Market Design: Externalities

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1 Market Design: Externalities Econ University of Notre Dame

2 Externalities In large markets where each individual agent has no control over aggregate outcomes, each agent might not take the full consequences of their actions into account:... driving a car or flying leads to noise and air pollution... getting vaccinated reduces the spread of disease, and benefits non-vaccinated people... being more educated makes the people around you more productive... taking a large risk in a financial market might have consequences for other people When one agent s consumption or production of a good affects the payoffs of another agent, it is an externality

3 Externalities In large markets where each individual agent has no control over aggregate outcomes, each agent might not take the full consequences of their actions into account:... driving a car or flying leads to noise and air pollution... getting vaccinated reduces the spread of disease, and benefits non-vaccinated people... being more educated makes the people around you more productive... taking a large risk in a financial market might have consequences for other people When one agent s consumption or production of a good affects the payoffs of another agent, it is an externality

4 Externalities In large markets where each individual agent has no control over aggregate outcomes, each agent might not take the full consequences of their actions into account:... driving a car or flying leads to noise and air pollution... getting vaccinated reduces the spread of disease, and benefits non-vaccinated people... being more educated makes the people around you more productive... taking a large risk in a financial market might have consequences for other people When one agent s consumption or production of a good affects the payoffs of another agent, it is an externality

5 Externalities In large markets where each individual agent has no control over aggregate outcomes, each agent might not take the full consequences of their actions into account:... driving a car or flying leads to noise and air pollution... getting vaccinated reduces the spread of disease, and benefits non-vaccinated people... being more educated makes the people around you more productive... taking a large risk in a financial market might have consequences for other people When one agent s consumption or production of a good affects the payoffs of another agent, it is an externality

6 Externalities In large markets where each individual agent has no control over aggregate outcomes, each agent might not take the full consequences of their actions into account:... driving a car or flying leads to noise and air pollution... getting vaccinated reduces the spread of disease, and benefits non-vaccinated people... being more educated makes the people around you more productive... taking a large risk in a financial market might have consequences for other people When one agent s consumption or production of a good affects the payoffs of another agent, it is an externality

7 Externalities In large markets where each individual agent has no control over aggregate outcomes, each agent might not take the full consequences of their actions into account:... driving a car or flying leads to noise and air pollution... getting vaccinated reduces the spread of disease, and benefits non-vaccinated people... being more educated makes the people around you more productive... taking a large risk in a financial market might have consequences for other people When one agent s consumption or production of a good affects the payoffs of another agent, it is an externality

8 Pollution externalities We ll start with a simple, classic problem: externalities from pollution The goal is to (1) precisely describe where the inefficiencies in the market arise, and (2) look at optimal policies to address these inefficiencies

9 Pollution externalities There is a representative household that takes price and pollution X as given, and maximizes its utility subject to its budget constraint: max v(q) pq X + w, q and a representative firm that takes price as given and maximizes profits, and aggregate pollution is max pq C(q), q X (q) = xq. What is the price-taking/perfectly competitive equilibrium?

10 Pollution externalities There is a representative household that takes price and pollution X as given, and maximizes its utility subject to its budget constraint: max v(q) pq X + w, q and a representative firm that takes price as given and maximizes profits, and aggregate pollution is max pq C(q), q X (q) = xq. What is the price-taking/perfectly competitive equilibrium?

11 Pollution externalities The household s demand is determined by the firm s supply is determined by and pollution is v (q ) = p, p = C (q ), xq. So in equilibrium, v (q ) = C (q ), and the market equates the private marginal benefit of consumption to the household with the marginal cost of the firm.

12 Pollution externalities But a utilitarian social planner would sum household welfare and firm profits, yielding or max {v(q) pq xq} + {pq C(q)}, q }{{}}{{} Household utility Firm profits max v(q) C(q) xq. q The social planner would then pick a q satisfying v (q o ) c (q o ) x = 0, so the socially optimal quantity is less than the perfectly competitive quantity: the market is inefficient.

