common and private ownership of exhaustible resources: theoretical implications for economic...
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K. Bosrissov, A. Surkov. Common and private ownership of exhaustible resources: theoretical implications for economic growth. Presented at PET10 – 11th Annual Conference of the Association for Public Economic Theory, Istanbul, Turkey, June 25-27, 2010TRANSCRIPT
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Common and private ownership of exhaustible resources:theoretical implications for economic growth
PET10 – 11th Annual Conference of the Association for Public Economic Theory, Istanbul, Turkey, June 25-27, 2010
European University at St. Petersburg, RussiaSt. Petersburg Institute for Economics & Mathematics RAS
Kirill Borissov & Alexander Surkov
Financial support of Exxon Mobil Corp. is acknowledged.
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Outlines• Consumers are heterogeneous in their inter-
temporal preferences– Their discount factors are different
• Model 1: private ownership of resource stocks– Owners invest their savings in resource stocks
and earn a rent• Model 2: collective ownership of resource
stock– The resource rent is equally divided among all
the consumers – Resource utilization rate is chosen by voting
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Model 1: private resources• Consumers
( ), , 11i t i t t t tS r S WC −+ ≤ + ⋅ +
( ) 1 2 1 211 ttt tY K L Eα α α αλ − −= + ⋅ ⋅ ⋅
• Production
( ),
,0
maxi t
ti t ct
i u Cβ∞
=
⋅ →∑
• Resources
( )1 1tt t t tER R Rρ+ = − = −
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Equilibrium path (1)
• Consumers maximize utility• Capital and labor are paid their
marginal product• Resource price is equal to its marginal
product
( )* * * * * * * *, , 1, , 0,1,
, ,1 , , , , ,t t t t t t i t i t i L tK R r W P E C S
= … = …+
( ),0 ,0 1, ,,i i i L
K R= …
starting from the initial state
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Equilibrium path (2)
• Consumer savings are equal to investments
* * *1t t tR R E+ = −
* * * *, 1 1
1
L
i t t t ti
S P R K+ +=
= ⋅ +∑• Natural balance of exhaustible resources is
fulfilled
• Hotelling’s rule holds true
( )* * *1 11t t tP r P+ += +
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Steady-state equilibrium
( )* * ** * * * * *
1 ,
*
,, , , ,1 , , , , ,i i i L
K R r W P E C Sργ= …
+
( )( ) ( )( ) ( )( ) ( )
* * *
* *
*
* * * * *
* * * *
* * * *, ,
*
*
* *
1 , 1 1 ,
1 , 1 ,
1 , 1 ,
1 , 1
t
t t
t t
t t
t t
t t
t t
i t i i t i
K K r r
W W P r P
R R E E
C C S S
ρ ρ
γ
γ
γ γ
= + + = +
= + = +
= − = −
= + = +
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In a steady-state equilibrium
• The equilibrium resource utilization rate
• The equilibrium growth rate
x*
ma1ρ β= −
( ) 21 1
11
x* 1
ma1 1 α α αγ βλ −− −⎡ ⎤+ = +⎣ ⎦
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Model 2: common resources
• Budget constraints
( ), , , 11i t i t t t ti tC S r S W−+ ≤ + +Ω+
• Equilibrium path
( )* * * * * * * * *, , 1, , 0,1,
, ,1 , , , , , ,t t t t t t t i t i t i L tK R r W P E C S
= … = …+ Ω
starting from the initial state ( ), 1 01, ,,i i L
S R− = …
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Equilibrium path (1)
• Consumers maximize utility• Capital is paid its marginal product• Consumer income consists of marginal
product of labor and resource income* *
* t tt
P EL
Ω =
• Resource price is equal to marginal product of the resource
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Equilibrium path (2)• Aggregate savings are equal to the
capital stock
( )* * * *1 1t t t t tR R E Rρ+ = − = −
* *, 1
1
L
i t ti
S K +=
=∑• Natural balance of exhaustible
resources is fulfilled
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Steady-state equilibrium
( )* * * * * * * * * *
1, ,
* , , ,1 , , , , , , ,i i i LK R r W P E C Sγ π
= …+ Ω
( ) ( )( )
( ) ( )( ) ( )
( )
* * * *, ,
* * * *
*
* *
*
* * * *
* * * *
* *
*
*
1 , 1
1 , 1 1 ,
1 , 1
1 , 1 ,
,
1
,
t t
i t i i t i
t
t t
t t
t t
t tt t
t
t
C C S S
K K r r
W W
R R E E
P P
γ γ
π
ρ ρ
γ
γ γ
= + = +
= + + = +
= + Ω = + Ω
= − = −
= +
• Let tρ ρ=
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In a steady-state equilibrium
• Hotelling’s rule may be violated
• The equilibrium growth rate
max*
*
11 1r
βρ
π+=
−+
( )( ) 1 12
11* 11 1 1 α α αργ λ − −−⎡ ⎤+ = + −⎣ ⎦
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Voting
• Consumer i is in favor of increasing ρt if
,0
ti i t
ti uV Cβ
∞
=
= ⋅
0/ tiV ρ∂ ∂ >
• Consumer i is in favor of decreasing ρt if
0/ tiV ρ∂ ∂ <
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Voting equilibrium path
• For each t the number of consumers who are in favor of increasing ρt and the number of those who are in favor of decreasing ρt are less than half the total number of consumers.
