SM14ce Micro Chap004.doc

Chapter 04 - Market Failures: Public Goods and Externalities Chapter 04 - Market Failures: Public Goods and Externalities McConnell Brue Flynn Barbiero Micro 14ce DISCUSSION QUESTIONS 1. Explain the two causes of market failures. Given their definitions, could a market be affected by both types of market failures simultaneously? LO4.1 Answer: A public good is one where consumption in non-rival and non-excludable. Private goods are not profitable because of the free rider problem. If we want to set off fireworks and charge for the event, we probably wouldn't generate much revenue. We can't keep people from watching the fireworks outside the event (non-excludability) and the fireworks display can be watched by all (non-rival: If one person watches the fireworks display this does not reduce or eliminate the someone else's ability to see the same fireworks display). This is the first type of market failure. The second potential market failure is the presence of an externality. Externalities occur when the costs or benefits accrue to someone other than the buyer or seller (third parties). For example, an individual may fully internalize the cost of smoking a cigarette (price, health, etc...), but he or she does not internalize the negative health effects that the cigarette may have on others (a third party). This will result in overconsumption (and production). Answer 1: Yes, it is possible for both to occur if an individual values the good, such as fireworks, even if the free-rider problem is present. For example, I would like to set off a fireworks display and charge for the event so it can be larger than the display I would pay for myself. However, since everyone free-rides on my display I only set off a small one (the public good is underprovided). Now if my fireworks display causes pollution (noise and smoke) or potential fire damage a negative externality may be present. Answer 2: No, because if the free-rider problem is present firms will not produce any of the good. Since no goods are produced or consumed there cannot be an externality. 2. Use the ideas of consumer surplus and producer surplus to explain why economists say competitive markets are efficient. Why are below- or above-equilibrium levels of output inefficient, according to these two sets of ideas? LO4.2 Answer: When the consumers’ utility exceeds the price paid, consumer surplus is generated. Likewise, when producers receive a price greater than marginal cost, producer surplus is created. By producing up to the point where MB = MC, the maximum potential consumer surplus and producer surplus is generated. Producing less than the equilibrium level means that potential surplus is left unrealized. Overproduction subtracts from the surplus because society values the use of the additional resources in other pursuits more than it values them in consumption of that good. 3. What are the two characteristics of public goods? Explain the significance of each for public provision as opposed to private provision. What is the free-rider problem as it relates to public goods? Is the Canadian border patrol a public good or a private good? Why? How about satellite TV? Explain. LO4.3 Answer: Public goods are nonrival (one person’s consumption does not prevent consumption by another) and nonexcludable (once the goods are produced nobody—including free riders—can be excluded from the goods’ benefits). If goods are nonrival, there is less incentive for private firms to produce them – those purchasing the good could simply allow others the use without compensation. Similarly, if goods are nonexcludable, private firms are unlikely to produce them as the potential for profit is low. The free-rider problem occurs when people benefit from the public good without contributing to the cost (tax revenue proportionate to the benefit received). The Canadian border patrol is a public good – my use and benefit does not prevent yours. Satellite TV is a private good – if the dish, receiver, and service go to my residence it can’t go to my neighbors. The fact that I could invite my neighbor over to watch does not change its status from being a private good. 4. What divergences arise between equilibrium output and efficient output when (a) negative externalities and (b) positive externalities are present? How might government correct these divergences? Cite an example (other than the text examples) of an external cost and an external benefit. LO4.4 Answers: (a) When negative externalities are present, the equilibrium output will be greater than the efficient output. This is because the producer, who is not bearing the full cost of production, will be able to produce more at a lower price than the efficient level, which would exist if true costs were reflected in the production decision. (b) When positive externalities are present, the equilibrium output will be smaller than the efficient output because the consumer is willing to pay a price equal to the consumer’s individual marginal benefit, but no more. Since social benefits exist in addition to the private benefit, the government must either aid the producer to encourage more output or engage in its own production of the item with the external