Non-renewable resource exploitation - The Economics Network
Transcript of Non-renewable resource exploitation - The Economics Network
Non-renewable resource exploitation:externalities, exploration, scarcity and rents
NRE - Lecture 3
Aaron Hatcher
Department of EconomicsUniversity of Portsmouth
Externalities
I External (social) costs
I Example: pollutionI E¤ects not covered by markets and so di¢ cult to valueI Trade o¤ between costs and bene�tsI MB = MCI Optimal pollution does not imply a fair distribution of costsand bene�ts!
Externalities
I External (social) costsI Example: pollution
I E¤ects not covered by markets and so di¢ cult to valueI Trade o¤ between costs and bene�tsI MB = MCI Optimal pollution does not imply a fair distribution of costsand bene�ts!
Externalities
I External (social) costsI Example: pollutionI E¤ects not covered by markets and so di¢ cult to value
I Trade o¤ between costs and bene�tsI MB = MCI Optimal pollution does not imply a fair distribution of costsand bene�ts!
Externalities
I External (social) costsI Example: pollutionI E¤ects not covered by markets and so di¢ cult to valueI Trade o¤ between costs and bene�ts
I MB = MCI Optimal pollution does not imply a fair distribution of costsand bene�ts!
Externalities
I External (social) costsI Example: pollutionI E¤ects not covered by markets and so di¢ cult to valueI Trade o¤ between costs and bene�tsI MB = MC
I Optimal pollution does not imply a fair distribution of costsand bene�ts!
Externalities
I External (social) costsI Example: pollutionI E¤ects not covered by markets and so di¢ cult to valueI Trade o¤ between costs and bene�tsI MB = MCI Optimal pollution does not imply a fair distribution of costsand bene�ts!
Externalities contd.
I A social planner would want a �rm to maximiseZ T
0[pq � c (q, x)� d (z , a)� θ (a)] e�rtdt
I Here z � αq is a pollutant generated by extraction; d (�) is adamage function and θ (a) are abatement costs
I Normalise α to 1 so that z = qI Optimality now requires
p � cq = λ+ dz , θa = �da
I If d (�) � d (z � a) then dz = �da and we can write
p � cq � θa = λ
for a �socially responsible��rm
Externalities contd.
I A social planner would want a �rm to maximiseZ T
0[pq � c (q, x)� d (z , a)� θ (a)] e�rtdt
I Here z � αq is a pollutant generated by extraction; d (�) is adamage function and θ (a) are abatement costs
I Normalise α to 1 so that z = qI Optimality now requires
p � cq = λ+ dz , θa = �da
I If d (�) � d (z � a) then dz = �da and we can write
p � cq � θa = λ
for a �socially responsible��rm
Externalities contd.
I A social planner would want a �rm to maximiseZ T
0[pq � c (q, x)� d (z , a)� θ (a)] e�rtdt
I Here z � αq is a pollutant generated by extraction; d (�) is adamage function and θ (a) are abatement costs
I Normalise α to 1 so that z = q
I Optimality now requires
p � cq = λ+ dz , θa = �da
I If d (�) � d (z � a) then dz = �da and we can write
p � cq � θa = λ
for a �socially responsible��rm
Externalities contd.
I A social planner would want a �rm to maximiseZ T
0[pq � c (q, x)� d (z , a)� θ (a)] e�rtdt
I Here z � αq is a pollutant generated by extraction; d (�) is adamage function and θ (a) are abatement costs
I Normalise α to 1 so that z = qI Optimality now requires
p � cq = λ+ dz , θa = �da
I If d (�) � d (z � a) then dz = �da and we can write
p � cq � θa = λ
for a �socially responsible��rm
Externalities contd.
I A social planner would want a �rm to maximiseZ T
0[pq � c (q, x)� d (z , a)� θ (a)] e�rtdt
I Here z � αq is a pollutant generated by extraction; d (�) is adamage function and θ (a) are abatement costs
I Normalise α to 1 so that z = qI Optimality now requires
p � cq = λ+ dz , θa = �da
I If d (�) � d (z � a) then dz = �da and we can write
p � cq � θa = λ
for a �socially responsible��rm
Externalities contd.
I Firms must have an incentive to incur abatement costs
I How?
I pollution taxesI standardsI tradeable permits
I Backed up by enforcement (inspections and penalties)I Firms forced to internalise the (social) costs of pollutionI Note: there may be stock as well as �ow e¤ects
Externalities contd.