13 Pollution externalities With externalities, markets are no longer efficient: P S =c ' (q) Equilibrium Efficient D=v ' (q) v ' (q) x q

14 Pollution externalities The key is that the private marginal benefit to the household is while the social marginal benefit is v (q) v (q) x. This is why many problems feel intractable: your incentives are to ignore your influence on the outcome, since you can t do much to change it, but you know that giving in and doing something that indirectly harms others is the root of the problem in the first place.

15 Pollution externalities The key is that the private marginal benefit to the household is while the social marginal benefit is v (q) v (q) x. This is why many problems feel intractable: your incentives are to ignore your influence on the outcome, since you can t do much to change it, but you know that giving in and doing something that indirectly harms others is the root of the problem in the first place.

16 Optimal policy We ll discuss three leading policies that are intended to solve externality problems: 1 Pgiouvian Taxes: allow agents to engage in the activity in a market, but tax/subsidize the activity to implement the optimal outcome 2 Quotas: mandate the level of the activity and punish transgressors harshly 3 Cap and trade: create a market to purchase permits for the right to engage in the activity, but adjust the amount of permits to implement the optimal outcome

17 Pollution Quotas The simplest policy: mandate that only q of the good be produced, and punish deviators severely Maximizing social surplus requires: and set q = q o max v(q) c(q) xq v (q o ) c (q o ) x = 0 q Two problems: this leaves no agency to the people in the market, who might respond poorly to such a policy, and if we get the quantity wrong, it can unravel the whole policy (e.g., the Kyoto protocol)

18 Pollution Quotas The simplest policy: mandate that only q of the good be produced, and punish deviators severely Maximizing social surplus requires: and set q = q o max v(q) c(q) xq v (q o ) c (q o ) x = 0 q Two problems: this leaves no agency to the people in the market, who might respond poorly to such a policy, and if we get the quantity wrong, it can unravel the whole policy (e.g., the Kyoto protocol)

19 Pollution Quotas The simplest policy: mandate that only q of the good be produced, and punish deviators severely Maximizing social surplus requires: and set q = q o max v(q) c(q) xq v (q o ) c (q o ) x = 0 q Two problems: this leaves no agency to the people in the market, who might respond poorly to such a policy, and if we get the quantity wrong, it can unravel the whole policy (e.g., the Kyoto protocol)

20 Pollution externalities Taxes allow people to decide how much of the activity to engage it and reduce behaviors at the margin, but what is the optimal tax? The household solves max v(q) (p + t)q + w X q where t is the tax. This gives the FONC s for the household and firm, v (q ) p t = 0, p c (q ) = 0. If we combine and compare with the social planner s FONC, we see at the social optimum, while the market picks v (q o ) c (q o ) x = 0 v (q ) c (q ) t = 0. Equating the tax, t to x, then implements the social optimum.

21 Pollution externalities Taxes allow people to decide how much of the activity to engage it and reduce behaviors at the margin, but what is the optimal tax? The household solves max v(q) (p + t)q + w X q where t is the tax. This gives the FONC s for the household and firm, v (q ) p t = 0, p c (q ) = 0. If we combine and compare with the social planner s FONC, we see at the social optimum, while the market picks v (q o ) c (q o ) x = 0 v (q ) c (q ) t = 0. Equating the tax, t to x, then implements the social optimum.

22 Pollution externalities Taxes allow people to decide how much of the activity to engage it and reduce behaviors at the margin, but what is the optimal tax? The household solves max v(q) (p + t)q + w X q where t is the tax. This gives the FONC s for the household and firm, v (q ) p t = 0, p c (q ) = 0. If we combine and compare with the social planner s FONC, we see at the social optimum, while the market picks v (q o ) c (q o ) x = 0 v (q ) c (q ) t = 0. Equating the tax, t to x, then implements the social optimum.

23 Pollution externalities What if we tax firms instead? Let the household and firm solve max v(q) pq + w X, q max(p t)q C(q) q where t is the tax. This gives the FONC s for the household and firm, v (q ) p = 0, p t c (q ) = 0. If we combine and compare with the social planner s FONC, we see at the social optimum, while the market picks v (q o ) c (q o ) x = 0 v (q ) c (q ) t = 0. So charge the firm x for each additional unit it produces to get the optimal outcome, just like with the households.