benefits. Government might correct external costs through regulation, which requires firms to internalize these external costs, or it might tax the externality until it becomes too expensive for the firm to incur these costs. This effectively shifts the supply curve to the left as costs of production rise, and the new equilibrium output will be less and closer to the efficient level. External benefits can be encouraged by government subsidies to the producers of these products or by government production. In either case, the supply curve shifts to the right which lowers the equilibrium price and leads to a greater equilibrium output level. Other examples of external costs might include secondhand smoke, noise from the stereo down the hall, or road congestion. External benefits might be generated from outdoor Christmas lights, music from the stereo down the hall, or attractive landscaping in the neighborhood. 5. Why are spillover costs and spillover benefits also called negative and positive externalities? Show graphically how a tax can correct for a negative externality and how a subsidy to producers can correct for a positive externality. How does a subsidy to consumers differ from a subsidy to producers in correcting for a positive externality? LO4.4 Answers: Spillover costs are called negative externalities because they are external to the participants in the transaction and reduce the utility of affected third parties (thus “negative”). Spillover benefits are called positive externalities because they are external to the participants in the transaction and increase the utility of affected third parties (thus “positive”). To show how taxes and subsidies can correct externalities, see Figures 4.7 and 4.8. Compare (b) and (c) in Figure 4.8. 6. An apple grower’s orchard provides nectar to a neighbor’s bees, while the beekeeper’s bees help the apple grower by pollinating his apple blossoms. Use Figure 4.6b to explain why this situation of dual positive externalities might lead to an underallocation of resources to both apple growing and beekeeping. How might this underallocation get resolved via the means suggested by the Coase theorem? LO4.4 Answers: Using Figure 4.6b in the text the following can be said: The market demand curves for apples and honey, Da and Dh, would not include the spillover benefits accruing to the production of the other good. The total benefits associated with the consumption and production of each good could be shown by Dat or Dht and the optimal outputs for each good would be Qao and Qho. Both of these outputs are greater than equilibrium outputs, Qae and Qhe, leading to an underallocation of resources to both applegrowing and beekeeping. Using the Coase theorem, we note that it will be to the advantage of individual apple growers and beekeepers to negotiate so that beekeepers (whose hives can be moved) locate their production in or near orchards. This negotiation will occur as long as property ownership is well defined, only a few people are involved, and bargaining costs are low. For example, an apple grower who owns an orchard could allow a beekeeper to use a portion of his or her land, charging belowmarket rents so that both parties gain from the agreement. 7. The LoJack car recovery system allows the police to track stolen cars. As a result, they not only recover 90% of LoJack-equipped cars that are stolen but also arrest many auto thieves and shut down many “chop shops” that take apart stolen vehicles to get at their used parts. Thus, LoJack provides both private benefits and positive externalities. Should the government consider subsidizing LoJack purchases? LO4.4 Answers: If the government were to subsidize LoJack purchases, this would reduce the private cost of the anti-theft devices. This reduction in the private cost would, in-turn, increase the purchase of the LoJack system. The fact that this good was under-utilized in the private sector without the subsidy because part of the benefit accrued to society, not the individual, in the form of reduced crime (shutting down "chop shops") implies this subsidy is appropriate. Yes, the government should consider subsidizing LoJack purchases. 8. Explain why zoning laws, which allow certain land uses only in specific locations, might be justified in dealing with a problem of negative externalities. Explain why in areas where buildings sit close together tax breaks to property owners for installing extra fire prevention equipment might be justified in view of positive externalities. Explain why excise taxes on beer might be justified in dealing with a problem of external costs. LO4.5 Answers: Zoning could force businesses producing negative externalities to locate in regions where these costs would not spill over onto third parties, or where such costs would at least be reduced. Businesses wanting to locate in regions where external costs would cause the most damage (but where zoning restricts their location) would be forced to eliminate or reduce those external costs. In either case, a more efficient allocation of resources would result. Tax breaks to property owners who install fire prevention equipment reduces the potential of fire spreading to nearby buildings. Thus, the fire prevention equipment will have positive externalities because of the additional benefit to the community. At the individual level the building owners take into account the benefits for their own business, which implies that fire prevention equipment will be underutilized without the tax break (which reduces direct cost). The over-consumption of beer can cause negative externalities.  