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Lecture 5: Externalities (chapter 9) Relation to lectures 1-4 Negative externalities Positive externalities: public goods and empathy Efficiency wage relation Nonconvexities Risk and uncertainty

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Aim of lecture 5 Show how positive and negative externalities can be included in general equilibrium models: public goods, empathy, pollution With specific emphasis on the effects of the introduction of an efficiency wage relation and social security arrangements

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Relation to lectures 1-4 Competitive equilibrium can be represented in various formats Time dependency can be introduced through commodity classification (implicit) or by explicitly describing dynamics of producer and consumer behavior (OLG and dynastic models) Agents are selfish (not fully so in dynastic models) Goods are not simultaneously effective in consumption and production Mathematical programs are assumed to be convex Until now: public consumption levels are set exogenously (lecture 3) and taxes are levied to finance this No welfare justification for level of public consumption

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Externalities Individual utilities and technology sets directly depend on demand and supply by other agents Positive externalities: –Non-rival consumption –Empathy –Interdependent consumption/production –Efficiency wage relation –Economies of scope and learning-by-doing Negative externalities: –Pollution: effects on health and production

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Negative externalities: pollution Interpretation of pollution as use of inputs instead of as joint output: “goods” instead of “bads” Then, analysis on positive externalities applies Recall lecture 3: previously free resources that are used as are priced: “double dividend” as efficiency of resource use is restored and revenue enables government to reduce other (distortionary) taxes

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Welfare program with non-rival commodities Where first-order conditions include:

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Lindahl equilibrium Negishi equilibrium where: –Consumers agree on provision of non-rival commodities: –Consumers jointly finance them: –Each consumer pays share –Since share falls as marginal utility of income increases, the rich pay more than the poor Remarks: –Public goods not desired by high income groups will have to be financed by low income groups, which may not be feasible –Implementation of Lindahl equilibrium: willingness of pay by the consumers. Underreporting will lead to undersupply –If level is determined, financing can be implemented by direct taxes

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Interdependency in utilities: empathy Where first-order conditions include:

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Interdependence in consumptions: external effects Where first order conditions include:

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Interdependency in utilities and consumptions Utility of other consumers cannot be observed; therefore, consumers imagine being the other person. Rawls’ “veil of ignorance” In a dynamic context, this other person could also represent the agent himself at an older age: savings result as transfers to this other person Note: consumption is a flow variable: consumers can also value the presence of stocks of commodities being available for (non-rival) consumption, such as nature parks. This requires representation of empathy within dynamic models of lecture 4

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Interdependence in production

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Efficiency wage relation Efficiency wage: endowments need to be produced:

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Migration model with efficiency wage Welfare program (compare lecture 1): Budgets:

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Efficiency wage In absence of transfers Hence, wage worker receives which is spent on consumption and decomposes into a payment for utility and a payment for work efficiency Worker pays for his own health, education and nutrition No external effects (e.g. public health, public safety).

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Efficiency wage and nonconvexities Shape of labor production function is decisive If is concave and homogeneous, there will be migration to different destinations until marginal productivities become equal. No need for interventions. If is concave with a set-up cost: specialize on a few: workers who are identical ex ante will end up differently ex post. (“better a few strong workers than many weak ones”). This is the Dasgupta (1997) result. If jobs are integer-valued ( ), the central planner sets the optimal values and uses premia and rations to implement solution

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Social security If in welfare program, and all budgets consolidate: this represents social security: there will be transfers across destinations and efficiency is preserved Equilibrium utilities and consumption levels, are not equal, even if preferences are identical but the differences only serve to feed the workers better:

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Efficiency wage and taxes Proportional tax on income: If endowments are given, no distortion However, in present formulation, consumer choice of consumption level is affected. In general, if consumption falls below critical level, productivity of consumers falls, and economy is trapped in underdevelopment equilibrium (Mirrlees, 1975).

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Non-convexities in production Within firm nonconvexities: –, with F a CRTS production function. Even if F is not concave, divisibility ensures ensures compact, nonempty production set Indivisibilities at firm level: –instead of continuous n,, with profit maximization program:. Supply response not usc, convex valued, so equilibrium may not exist –Note: welfare program with indivisibilities has solution. Nonconvexities at above-firm level –Large firms –Firms may need non-rival input supplied or used in non-convex way

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Above-firm non-convexities Recall welfare program with production and non-rival good: If are strictly quasiconvex (sqc), we are back in previous situation If, program is non-convex and and have to be set centrally If, then program is non-convex and all the g have to be set equal to by the central planner

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Risk and uncertainty Welfare program with groups i and possible destinations s: is the probability of group i to be in s

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Risk and uncertainty (continued) Risks –Idiosyncratic risk: probabilities materialize fully in each period –Aggregate risk: not all probabilities materialize (extreme: there is only a single draw of the distribution in each period) In both cases, risks are equal for all individuals:

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Risk and uncertainty (continued) First-order conditions include: Which illustrate the public good character of risk and the prevention input y

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