24 Pollution externalities What if we tax firms instead? Let the household and firm solve max v(q) pq + w X, q max(p t)q C(q) q where t is the tax. This gives the FONC s for the household and firm, v (q ) p = 0, p t c (q ) = 0. If we combine and compare with the social planner s FONC, we see at the social optimum, while the market picks v (q o ) c (q o ) x = 0 v (q ) c (q ) t = 0. So charge the firm x for each additional unit it produces to get the optimal outcome, just like with the households.

25 Pollution externalities What if we tax firms instead? Let the household and firm solve max v(q) pq + w X, q max(p t)q C(q) q where t is the tax. This gives the FONC s for the household and firm, v (q ) p = 0, p t c (q ) = 0. If we combine and compare with the social planner s FONC, we see at the social optimum, while the market picks v (q o ) c (q o ) x = 0 v (q ) c (q ) t = 0. So charge the firm x for each additional unit it produces to get the optimal outcome, just like with the households.

26 Tax wedges It doesn t actually matter how you set up the legal incidence of the tax: P S =c ' (q) Consumer pays... t=x Firm receives... Tax revenue Efficient Equilibrium D=v ' (q) v ' (q) x q o q

27 Pigouvian Taxes in general Sum the payoffs of the agents to get a social planner s problem, but include the externality in the social planner s decision problem Maximize the social planner s problem to find the optimal level of activity Add a linear tax t i q i to agent i s maximization problem Maximize each agent s utility, and set the tax equal to the missing terms from the FONCs from the social planner s problem This will implement the socially efficient outcome when agents have decreasing marginal benefit or increasing marginal cost of the activity.

28 Pigouvian Taxes in general Sum the payoffs of the agents to get a social planner s problem, but include the externality in the social planner s decision problem Maximize the social planner s problem to find the optimal level of activity Add a linear tax t i q i to agent i s maximization problem Maximize each agent s utility, and set the tax equal to the missing terms from the FONCs from the social planner s problem This will implement the socially efficient outcome when agents have decreasing marginal benefit or increasing marginal cost of the activity.

29 Pigouvian Taxes in general Sum the payoffs of the agents to get a social planner s problem, but include the externality in the social planner s decision problem Maximize the social planner s problem to find the optimal level of activity Add a linear tax t i q i to agent i s maximization problem Maximize each agent s utility, and set the tax equal to the missing terms from the FONCs from the social planner s problem This will implement the socially efficient outcome when agents have decreasing marginal benefit or increasing marginal cost of the activity.

30 Pigouvian Taxes in general Sum the payoffs of the agents to get a social planner s problem, but include the externality in the social planner s decision problem Maximize the social planner s problem to find the optimal level of activity Add a linear tax t i q i to agent i s maximization problem Maximize each agent s utility, and set the tax equal to the missing terms from the FONCs from the social planner s problem This will implement the socially efficient outcome when agents have decreasing marginal benefit or increasing marginal cost of the activity.

31 Pigouvian Taxes in general Sum the payoffs of the agents to get a social planner s problem, but include the externality in the social planner s decision problem Maximize the social planner s problem to find the optimal level of activity Add a linear tax t i q i to agent i s maximization problem Maximize each agent s utility, and set the tax equal to the missing terms from the FONCs from the social planner s problem This will implement the socially efficient outcome when agents have decreasing marginal benefit or increasing marginal cost of the activity.

