6
Production
Method 2
Number of
cars
washed per
hour
FC ($) MC ($) VC ($) TC ($) ATC($)
0 10 1 10 1 1 11 11 2 10 1 2 12 6 3 10 1 3 13 4 1/3 4 10 1 4 14 3 ½ 5 10 1 5 15 3 6 10 1 6 16 2 2/3
$
qty
1 2 3 4 5 6
Production method 2
Production method 1
Bold = LRATC
11
3
Part (b): Price Quantity demanded TR MR MC (Production method 1) 12 0 11 1 11 11 1 10 2 20 9 2 9 3 27 7 3 8 4 32 5 4 7 5 35 3 5 6 6 36 1 6 Hence Phil should choose to do 4 car washes and set a price equal to 8. In the short-run his revenue is therefore 4x8 = 32, and his VC equals 10. Hence he should be willing to operate. Part c): Price QD QD by 4WD owners TR – 4WD MR – 4WD QD by other car owners TR – Other MR – Other MC 12 0 11 1 1 11 11 1 10 2 2 20 9 1 9 3 2 1 9 9 1 8 4 2 2 16 7 1 7 5 2 3 21 5 1 6 6 2 4 24 3 1 With the scope to set different prices for car washes for 4WD and other cars, Phil should choose to wash 2 4WDs at a price of 10, and should choose to wash 4 other cars at a price of 6. Hence TR equals: (2)(10) + (4)(6) = 44. VC equals 6. Hence, Phil will be willing to operate in the short-run. Part (d): Profits (part b) = 32 – 2 - 10 = 20. Profits (part c) = 44-10-6 = 28. Profits are higher in part c) because Phil has been able to engage in price discrimination, targeting price at the willingness to pay of the two types of car drivers.
The main approach for earning higher profits that I have in mind is first-degree price discrimination – being able to charge each driver a price equal to their exact willingness to pay. Part (e): This is because the number of cars that it is profit-maximising for Phil to wash increases from 4 to 6 when he switches from charging the same price to all customers to engaging in price discrimination.
Question C3 (15% of total marks)
Two players are involved in a game. In the game each player begins with $10. Each player must simultaneously make a choice of how much of the $10 to allocate between two accounts: a ‘private’ account, and a ‘public’ account. Money allocated to the private account by a player is kept by that player. Money allocated to the public account is multiplied by 1.5, and then distributed back equally to each of the two players. Each player has two possible choices: (i) Allocate $0 to the public account; (ii) Allocate $10 to the public account. A player’s payoff from each outcome is equal to the sum of their private account money and one-half of the total public account money. For example, if both players allocated $10 to the public account, they each have a payoff equal to $0 + (1/2)($20)(1.5) = $15.00. a) (5 marks) Draw a game table to represent this game. b) (3 marks) Do players have a strict dominant strategy in this game? c) (2 marks) What is the Nash equilibrium of the game? d) (1 mark) Does the Nash equilibrium outcome maximise the total payoff to players? How can you explain this result? Now suppose that the game is played sequentially. One player chooses which amount to allocate to the public account; after which the other player, having observed the choice made by the first player, makes their own choice of how much to allocate to the public account. e) (3 marks) Draw the game tree for the sequential game. f) (2 marks) What is the rollback equilibrium of the sequential game? Solution a) Player 2 $0 $10 Player 1 $0 10,10 17.5, 7.5
$10 7.5, 17.5 15, 15 b) Each player has a strict dominant strategy to choose ‘$0’. c) The Nash equilibrium is for each player to choose ‘$0’. (Because each player has a strict DS, this combination of strategies is also a strict DS equilibrium.) d) The payoff-maximising outcome would be for each player to choose $10. However, this game has the same structure as the prisoners’ dilemma game. There is a combination of strategies that would make each player better off, but they both have a different strategy, to give $0, which is a strict DS. e)/f) Rollback equilibrium: Player 1: $0; Player 2: ($0 if player 1 chooses $0; $0 if player 1 chooses $10)