( )* * * * * * * * *, , 1, , 0, ,
*
1, , ,1 , , , , , ,t t t t t t t i t i t it L tK R r W P E C Sρ
= … = …+ Ω
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Voting steady-state equilibrium
( )* * * * * * * * * *
1, ,
**, , , ,1 , , , , , , ,i i i LK R r W P E C Sρ γ π
= …+ Ω
( )( ) ( )( ) ( )( ) ( )
( )
* * * * *
* * * *
* * * *
*
* *
* ** * * *, ,
* * *
*
* *
, 1 , 1 1 ,
1 , 1 ,
1 , 1 ,
1 , 1
1
,
t
t t t
t t
t t
t t
t t
t t
i t i i t i
t
t
K K r r
W W
R R E E
C C S S
P P
γ
γ γ
γ
ρ
γ
π
ρ
ρ
ρ = = + + = +
= + Ω = + Ω
= − = −
= + = +
= +
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Median voter theorem
• Hotelling’s rule may be violated
• The equilibrium growth rate
*
*max1
1 mr βπ β+
=+
( ) 1 2 1
11* 11 1 mα α αγ λ β −− −⎡ ⎤+ = +⎣ ⎦
• In a voting steady state equilibrium* 1 mρ β= −
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Common vs. private• Common resources
( ) 1 2 1
11* * 11 , 1 1m mα α αρ γ λβ β − − −⎡ ⎤= − + = +⎣ ⎦
• Private resources
( ) 1 12max m
11* * 1
ax1 , 1 1 α α αρ γ λβ β − − −⎡ ⎤= − + = +⎣ ⎦
Private ownership of resource stocks may be favorable for the economic growth
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Further speculations (1)
• Risk of nationalization may decrease patience of the most patient consumers who own the resources thus decreasing the economic growth rate
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Further speculations (2)• Borissov, K. and S. Lambrecht. Growth and
distribution in an AK-model with endogenous impatience. Economic Theory. 2009. 39(1). 93-112
• Model of endogenous growth where discount factors of heterogeneous consumers are determined endogenously and depend on economic inequality: – positively related to individual consumer's relative
wealth– negatively affected by a possibility of social
conflict increasing with inequality
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Further speculations (3)• Private ownership of resource stocks
increases economic inequality and thus can have an ambiguous effect on economic growth: – positive influence in the case of moderate
inequality– negative effect due to decrease in the discount
factors of capital owners induced by increased risk of social conflict at high level of inequality
• There can be a range of parameters where common ownership of resource stocks may lead to even larger economic growth rate then in the case of private resources
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Conclusion (1)• Two models of economic growth with
heterogeneous consumers and exhaustible resources are developed– a model with private ownership of the resource
stocks– a model with collectively owned resource stocks
and the resource rent equally divided among all the consumers
• Equilibrium paths are defined and some properties of steady-state equilibria are analyzed
• In the second model the notion of voting equilibrium is introduced and properties of steady-state voting equilibria are described
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Conclusion (2)• In the case of common resources in a voting
steady-state equilibrium the resource utilization rate as well as the steady-state rate of growth is determined by patience of the median consumer.
• In the case of private resource stocks the resource utilization rate and the steady state rate of growth are determined by the patience of the most patient consumers.
• If the median consumer is less patient than the most patient one, in the case of privateresources the resource utilization rate is lower and the economic growth rate is higherthan in the case of common resources.