Dynamic inefficiency in an overlapping generation economy with pollution and health costs
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Dynamic Inefficiency in an Overlapping Generation Economy with Pollution and Health Costs. Maria-Jose Gutierrez University of the Basque Country Journal of Public Economic Theory, 10 (4), 2008, pp. 563-594. Presented by Juan. Introduction.

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Dynamic Inefficiency in an Overlapping Generation Economy with Pollution and Health Costs

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Dynamic inefficiency in an overlapping generation economy with pollution and health costs

Dynamic Inefficiency in an Overlapping Generation Economy with Pollution and Health Costs

Maria-Jose Gutierrez

University of the Basque Country

Journal of Public Economic Theory, 10 (4), 2008, pp. 563-594

Presented by Juan


Introduction

Introduction

  • Environment affects economy through amenity, productivity and health channels

  • Aim of the paper: analyze effects of pollutionon the economy thought health channel forcing increase of health expenditure when old, not affecting productivity of workers.

  • Innovation: 2nd dynamical model done using health channels, 1th to affect old health expenditure and focus on taxes


Introduction ii

Introduction II

  • Paper focuses on optimal taxation, not on long run growth effects.

  • Findings:

    • pollution makes more likely CE to be dynamic inefficient.

    • Over accumulation of capital above super golden rule is not PO.

    • Taxes on production and on capital and wages can increase welfare


The model

The model

  • Two period OGM with production

  • Constant population growth

  • Preferences are

  • One unit of labor when young

  • Income from savings when old

  • When old expenditure on consumption and health

  • Pollution costs of elders depend on pollution stock:

  • Firms have CRS:


Dynamics of the stock of pollution

Dynamics of the stock of pollution

  • Per worker


Competitive equilibrium

Competitive equilibrium

  • Agent’s problem

  • FOC

  • Savings


Competitive equilibrium ii

Competitive equilibrium II

  • Firms max profits:

  • Market clears:

  • Law of motion:


Steady state

Steady State

  • Proposition 1: The SS is a sink if

    Then:

    Standard Diamond’s model results hold


Implications

Implications

  • Higher population growth economies have lower capital and pollution per worker (but higher total).

  • Higher capital depreciation rate leads to less capital and pollution

  • Economies with Higher pollutant technologies and higher toxic pollutants accumulate more capital to pay for health!!!


Efficiency

Efficiency

  • CP Problem:

  • FOC:


Efficient ss and golden rule

Efficient SS and Golden Rule

  • 2 FOC + 2 constraints in SS define efficient capital per capita, c1, c2, and pollution stock per capita.

  • The golden rule is:

  • Not true that above golden rule economy is dynamically inefficient!!


Efficient ss and golden rule ii

Efficient SS and Golden Rule II

  • Lemma 1: If

    then there are always efficient capital ratios that exceed the golden rule capital ratio. Otherwise, the maximum efficient capital ratio is given by the golden rule allocation

  • Idea: double effect of planner’s discount rate (R=0): the lower the higher the savings (transfer consumption to the future), but also less pollution must be transmitted to the future, thus less capital less saving.


Efficient ss and golden rule iii

Efficient SS and Golden Rule III

  • Super golden rule:

  • Proposition 2: Above capital of super golden rule the economy is dynamically inefficient

  • Idea: Pollution is cumulative, when delta is 1, super golden and golden rules are the same.

  • Let kmax the capital ratio associated with central planner:

kmax

kG

kSG


Efficient ss and golden rule iv

Efficient SS and Golden Rule IV

  • Proposition 3: The higher pollution externalities, the higher the competitive stationary capital ratio is and the lower the supergolden rule capital ratio is.

  • Idea: First part is by proposition 1(more capital to pay more healthcare), second is because kSG is decreasing in the pollution parameters


Taxes on production

Taxes on Production

  • Tax per unit of output and lump sum transfer to youngs and or olds.

  • Competitive equilibrium leads to:

  • Proposition 4: Optimal tax is


Taxes on production ii

Taxes on Production II

  • The existence of two sources of inefficiency is the reason for:

  • If CE is efficient without pollution then inclusion of pollution generates an inefficiency in where both young and olds share revenue from tax

  • IF CE was already non-efficient pollution increases the problem and only olds receive revenue from taxes.


Taxes on capital and wages

Taxes on Capital and Wages

  • Taxes are levied on consumers so firms face same problem.

  • Proposition 5: Golden rule allocation can be achieved by imposing taxes and transfers to old:

  • If the economy over accumulates capital without pollution then:

  • Olds and youngs can be tax payers or receivers


Taxes on production vs on capital and wages

Taxes on production vs. on capital and wages

  • Idea: agents would prefer less amount of taxes to be paid.

  • Proposition 6: Youngs and elderly agents pay more taxes with the capital-wage system than with the production tax system.

  • Idea: Production tax scheme is superior in an electoral context


Dynamic inefficiency in an overlapping generation economy with pollution and health costs

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