Player 1
Player 2
Player 2
$10
$0
$0
$0
$10
$10
10, 10
7.5, 17.5
17.5, 7.5
15, 15
Introductory Microeconomics
Semester 2, 2020
Solution Guide
SECTION A 1] C 2] A 3] C 4] B 5] D 6] B 7] A 8] B 9] D 10] C
SECTION B
Question B1 Recently a Pablo Picasso painting, ‘Women of Algiers’, sold for $(AUS)180 million. Alan Accountant and Edwina Economist have been discussing why the painting sold for such a high price. They agree that demand for Picasso’s art has increased in the past 10 years. Alan says: “There are just no close substitutes for Picasso’s art. Hence demand for Picasso’s paintings is price-inelastic, and therefore any increase in demand will cause a large price increase”. Edwina disagrees. She replies: “But the real problem is that since Pablo Picasso is deceased, there will never be any addition to the existing stock of Picassos. Therefore, supply is relatively price-inelastic. This is why prices are increasing so much as demand grows.” Solution Alan is incorrect and Edwina is correct. First, the size of increase in price caused by an increase in demand will depend on the own-price elasticity of supply; not the own-price elasticity of demand. That is, when there is an increase in demand, the new equilibrium will shift up the supply curve; and therefore, the extent to which the increase in demand
translates into changes in the equilibrium price and quantity traded depends on the own-elasticity of demand. Second, it is when the own-price elasticity of supply is relatively inelastic that the increase in demand will cause the largest size of increase in the equilibrium price. Third, Edwina’s logic that the number of Picasso paintings being fixed implies that the own-price elasticity of supply will be relatively inelastic seems correct.
Question B2 Alan Accountant and Edwina Economist are discussing whether the two suppliers of air flights within Ozland, Cheap Flights and Qanwings, should be allowed to merge to become a single supplier. Alan says: ‘A single supplier will mean that the average cost of supply is lower due to economies of scale in the supply of air flights. Hence allowing the merger will definitely increase total surplus in the market for flights within Australia’. Edwina Economist disagrees. She says: ‘I agree about the potential benefits from a merger coming from lower costs. But we cannot say that total surplus will definitely increase. It is also necessary to take into account how the merger affects market power’. Solution Alan is incorrect and Edwina is correct. Alan’s point that a single supplier will cause a lower average cost of production where long-run costs exhibit economies of scale is valid. That is, if there are economies of scale, it implies that average total cost decreases with the total quantity a firm supplies. Hence, the average total cost of having a single firm supply the whole output in a market will be lower than if there are (for example) two firms which each supply one-half of the market’s output. Alan is also correct that a lower cost of production will increase total surplus – that is, lower cost implies the same amount of output is being produced at lower opportunity cost. However, Alan is not correct that the lower cost of production will definitely imply an increase in total surplus. The reason that Alan is wrong is the reason provided by Edwina. The merger will mean that there is now a single supplier in the market for air flights in Australia. A monopoly supplier will have more market power than the two separate suppliers. The monopoly supplier is likely to use that power to restrict output compared to if there were two suppliers (in order to increase the price and hence profits). Where that happens, then the merger would also cause a decrease in total surplus. If the effect of higher market power outweighs the effect of decreased costs, then total surplus would be decreased due to the merger.
