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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

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Introduction

Environment affects economy through amenity, productivity and health channels

Aim of the paper: analyze effects of pollution on 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

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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

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0(.)0(.))( ffN

Kkkf

t

ttt

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:

0(.)0(.))()( 1,2,1 uanducucu tt

ttt enisoldperEH )1(

5

Dynamics of the stock of pollution

Per worker

),()1( 1 tttt LKFEE

)(1

11 ttt kfe

ne

6

Competitive equilibrium

Agent’s problem

FOC

Savings

tttt

ttt

ttcc

srenc

wscst

cucuMaxtt

)1()1(

:

)()(

111,2

,1

1,2,1, 1,2,1

)()1()( 1,21,1 ttt curcu

),|,,( 11 tttt erwss

0;0;0;0);1,0(11

tt

t

t

t

t

t

t ss

r

s

e

s

w

s

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Firms max profits:

Market clears:

Law of motion:

)(

)()(

tt

tttt

kfr

kkfkfw

),,()1( 111 tttt erwskn

)),(,)()(()1( 111 tttttt ekfkkfkfskn

)(1

111

ttt kfen

e

Competitive equilibrium II

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Steady State

)),(,)()(()1( ekfkkfkfskn )(1

1kfe

ne

0)(1

)()()1(

kfn

nskkfskfsn ewr

Proposition 1: The SS is a sink if

Then:

Standard Diamond’s model results hold

0000

0000

eenee

kknkk

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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!!!

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Efficiency

CP Problem:

FOC:),()1(

)(),(..

)()(

1

1,21,1

1,2,1},,{ ,2,11

tttt

tttttttt

ttcck

NKFEE

EHKcNcNNKFts

cucuMaxttt

1)()(

)(1)(1

)(

)(

)()1()(

11,1

2,21

1,2

,1

1,2,1

tt

tt

t

t

tt

kfcu

cukf

cu

cu

cuncu

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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!!

nkfn

n G

1)()1(

1

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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.

)1()1(

)(2

2

n

n

Efficient SS and Golden Rule II

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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:

1

1)(

nkf SG

kmax kSGkG

Efficient SS and Golden Rule III

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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

Efficient SS and Golden Rule IV

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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

nkf Cp 1)(1

n

np

)1(*

0)1()()()1( 1** GGGGGpy knckkfkf

0)1()( *** nkf yG

po

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Taxes on Production II

0* y

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.

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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

0110 *** wk

w*0

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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

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Thanks