32 Pollution externalities Pros: Cons: The intuition is simple: internalize the externality that people are creating A simple tax scheme can implement the optimal outcome Requires knowing the marginal social cost of pollution, at the optimal quantity: this is really hard to guess Measuring the cost of pollution is difficult, especially in health/life-years terms Getting such a policy passed is difficult Monitoring and enforcing policies can be very difficult (VW diesels)

33 Pollution externalities Pros: Cons: The intuition is simple: internalize the externality that people are creating A simple tax scheme can implement the optimal outcome Requires knowing the marginal social cost of pollution, at the optimal quantity: this is really hard to guess Measuring the cost of pollution is difficult, especially in health/life-years terms Getting such a policy passed is difficult Monitoring and enforcing policies can be very difficult (VW diesels)

34 Taxes, quotas, and uncertainty Deciding the optimal tax or quota requires a significant amount of economic and scientific knowledge that we just don t really have Taxes allow agents to respond to the incentives they face, but are hard to adjust if the incentives are wrong and too many people end up polluting: if technology improves and marginal costs fall, pollution might increase, for example Quotas ensure the exact amount of pollution intended, but setting them is a very difficult process and once decided, they are somewhat set in stone

35 Taxes, quotas, and uncertainty Deciding the optimal tax or quota requires a significant amount of economic and scientific knowledge that we just don t really have Taxes allow agents to respond to the incentives they face, but are hard to adjust if the incentives are wrong and too many people end up polluting: if technology improves and marginal costs fall, pollution might increase, for example Quotas ensure the exact amount of pollution intended, but setting them is a very difficult process and once decided, they are somewhat set in stone

36 Taxes, quotas, and uncertainty Deciding the optimal tax or quota requires a significant amount of economic and scientific knowledge that we just don t really have Taxes allow agents to respond to the incentives they face, but are hard to adjust if the incentives are wrong and too many people end up polluting: if technology improves and marginal costs fall, pollution might increase, for example Quotas ensure the exact amount of pollution intended, but setting them is a very difficult process and once decided, they are somewhat set in stone

37 Cap and Trade Instead, why don t we create a new market for pollution permits? We decide the total number of permits, Q, and let firms buy them in a market that the government oversees and administers Suppose again that we have one representative household, j = 1, 2,..., J firms with total cost functions c j (q j ) and permits m j, an externality xq, but two markets: one for production/consumption, and one for permits to produce We ll start by solving for the equilibrium in the production/consumption market, then figure out how firms decide on the number of permits to purchase

38 Cap and Trade Instead, why don t we create a new market for pollution permits? We decide the total number of permits, Q, and let firms buy them in a market that the government oversees and administers Suppose again that we have one representative household, j = 1, 2,..., J firms with total cost functions c j (q j ) and permits m j, an externality xq, but two markets: one for production/consumption, and one for permits to produce We ll start by solving for the equilibrium in the production/consumption market, then figure out how firms decide on the number of permits to purchase

39 Cap and Trade Instead, why don t we create a new market for pollution permits? We decide the total number of permits, Q, and let firms buy them in a market that the government oversees and administers Suppose again that we have one representative household, j = 1, 2,..., J firms with total cost functions c j (q j ) and permits m j, an externality xq, but two markets: one for production/consumption, and one for permits to produce We ll start by solving for the equilibrium in the production/consumption market, then figure out how firms decide on the number of permits to purchase

40 Cap and Trade Instead, why don t we create a new market for pollution permits? We decide the total number of permits, Q, and let firms buy them in a market that the government oversees and administers Suppose again that we have one representative household, j = 1, 2,..., J firms with total cost functions c j (q j ) and permits m j, an externality xq, but two markets: one for production/consumption, and one for permits to produce We ll start by solving for the equilibrium in the production/consumption market, then figure out how firms decide on the number of permits to purchase

41 Cap and Trade: social planner The social planner in this economy solves J J max v q j c j (q j ) x q 1,...,q J j=1 j=1 which has the first-order condition for each q j of J c j (qj o ) x = 0, v j=1 q o j J q j, so the difference between the household s marginal benefit of consumption and the marginal cost of every firm equals the magnitude of the externality. j=1

42 Cap and Trade: the market The representative household solves the problem: max v(q) pq + m xq q and the demand curve is determined by v (q) p = 0. If the quota Q is binding so that less of the good is produced than at the price-taking equilibrium then the equilibrium price will be determined by v ( Q) = p. Then each firm j knows the price of consumption p = v ( Q), and decides how many permits to purchase taking the price of a permit π as given: max m j v ( Q)m j c j (m j ) πm j, each with a FONC v ( Q) c j (m j ) = π.