Question B3 A group of developed countries and a group of developing countries must decide whether to ‘Cut’ or ‘Keep at current levels’ emission of pollutants. If both groups of countries decide to ‘Cut’ there will be a significant improvement in the global environment, and hence in the well-being of both groups of countries. But if either or both groups of countries decide to
‘Keep at current levels’, then there will be no improvement in the global environment. Alan Accountant says: ‘Both groups of countries will know they are best off by both choosing ‘Cut’. Therefore, this will happen.’ Edwina Economist has a different view: ‘I agree that both countries choosing to ‘Cut’ is the most likely outcome. But I also think that a possible equilibrium would be for both countries to choose to ‘Keep at current levels’’. Solution The game table for this game is shown below (It is assumed that B > 0). Alan is correct to say that both groups of countries are made best off if they both choose ‘Cut’. As can be seen from the game table below, {‘Cut’, ‘Cut’} is a weak dominant strategy equilibrium, and hence we would generally consider this to be the best prediction of the outcome in the game. However, Alan may not be correct to say that this will definitely be the outcome in the game. In addition to {‘Cut’, ‘Cut’}, there is also another Nash equilibrium in the game, which is {‘Keep at current levels’, ‘Keep at current levels’}. That is, given that the other group of countries chooses to ‘Keep at current levels’, neither group of countries can do strictly better by switching from ‘Keep at current levels’. Hence Edwina’s judgement about the likely outcome is probably better than Ed’s – since she recognizes that {‘Cut’, ‘Cut’} is the most likely outcome, but that there is some possibility that both groups of countries might choose ‘Keep at current levels’ since this is also a Nash equilibrium. Developing countries Cut Keep at current levels Developed countries Cut B,B 0,0 Keep at current levels 0,0 0,0
SECTION C
Question C1 (15% of total marks)
a) (5 marks) ‘Jet fuel consumption remains the hardest hit section of the global oil market as passengers avoid air travel as a result of the pandemic and government travel restrictions. The specific problems of the jet market explain why prices for distillates such as diesel are being hit much harder than benchmark oil prices’ (John Kemp, ‘Oil market rebound hinges on return of international flights’, The Age, 22/9/2020, pp.24-25): i) Use the demand/supply model to explain how the larger decrease in the price of distillates than benchmark oil prices could be explained by different sizes of decrease in demand. Is your explanation consistent with information in the newspaper article excerpt above? ii) Can you think of another possible explanation – using the demand/supply model - for why there has been a larger decrease in the price of distillates than benchmark oil prices? Solution i) The larger decrease in price for the distillates than benchmark oil prices can be explained by there being a larger decrease in demand for distillates than benchmark oil. This is consistent with the newspaper article excerpt which describes how there has been a large decrease in demand for distillate products due to them being used in aviation transport – which has been one of the areas of economic activity most adversely affected by COVID-19. ii) Other possible explanations would be that: • The supply of distillates could be relatively own-price inelastic compared to the supply of benchmark oil. In that case, even if the decrease in demand was similar for the two products, there would be a larger decrease in the price of distillates than benchmark oil. • A price floor for benchmark oil might prevent its price decreasing by as much as for distillates.
b) (5 marks) ‘Consumers are being warned of price hikes for fresh food if farmers cannot secure more workers to pick their fruit and vegetables…National Farmers’ Federation chief executive Tony Mahar said…’We know that some farmers are planning to decrease the size of their next crop…’’ (David Crowe, ‘Farmers fear price hikes amid slavery attack’, The Age, 1/10/20, p.17): i) Use the demand/supply model to explain why a shortage of workers to pick agricultural crops could cause an increase in prices of fruit and vegetables? ii) Is there a type of government policy that could be used to increase the supply of workers to pick fruit and vegetables? Explain briefly how the policy would have that effect.
Solution i) First, a shortage of workers is likely to decrease the supply of fruit and vegetables. This could happen because the shortage of workers causes an increase in the price of workers used as an input to supply of fruit and vegetables – which then causes a decrease in supply. Or perhaps the number of workers implies an upper limit on the amount of fruit and vegetables than can be picked and hence supplied – similar to the effect of a quota. Second, the decrease in supply of fruit and vegetables would be predicted to increase the equilibrium price. ii) The main policy I had in mind is a subsidy; that is, some type of monetary payment intended to increase the incentive for labour supply to picking fruit and vegetables. The predicted effect of a subsidy is to increase the wage paid to workers doing fruit picking, and hence increase the equilibrium quantity of workers employed.