An excise tax can be used to discourage supply of beer, by making it less profitable to suppliers since they have to give more back to the government, this would shift the supply curve to the left.  If the supplier chooses to pass on the tax burden to the consumer by raising the price of beer, this would decrease the quantity demanded of beer, also reducing the negative externality. The LAST WORD Distinguish between a carbon-tax and a cap-and-trade strategy for reducing carbon dioxide and other so-called greenhouse gases (that are believed by many scientists to be causing global warming). Which of the two strategies do you think would have the most political support in an election in your home state? Explain your thinking. Answers: Scientific evidence suggests that carbon dioxide and other gas emissions are accumulating and causing the average temperature of the atmosphere to increase. In the Kyoto Protocol, the industrialized nations agreed to cut emissions 6 to 8 percent below 1990 by 2012. Flooding may occur in some regions, thus decreasing the land upon which the population lives, whereas temperatures in the northern parts of the globe may moderate and make these areas more habitable. (Al Gore’s film An Inconvenient Truth illustrates this effectively.) A carbon-tax affects each polluting firm by charging them for emissions. The cap-and-trade strategy would allow more efficient firms to sell their permits to the less efficient firms resulting in greater efficiency (Heavier polluters must pay more to maintain the same level of production). REVIEW QUESTIONS 1. Draw a supply and demand graph and identify the areas of consumer surplus and producer surplus. Given the demand curve, what impact will an increase in supply have on the amount of consumer surplus shown in your diagram? Explain why. LO4.2 Answer: An increase in supply will lower the price and increase the amount of consumer surplus for a given demand curve.  Any individual that was receiving consumer surplus before the change in supply will realize an increase in consumer surplus as the price falls and the difference between their maximum willingness to pay and the market price widens. 2. Assume that candle wax is traded in a perfectly competitive market in which the demand curve captures buyers’ full willingness to pay while the supply curve reflects all production costs. For each of the following situations, indicate whether the total output should be increased, decreased, or kept the same in order to achieve allocative and productive efficiency. LO4.2 a. The maximum willingness to pay exceeds minimum acceptable price. b. Marginal Cost > Marginal Benefit. c. Total surplus is at a maximum. d. The current quantity produced exceeds the market equilibrium quantity. Answer: a. increased More candle wax should be produced and sold because doing so would increase allocative efficiency and help to ensure that society’s limited supply of resources are being used to produce the products that consumers most highly desire. That is true because the minimum acceptable price demanded by producers takes into account the opportunity costs of everything else that they could possibly produce from the resources needed to make more candle wax.  Thus, the fact that buyers have a maximum willingness to pay that exceeds the producers’ minimum acceptable price means that the buyers value turning those resources into additional candle wax more than they would if the resources were turned into any other possible product. Therefore, increasing the production of candle wax would increase allocative efficiency.  b. decreased Output should be reduced in order to improve allocative efficiency.  Because MC > MB at the current level of production, we know that the cost of producing the final unit of candle wax exceeds the benefit felt by consumers from consuming it.  This implies that the resources currently being used to produce the final unit of candle wax could be put to better use producing other goods and services.  This is true because the MC of the final unit of candle wax includes the opportunity cost of producing other products from the resources currently being used to produce the final unit of candle wax.  Therefore, we can improve allocative efficiency by reducing the production of candle wax so that those resources can be freed up and directed toward the production of products that are more highly valued than the final unit of candle wax. c. kept the same Production should be kept at the same level because the level of output that maximizes total surplus is also the level of output that guarantees allocative efficiency. The easiest way to see this is by nothing that both reducing production and increasing production will cause allocative inefficiencies.  First consider a decrease in candle wax production.  