43 Cap and Trade: the market The representative household solves the problem: max v(q) pq + m xq q and the demand curve is determined by v (q) p = 0. If the quota Q is binding so that less of the good is produced than at the price-taking equilibrium then the equilibrium price will be determined by v ( Q) = p. Then each firm j knows the price of consumption p = v ( Q), and decides how many permits to purchase taking the price of a permit π as given: max m j v ( Q)m j c j (m j ) πm j, each with a FONC v ( Q) c j (m j ) = π.

44 Cap and Trade: the market The representative household solves the problem: max v(q) pq + m xq q and the demand curve is determined by v (q) p = 0. If the quota Q is binding so that less of the good is produced than at the price-taking equilibrium then the equilibrium price will be determined by v ( Q) = p. Then each firm j knows the price of consumption p = v ( Q), and decides how many permits to purchase taking the price of a permit π as given: max m j v ( Q)m j c j (m j ) πm j, each with a FONC v ( Q) c j (m j ) = π.

45 Cap and Trade: production/consumption Then in equilibrium J j=1 m j = Q, yielding J v mj 1 J c j (mj ) = π J j=1 So if we select the optimal quantity of permits, Q = Q o, the price of the permits satisfies j=1 v (Q o ) 1 J J c j (qj o ) = π j=1 and π = x solves the market-clearing conditions, so the socially efficient outcome is a solution.

46 Cap and Trade: production/consumption Then in equilibrium J j=1 m j = Q, yielding J v mj 1 J c j (mj ) = π J j=1 So if we select the optimal quantity of permits, Q = Q o, the price of the permits satisfies j=1 v (Q o ) 1 J J c j (qj o ) = π j=1 and π = x solves the market-clearing conditions, so the socially efficient outcome is a solution.

47 Cap and Trade Pros: Cons: Combines the good parts of taxes and quotas into one policy Uses basic market principles to implement the efficient solution If we re wrong about the right Q today, we can issue more permits later or buy permits back from firms to increase or reduce the activity Dynamics and Investment: firms might hold onto permits rather than trade because the permits have option value, meaning they might be useful in the future Speculation: firms might hold onto permits rather than trade because they expect the price to go up in the future, giving them a better deal Power in the Market for Permits: firms might hold onto permits rather than trade because it constraints rival firms, making the firms who hoard permits more profitable

48 Cap and Trade Pros: Cons: Combines the good parts of taxes and quotas into one policy Uses basic market principles to implement the efficient solution If we re wrong about the right Q today, we can issue more permits later or buy permits back from firms to increase or reduce the activity Dynamics and Investment: firms might hold onto permits rather than trade because the permits have option value, meaning they might be useful in the future Speculation: firms might hold onto permits rather than trade because they expect the price to go up in the future, giving them a better deal Power in the Market for Permits: firms might hold onto permits rather than trade because it constraints rival firms, making the firms who hoard permits more profitable

49 Information If taxes/quotas/cap-n -trade can solve externality problems, why isn t the economy running perfectly? The market designer typically does not know the preferences or characteristics of each agent. Firms wish to overstate their costs of pollution abatement, households want to overstate their benefits of environmental goods Students and universities wish to overstate the benefits of education CEOs wish to overstate the costs of their effort Borrowers wish to overstate their credit-worthiness Insurance buyers wish to overstate their health Sellers wish to overstate the quality of their goods How do we incorporate the ideas of information and agency into markets?

50 Information If taxes/quotas/cap-n -trade can solve externality problems, why isn t the economy running perfectly? The market designer typically does not know the preferences or characteristics of each agent. Firms wish to overstate their costs of pollution abatement, households want to overstate their benefits of environmental goods Students and universities wish to overstate the benefits of education CEOs wish to overstate the costs of their effort Borrowers wish to overstate their credit-worthiness Insurance buyers wish to overstate their health Sellers wish to overstate the quality of their goods How do we incorporate the ideas of information and agency into markets?