c) (5 marks) ‘Coca-Cola Amatil fears its secret bottled water source in the NSW Southern Highlands is under threat from a major sand mine proposed for neighbouring land. The beverages giant – which manufactures popular brands Mount Franklin and Pump – is alarmed at the quarry’s potential to pollute its pristine water source…’ (Carrie Fellner, ‘Coca-Cola fears mine to spoil water source’, The Age, 28/9/20, p.14): i) What is market failure? ii) What type of market failure is described in the excerpt from the article above? iii) What would be the consequences of that market failure? iv) Can you suggest a policy that government could use to remedy the market failure? Briefly explain how the policy would work. Solution i) Market failure exists where the equilibrium market quantity traded (outcome) is not efficient. Possible sources are external effects; public goods; and imperfect competition. ii) The type of market failure is a negative external effect. First, the sand mine is going to take an action (mining sand) that affects the well-being (profitability) of Coca-Cola. Second, the sand mine would not take into account the impact on the profitability of Coca-Cola of its decision about whether and how much sand to mine. iii) The consequences of there being a negative external effect would be that the quantity of sand mined would be above the socially optimal quantity – because the sand mining company does not take into account the negative consequences of its actions on Coca-Cola. iv) A variety of policies could remedy the market failure – by shifting the quantity of output towards the socially optimal quantity: (i) A tax on the output of the sand mining company – This would increase the opportunity cost to the sand mining company and
hence cause it to reduce its quantity of output; (ii) Direct regulation of the quantity of output supplied by the sand mining company to the social optimal level; or (iii) Assigning property rights over the water in a way that would – for example – allow Coca-Cola to require a payment from the sand mine if it affects water quality. By being required to make a payment, the opportunity cost to the sand mining company would increase, causing it to reduce its quantity of output.
Question C2 (20% of total marks) Phil’s Car Wash Inc. has alternative production methods it can use. Some details of the costs of using these methods are described in the table below:
Production
Method 1
Production
Method 2
Number of
cars washed
per hour
Fixed cost ($) Marginal
Cost ($)
Fixed cost ($) Marginal
Cost ($) 0 2 10 1 2 1 10 1 2 2 2 10 1 3 2 3 10 1 4 2 4 10 1 5 2 5 10 1 6 2 6 10 1 a) (5 marks) What is the ATC of washing from one to six cars per hour using production method 1 and production method 2? Draw a graph of the Long-run Average total cost of washing from one to six cars per hour. How many cars would Phil need to expect to wash per hour for it to be optimal for his business to use production method 2?
Phil’s business operates in a monopolistically competitive market. Demand for car washes from his firm is: Price Quantity demanded 11 0 10 1 9 2 8 3 7 4 6 5 5 6 b) (5 marks) Suppose Phil is using production method 1. Assume that his business must set the same price for each car wash. What will be the profit-maximising price for him to choose? Will Phil be willing to operate his business in the short-run? Suppose that there are two types of customers for car washes – Owners of 4 Wheel Drives (4WDs) and owners of other cars, and that total demand for car washes at Phil’s is made up of demand by each type of owner as follows: Price Quantity demanded Quantity demanded by 4WD owners Quantity demanded by other car owners 12 0 11 1 1 10 2 2 9 3 2 1 8 4 2 2 7 5 2 3 6 6 2 4 c) (5 marks) Suppose Phil is using production method 2. Assume that his business can set a different price for car washes for 4WDs and other cars. What will be the profit-maximising price for him to choose for each type of car? Will Phil be willing to operate his business in the short-run? d) (3 marks) Does Phil earn higher profits in part (b) or (c)? Explain this result. Can you suggest an approach to pricing for Phil that would earn his business even higher profits? e) (2 marks) Why would it be profit-maximising for Phil to use production method 1 in part (b), and to switch to production method 2 in part (c)?
Solution Part (a): In order to use production method 2, Phil would need to wash at least 5 cars (ATC is lower for 5 cars or more).