If fewer units are produced, total surplus will fall as units for which consumers’ maximum willingness to pay exceeds producers’ minimum acceptable price will no longer be produced.  That implies a reduction in allocative efficiency because the resources that are freed up by the reduction in candle wax production will end up being used to produce units of other products that are not as highly valued as the foregone units of candle wax.   Next consider an increase in candle wax production.  If output is increased, total surplus will also fall because the increased production would involve units of candle wax for which consumers’ maximum willingness to pay is less than producers’ minimum acceptable price.  That implies a reduction in allocative efficiency because the resources used to increase candle wax production could have gone instead into the production of products that would have been more highly valued than the additional candle wax. d. decreased The most amazing thing about equilibrium in competitive markets is that when demand curves fully reflect buyers’ willingness to pay and supply curves fully reflect all production costs, the market equilibrium quantity will be the same as the unique level of output that is both allocatively and productively efficient.  Thus, we know that any level of output in excess of the market equilibrium quantity will not be allocatively or productively efficient.  We also know that the remedy would be to decrease production back down to the market equilibrium quantity.  3. Efficiency losses ____________________________. LO4.2 a. Are not possible if suppliers are willing to produce and sell a product. b. Can only result from underproduction. c. Can only result from overproduction. d. None of the above. Answer: d; none of the above. Efficiency losses can result from either overproduction or underproduction.  The fact that suppliers are willing to produce and sell a product does not by itself guarantee that the allocatively efficient amount of that product will be produced. In fact, it is possible for them to either underproduce or overproduce relative to the efficient output level.  Either will cause an efficiency loss.  Thus, answers a, b, and c are all incorrect. 4. Draw a production possibilities curve with public goods on the vertical axis and private goods on the horizontal axis. Assuming the economy is initially operating on the curve, indicate how the production of public goods might be increased. How might the output of public goods be increased if the economy is initially operating at a point inside the curve? LO4.3 Answer: On the curve, the only way to obtain more public goods is to reduce the production of private goods. An economy operating inside the curve can expand the production of public goods without sacrificing private goods by making use of unemployed resources. 5. Use the distinction between the characteristics of private and public goods to determine whether the following should be produced through the market system or provided by government: (a) French fries, (b) court systems, (c) mail delivery, and (d) medical care. State why you answered as you did in each case. LO4.3 Answer: French fries—market system (rival and excludable). Court systems—government (nonrival and nonexcludable). Mail delivery—combined market and government; the law gives the postal. service a monopoly but services such as package delivery have private competition. Medical care—combined market and government; the mix of private and public production is a controversial topic addressed in the chapter on the economics of health care. 6. Match each of the following characteristics or scenarios with either the term negative externality or the term positive externality. LO4.4 a. Overallocation of resources. b. Tammy installs a very nice front garden, raising the property values of all the other houses on her block. c. Market demand curves are too far to the left (too low). d. Underallocation of resources. e. Water pollution from a factory forces neighbors to buy water purifiers. Answer: a. negative externality Resources are overallocated to products that impose negative externalities on third parties. This happens because the firms imposing negative externalities on third parties fail to take into account the costs that would be needed to either prevent the negative externalities or compensate those who suffer from them. Not taking those costs into account renders the firms’ profits artificially high—which leads them to overproduce.  As they do so, resources are overallocated to the production of their products and taken away from the production of other products that would have produced greater net benefits for society.  In terms of a supply and demand diagram, the negative externalities lower the polluting firms’ MC curves and shift the market supply curve to the right.  This results in an equilibrium quantity in excess of the optimal output level that would prevail if the firms MC curves correctly accounted for the negative externalities. b. positive externality Tammy’s garden provides a positive externality for her neighbors because while her main intent was to make herself happy by improving the look of her own property, she has also provided a free benefit to her neighbors.  