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

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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

Maria-Jose Gutierrez

University of the Basque Country

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

Presented by Juan

- 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

- 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

- 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:

- Per worker

- Agent’s problem
- FOC
- Savings

- Firms max profits:
- Market clears:
- Law of motion:

- Proposition 1: The SS is a sink if
Then:

Standard Diamond’s model results hold

- 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!!!

- CP Problem:
- FOC:

- 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!!

- 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.

- 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

- 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

- Tax per unit of output and lump sum transfer to youngs and or olds.
- Competitive equilibrium leads to:
- Proposition 4: Optimal tax is

- 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 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

- 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

Thanks