Production
Method 1
Number of
cars
washed per
hour
FC ($) MC ($) VC ($) TC ($) ATC($)
0 2 1 2 1 1 3 3 2 2 2 3 5 2 ½ 3 2 3 6 8 2 2/3 4 2 4 10 12 3 5 2 5 15 17 3 2/5 6 2 6 21 23 3 5/6
Production
Method 2
Number of
cars
washed per
hour
FC ($) MC ($) VC ($) TC ($) ATC($)
0 10 1 10 1 1 11 11 2 10 1 2 12 6 3 10 1 3 13 4 1/3 4 10 1 4 14 3 ½ 5 10 1 5 15 3 6 10 1 6 16 2 2/3
$
qty
1 2 3 4 5 6
Production method 2
Production method 1
Bold = LRATC
11
3
Part (b): Price Quantity demanded TR MR MC (Production method 1) 12 0 11 1 11 11 1 10 2 20 9 2 9 3 27 7 3 8 4 32 5 4 7 5 35 3 5 6 6 36 1 6 Hence Phil should choose to do 4 car washes and set a price equal to 8. In the short-run his revenue is therefore 4x8 = 32, and his VC equals 10. Hence he should be willing to operate. Part c): Price QD QD by 4WD owners TR – 4WD MR – 4WD QD by other car owners TR – Other MR – Other MC 12 0 11 1 1 11 11 1 10 2 2 20 9 1 9 3 2 1 9 9 1 8 4 2 2 16 7 1 7 5 2 3 21 5 1 6 6 2 4 24 3 1 With the scope to set different prices for car washes for 4WD and other cars, Phil should choose to wash 2 4WDs at a price of 10, and should choose to wash 4 other cars at a price of 6. Hence TR equals: (2)(10) + (4)(6) = 44. VC equals 6. Hence, Phil will be willing to operate in the short-run. Part (d): Profits (part b) = 32 – 2 - 10 = 20. Profits (part c) = 44-10-6 = 28. Profits are higher in part c) because Phil has been able to engage in price discrimination, targeting price at the willingness to pay of the two types of car drivers.
The main approach for earning higher profits that I have in mind is first-degree price discrimination – being able to charge each driver a price equal to their exact willingness to pay. Part (e): This is because the number of cars that it is profit-maximising for Phil to wash increases from 4 to 6 when he switches from charging the same price to all customers to engaging in price discrimination.
Question C3 (15% of total marks)
Two players are involved in a game. In the game each player begins with $10. Each player must simultaneously make a choice of how much of the $10 to allocate between two accounts: a ‘private’ account, and a ‘public’ account. Money allocated to the private account by a player is kept by that player. Money allocated to the public account is multiplied by 1.5, and then distributed back equally to each of the two players. Each player has two possible choices: (i) Allocate $0 to the public account; (ii) Allocate $10 to the public account. A player’s payoff from each outcome is equal to the sum of their private account money and one-half of the total public account money. For example, if both players allocated $10 to the public account, they each have a payoff equal to $0 + (1/2)($20)(1.5) = $15.00. a) (5 marks) Draw a game table to represent this game. b) (3 marks) Do players have a strict dominant strategy in this game? c) (2 marks) What is the Nash equilibrium of the game? d) (1 mark) Does the Nash equilibrium outcome maximise the total payoff to players? How can you explain this result? Now suppose that the game is played sequentially. One player chooses which amount to allocate to the public account; after which the other player, having observed the choice made by the first player, makes their own choice of how much to allocate to the public account. e) (3 marks) Draw the game tree for the sequential game. f) (2 marks) What is the rollback equilibrium of the sequential game? Solution a) Player 2 $0 $10 Player 1 $0 10,10 17.5, 7.5
$10 7.5, 17.5 15, 15 b) Each player has a strict dominant strategy to choose ‘$0’. c) The Nash equilibrium is for each player to choose ‘$0’. (Because each player has a strict DS, this combination of strategies is also a strict DS equilibrium.) d) The payoff-maximising outcome would be for each player to choose $10. However, this game has the same structure as the prisoners’ dilemma game. There is a combination of strategies that would make each player better off, but they both have a different strategy, to give $0, which is a strict DS. e)/f) Rollback equilibrium: Player 1: $0; Player 2: ($0 if player 1 chooses $0; $0 if player 1 chooses $10)
Player 1
Player 2
Player 2
$10
$0
$0
$0
$10
$10
10, 10
7.5, 17.5
17.5, 7.5
15, 15