They receive higher property values without having to pay Tammy anything for them. c. positive externality Positive externalities cause market demand curves to be too far to the left (too low) relative to total-benefit demand curves.  The problem is that when there are positive externalities, the people receiving the positive externalities do not have to pay for the benefits that they receive.  Thus, their willingness to pay for those benefits is not captured by the market demand curve.  This causes the market demand curve to end up too far to the left, leading to a market equilibrium quantity that is less than the optimal output.  And because output is less than optimal, resources that should have flowed to producing more of the good in question flow instead to the production of other products that are less valued by consumers. d. positive externality Resources are underallocated to products that impose positive externalities on third parties.  The problem is that when there are positive externalities, the people receiving the positive externalities do not have to pay producers for the benefits that they are receiving.  This lowers producer profits and causes them to produce less than the socially optimal output. Because output is below the optimal level, resources that should have flowed to producing more of the goods in question flow instead to the production of other products that are less valued by consumers. In terms of a supply and demand diagram, the positive externality means that the demand curve is too far to the left (too low) relative to the total-benefit demand curve that includes the willingness to pay of the people receiving the positive externalities.  With the demand curve shifted to the left in this way, the market equilibrium output ends up lower than the optimal output. e. negative externality The factory’s water pollution imposes a negative externality on its neighbors because the factory does not take into account the costs that it imposes on them. 7. Use marginal cost/marginal benefit analysis to determine if the following statement is true or false: “The optimal amount of pollution abatement for some substances, say, dirty water from storm drains, is very low; the optimal amount of abatement for other substances, say, cyanide poison, is close to 100 percent.” LO4.5 Answer: Reducing water flow from storm drains has a low marginal benefit, meaning the MB curve would be located far to the left of where it is in the text diagram. It will intersect the MC curve at a low amount of pollution abatement, indicating the optimal amount of pollution abatement (where MB = MC) is low. Any cyanide in public water sources could be deadly. Therefore, the marginal benefit of reducing cyanide is extremely high and the MB curve in the figure would be located to the extreme right where it would intersect the MC curve at or near 100 percent. PROBLEMS 1. Refer to Table 4.1. If the six people listed in the table are the only consumers in the market and the equilibrium price is $11 (not the $8 shown), how much consumer surplus will the market generate? LO4.2 Answer: $3 Feedback: Consider the following table as an example: Using the values above, and assuming an equilibrium price of $11 (not the $8 shown), we first note that an individual will only purchase the good if his or her "maximum price willing to pay" is greater than or equal to the price of the product ($11). This implies that only Bob, Barb, and Bill are willing to purchase the good at the price of $11. Now we can calculate the consumer surplus by adding up the difference between the "maximum price willing to pay" and the actual price paid. Bob's consumer surplus is $2 (= $13 - $11) Barb's consumer surplus is $1 (= $12 - $11) Bob's consumer surplus is $0 (= $11 - $11) Thus, the total consumer surplus equals $3 (= $2 + $1 + $0) 2. Refer to Table 4.2. If the six people listed in the table are the only producers in the market and the equilibrium price is $6 (not the $8 shown), how much producer surplus will the market generate? LO4.2 Answer: $6 Feedback: Consider the following table as an example: Using the values above, and assuming an equilibrium price of $6 (not the $8 shown), we first note that an individual will only sell the good if his or her "minimum acceptable price" is less than or equal to the price of the product ($6). This implies that only Carlos, Courtney, Chuck, and Cindy are willing to sell the good at the price of $6. Now we can calculate the producer surplus by adding up the difference between the actual (equilibrium) price and the "minimum acceptable price". Carlos's producer surplus is $3 (= $6 - $3) Courtney's producer surplus is $2 (= $6 - $4) Chuck's producer surplus is $1 (= $6 - $5) Cindy's Producer surplus is $0 (= $6 - $6) Thus, the total producer surplus equals $6 (=$3 + $2 + $1 + $0) 3. Look at Tables 4.1 and 4.2 together. What is the total surplus if Bob buys a unit from Carlos? If Barb buys a unit from Courtney? If Bob buys a unit from Chad? If you match up pairs of buyers and sellers so as to maximize the total surplus of all transactions, what is the largest total surplus that can be achieved? LO4.2 Answers: $10 (= $13 - $3); $8 (= $12 - $4); $5 = ($13 - $8); $30. Feedback: Consider the following tables as an example: If Bob buys a unit of the good from Carlos, then the economic surplus is the difference between Bob's "maximum price willing to pay" and Carlos's the "minimum acceptable price." The economic surplus is $10 (= $13- $3) If Barb buys a unit form Courtney, then the economic surplus equals $8 (= $12 - $4). If Bob buys a unit form Chad, then the economic surplus is $5 (= $13 - $8). If we match up buyers and sellers to maximize the total economic surplus then we need to choose the pairs with the largest gap between "maximum price willing to pay" and the "minimum acceptable price." This implies the following pairs (Bob, Carlos) with an economic surplus of $10, (Barb, Courtney) with an economic surplus of $8, (Bill, Chuck) with an economic surplus of $6, (Bart, Cindy) with an economic surplus of $4, (Brent, Craig) with an economic surplus of $2, and (Betty, Chad) with an economic surplus of $0. Adding this up across all pairs gives us a total economic surplus of $30. 4. ADVANCED ANALYSIS Assume the following values for Figures 4.4a and 4.4b. Q1 = 20 bags. Q2 = 15 bags. Q3 = 27 bags. The market equilibrium price is $45 per bag. The price at a is $85 per bag. The price at c is $5 per bag. The price at f is $59 per bag. The price at g is $31 per bag. Apply the formula for the area of a triangle (Area = ½ x Base x Height) to answer the following questions. LO4.2 a. What is the dollar value of the total surplus (producer surplus plus consumer surplus) when the allocatively efficient output level is being produced? How large is the dollar value of the consumer surplus at that output level? b. What is the dollar value of the deadweight loss when output level Q2 is being produced? What is the total surplus when output level Q2 is being produced? c. What is the dollar value of the deadweight loss when output level Q3 is produced? What is the dollar value of the total surplus when output level Q3 is produced? Answers: (a) At output level Q1, total surplus is $800; consumer surplus at Q1 is $400. (b) The deadweight loss at Q2 is $50; the total surplus at Q2 is $750. (c) The deadweight loss at Q3 is $98; the dollar value of the total surplus at Q3 is $702. Feedback: To answer this question, let us first find the mathematical representation of the supply and demand schedules. To help us accomplish this objective we us the following figures. Now consider the following values as an example. Assume the following values for Figures 5.4a and 5.4b: The equilibrium quantity Q1 = 20, the market equilibrium price is $45 per bag, the price at a is $85 per bag, the price at c is $5 per bag. To derive the demand schedule (inverse demand schedule), we use the following ordered pairs: (20,45) equilibrium and (0,85) point a. We know the form of the demand schedule will be P=C1 + C2Q where C1 and C2 are unknown constants. The intercept, C1, can be found by setting Q equal to zero. This is point a, so C1 equals 85. To find the slope, C2, we divide the change in quantity by the change in price using our two ordered pairs above (rise-over-run). This implies C2 equals (20 - 0) / (45 - 85) = -2. Thus, we have the following demand schedule: P = 85 - 2Q To derive the supply schedule (inverse supply schedule), we use the following ordered pairs: (20,45) equilibrium and (0,5) point c. We know the form of the supply schedule will also be P = C1 + C2Q where C1 and C2 are once again unknown constants. The intercept, C1, can be found by setting Q equal to zero. This is point c, so C1 equals 5. To find the slope, C2, we divide the change in quantity by the change in price using our two ordered pairs above (rise-over-run). This implies C2 equals (20 - 0) / (45 - 5) = 2. Thus, we have the following supply schedule: P = 5 + 2Q With these schedules we can now answer the following questions: Part (a): What is the dollar value of the total surplus (producer surplus plus consumer surplus) when the allocatively efficient output level is being produced? How large is the dollar value of the consumer surplus at that output level? To calculate total surplus we use the following formula for the area of a triangle (Area = ½ (Base x Height)). The area between the demand schedule P = 85 - 2Q and the supply schedule P = 5 + 2Q for the quantity ranging from 0 to 20 is the total economic surplus. This is a triangle with a base of 80 (the price difference at Q = 0, or points a and c) and a height of 20 (the number of units purchased in equilibrium). Using these values we have a total surplus = (1/2) x 80 x 20 = 800. The consumer surplus is the area between the demand curve and the equilibrium price line. Here we have a base of 40 (the price difference between the demand schedule price at Q = 0, which is $85, and the equilibrium price of $45). The height of the triangle is once again 20 (the number of units purchased in equilibrium). Using these values we have a consumer surplus = (1/2) x 40 x 20 = 400. Consider the following additional values for the figures above: Q2 = 15 bags. Q3 = 27 bags, the price at f is $59 per bag, and the price at g is $31 per bag. Part (b): What is the dollar value of the deadweight loss when output level Q2 is being produced? What is the total surplus when output level Q2 is being produced? The first thing we need to do is calculate the price at Q2 = 15 for the supply and demand schedules. The price on the supply schedule is P = 5 + 2 x 15 = 35. The price on the demand schedule is P = 85 – 2 x 15 = 55. The difference between these two prices is our base, which equals 20. The height is the quantity difference between the equilibrium quantity Q1 = 20 and the underproduction quantity Q2 = 15 (= 5). Thus, the deadweight loss from underproduction is (1/2) x 20 x 5 = 50. The total surplus can be found by subtracting the deadweight loss from the original total surplus that maximized efficiency. This is 800 (maximum total surplus) - 50 (deadweight loss) = 750. Part (c): What is the dollar value of the deadweight loss when output level Q3 is produced? What is the dollar value of the total surplus when output level Q3 is produced? Here we follow the same procedure. We are given the price at point f is $59 and the price at point g is $31 (we do not need to calculate these prices using the demand and supply schedule). The quantity Q =27 represents over production (the marginal cost to society exceeds the marginal benefit to society) of 7 units. To calculate the deadweight loss from this overproduction we use the price difference as the base, which is 28 (= 59 - 31), and the amount of overproduction as the height, which is 7 (= 27 - 20). This results in a deadweight loss of 98 (= (1/2) x 28 x 7). The total surplus can be found by subtracting the deadweight loss from the original total surplus that maximized efficiency. This is 800 (maximum total surplus) - 98 (deadweight loss) = 702. Note here that we capture all of the surplus from producing the equilibrium quantity, but we lose surplus from overproduction (inefficient use of resources). 5. On the basis of the three individual demand schedules below, and assuming these three people are the only ones in the society, determine (a) the market demand schedule on the assumption that the good is a private good and (b) the collective demand schedule on the assumption that the good is a public good. LO4.3 Answers: (a) Market demand schedule Quantity Demanded Price 1 $8 2 $7 4 $6 7 $5 10 $4 13 $3 16 $2 19 $1 (b) Collective demand schedule Quantity Amount Society is Willing to Pay 1 $19 2 $16 3 $13 4 $10 5 $7 6 $4 7 $2 8 $1 Feedback: Consider the following table: Part (a): Derive the market demand schedule on the assumption that the good is a private good. To accomplish we use the principle of horizontal summation. That is, we fix price and add up the quantities demanded by the individuals. At a price of $8: individual 1 (I1) demands 0, individual 2 (I2) demands 1, and individual 3 (I3) demands 0. Thus, we have the following market demand ordered pair (1,8). At a price of $7: I1 demands 0, I2 demands 2, and I3 demands 0. Thus, we have the following market demand ordered pair (2,7). At a price of $6: I1 demands 0, I2 demands 3, and I3 demands 1. Thus, we have the following market demand ordered pair (4 [=3+1],6). At a price of $5: I1 demands 1, I2 demands 4, and I3 demands 2. Thus, we have the following market demand ordered pair (7[=1+4+2],5). At a price of $4: I1 demands 2, I2 demands 5, and I3 demands 3. Thus, we have the following market demand ordered pair (10,4). At a price of $3: I1 demands 3, I2 demands 6, and I3 demands 4. Thus, we have the following market demand ordered pair (13,3). At a price of $2: I1 demands 4, I2 demands 7, and I3 demands 5. Thus, we have the following market demand ordered pair (16,2). At a price of $1: I1 demands 5, I2 demands 8, and I3 demands 6. Thus, we have the following market demand ordered pair (19,1). Part (b): Derive the collective demand schedule on the assumption that the good is a public good. To accomplish we use the principle of vertical summation. That is, we fix quantity and add up the price (willingness to pay) for the individuals. The logic here is that the individuals (society) can pool resources to purchase a given quantity because this good will be shared (public good). At the quantity 1: I1 is willing to pay $5, I2 is willing to pay $8, and I3 is willing to pay $6. Thus, we have the following collective demand ordered pair (1,19=5+8+6). At the quantity 2: I1 is willing to pay $4, I2 is willing to pay $7, and I3 is willing to pay $5. Thus, we have the following collective demand ordered pair (2,16). At the quantity 3: I1 is willing to pay $3, I2 is willing to pay $6, and I3 is willing to pay $4. Thus, we have the following collective demand ordered pair (3,13). At the quantity 4: I1 is willing to pay $2, I2 is willing to pay $5, and I3 is willing to pay $3. Thus, we have the following collective demand ordered pair (4,10). At the quantity 5: I1 is willing to pay $1, I2 is willing to pay $4, and I3 is willing to pay $2. Thus, we have the following collective demand ordered pair (5,7). At the quantity 6: I1 is willing to pay $0, I2 is willing to pay $3, and I3 is willing to pay $1. Thus, we have the following collective demand ordered pair (6,4). At the quantity 7: I1 is willing to pay $0, I2 is willing to pay $2, and I3 is willing to pay $0. Thus, we have the following collective demand ordered pair (7,2). At the quantity 8: I1 is willing to pay $0, I2 is willing to pay $1, and I3 is willing to pay $0. Thus, we have the following collective demand ordered pair (8,1). 6. Use your demand schedule for a public good, determined in Problem 5, and the following supply schedule to ascertain the optimal quantity of this public good. LO4.3 Answer: 4 units Feedback: From the example table in problem 5, we calculated the collective demand schedule from the individual demand schedules: Collective Demand Schedule: Quantity Price Society is Willing to Pay 1 $19 2 $16 3 $13 4 $10 5 $7 6 $4 7 $2 8 $1 Combining this collective demand schedule with the following supply schedule, we can determine the optimal provision (quantity) of the public good. The optimal quantity can be found by finding the price where the willingness to pay equals price required by the firm to supply that last unit (basically the price that clears the market). For example, at $19 society demands one unit but firms are willing to supply 10 units. At $16 society demands 2 units but firms are willing to supply 8 units. This continues until we reach the price of $10 where society demands 4 units and firms are willing to supply 4 units. Thus, the optimal quantity is 4 units. 7. Look at Tables 4.1 and 4.2, which show, respectively, the willingness to pay and willingness to accept of buyers and seller of bags of oranges. For the following questions, assume that the equilibrium price and quantity will depend on the indicated changes in supply and demand. Assume that the only market participants are those listed by name in the two tables. LO4.4 a. What are the equilibrium price and quantity for the data displayed in the two tables? b. What if instead of bags of oranges, the data in the two tables dealt with a public good like fireworks displays. If all the buyers free ride, what will be the quantity supplied by private sellers? c. Assume that we are back to talking about bags of oranges (a private good), but that the government has decided that tossed orange peels impose a negative externality on the public that must be rectified by imposing a $2-per-bag tax on sellers. What is the new equilibrium price and quantity? If the new equilibrium quantity is the optimal quantity, by how many bags were oranges being overproduced before? Answers: P* = $8 and Q* = 6 bags; Q* = 0; P* = $9 and Q* = 5 bags. Feedback: Here we consider the tables from Problems 1 and 2. Part (a): To determine the equilibrium price of oranges, we begin by comparing the highest willingness to pay with the lowest minimum acceptable price. Bob is willing to pay $13 and Carlos is willing to accept at minimum $3. This trade is made because Bob is willing to pay more than Carlos requires for the sale. We then move on to the trade between Barb and Courtney. This trade is also made because Barb is willing to pay $12 and Courtney only requires $4 to make the sale. This goes on until the "maximum willingness to pay" equals the "minimum acceptable price". This occurs for the trade between Betty and Chad. Betty's "maximum willingness to pay" is $8 and Chad's "minimum acceptable price" is also $8. Since the six purchasers (each purchases 1 unit) buy the 6 units produced by the six producers (each produces 1 unit), the equilibrium quantity is 6 at the equilibrium price of $8. Part (b): If instead of bags of oranges, the data in the two tables dealt with a public good like fireworks displays, and all the buyers free ride, then the quantity supplied will be zero. Everyone will try to pay a zero price. Part (c): If the government decides that tossed orange peels impose a negative externality on the public that must be rectified by imposing a $2-per-bag tax on sellers, then the "minimum acceptable price" will increase by the amount of the tax. The reason is that the producers must now pay an additional $2 on top production costs. This implies that the "minimum acceptable price" for Carlos is $5(= $3 + $2), Courtney $6, Chuck $7, Cindy $8, Craig $9, and Chad $10. Comparing this new "minimum acceptable price" schedule with the original "maximum willingness to pay" schedule we have the following new equilibrium. Bob is willing to pay $13 and Carlos is willing to accept at minimum $5. This trade is made because Bob is willing to pay more than Carlos requires for the sale. We then move on to the trade between Barb and Courtney. This trade is also made because Barb is willing to pay $12 and Courtney only requires $6 to make the sale. This goes on until the "maximum willingness to pay" equals the "minimum acceptable price". This occurs for the trade between Brent and Craig now. Brent's "maximum willingness to pay" is $9 and Craig's "minimum acceptable price" is also $9. The potential trade between Betty and Chad no longer takes place. Betty is only willing to pay $8 and Chad requires $10 to make the sale. Since only five purchasers (each purchases 1 unit) buy the 5 units produced by the five producers (each produces 1 unit), the new equilibrium quantity is 5 at the equilibrium price of $9. If this is the optimal quantity, then the market was overproducing by 1 unit before the tax was imposed on orange producers. 4-1 Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.