I Firms must have an incentive to incur abatement costsI How?
I pollution taxesI standardsI tradeable permits
I Backed up by enforcement (inspections and penalties)I Firms forced to internalise the (social) costs of pollutionI Note: there may be stock as well as �ow e¤ects
Externalities contd.
I Firms must have an incentive to incur abatement costsI How?
I pollution taxes
I standardsI tradeable permits
I Backed up by enforcement (inspections and penalties)I Firms forced to internalise the (social) costs of pollutionI Note: there may be stock as well as �ow e¤ects
Externalities contd.
I Firms must have an incentive to incur abatement costsI How?
I pollution taxesI standards
I tradeable permits
I Backed up by enforcement (inspections and penalties)I Firms forced to internalise the (social) costs of pollutionI Note: there may be stock as well as �ow e¤ects
Externalities contd.
I Firms must have an incentive to incur abatement costsI How?
I pollution taxesI standardsI tradeable permits
I Backed up by enforcement (inspections and penalties)I Firms forced to internalise the (social) costs of pollutionI Note: there may be stock as well as �ow e¤ects
Externalities contd.
I Firms must have an incentive to incur abatement costsI How?
I pollution taxesI standardsI tradeable permits
I Backed up by enforcement (inspections and penalties)
I Firms forced to internalise the (social) costs of pollutionI Note: there may be stock as well as �ow e¤ects
Externalities contd.
I Firms must have an incentive to incur abatement costsI How?
I pollution taxesI standardsI tradeable permits
I Backed up by enforcement (inspections and penalties)I Firms forced to internalise the (social) costs of pollution
I Note: there may be stock as well as �ow e¤ects
Externalities contd.
I Firms must have an incentive to incur abatement costsI How?
I pollution taxesI standardsI tradeable permits
I Backed up by enforcement (inspections and penalties)I Firms forced to internalise the (social) costs of pollutionI Note: there may be stock as well as �ow e¤ects
Exploration
I Few general conclusions
I Costly and subject to uncertaintyI New discoveries may not be developed immediately,depending on extraction costs
I Models of exploration are complex!
Exploration
I Few general conclusionsI Costly and subject to uncertainty
I New discoveries may not be developed immediately,depending on extraction costs
I Models of exploration are complex!
Exploration
I Few general conclusionsI Costly and subject to uncertaintyI New discoveries may not be developed immediately,depending on extraction costs
I Models of exploration are complex!
Exploration
I Few general conclusionsI Costly and subject to uncertaintyI New discoveries may not be developed immediately,depending on extraction costs
I Models of exploration are complex!
Scarcity
I An economic de�nition of scarcity
I Must depend on demand (price) and extraction costsI A resource becomes more scarce if demand (price) increasesand less scarce if demand decreases
I Economic scarcity is decreasing if extraction costs increaseand prices don�t
I The shadow price λ (the di¤erence between price andmarginal cost) is regarded as the correct measure of economicscarcity
I A trend in the shadow price is the best indicator of resourcescarcity
I Sincep = λ+ cq ,
clearly p and λ can have opposite signs
Scarcity
I An economic de�nition of scarcityI Must depend on demand (price) and extraction costs
I A resource becomes more scarce if demand (price) increasesand less scarce if demand decreases
I Economic scarcity is decreasing if extraction costs increaseand prices don�t
I The shadow price λ (the di¤erence between price andmarginal cost) is regarded as the correct measure of economicscarcity
I A trend in the shadow price is the best indicator of resourcescarcity
I Sincep = λ+ cq ,
clearly p and λ can have opposite signs
Scarcity
I An economic de�nition of scarcityI Must depend on demand (price) and extraction costsI A resource becomes more scarce if demand (price) increasesand less scarce if demand decreases
I Economic scarcity is decreasing if extraction costs increaseand prices don�t
I The shadow price λ (the di¤erence between price andmarginal cost) is regarded as the correct measure of economicscarcity
I A trend in the shadow price is the best indicator of resourcescarcity
I Sincep = λ+ cq ,
clearly p and λ can have opposite signs
Scarcity
I An economic de�nition of scarcityI Must depend on demand (price) and extraction costsI A resource becomes more scarce if demand (price) increasesand less scarce if demand decreases
I Economic scarcity is decreasing if extraction costs increaseand prices don�t
I The shadow price λ (the di¤erence between price andmarginal cost) is regarded as the correct measure of economicscarcity
I A trend in the shadow price is the best indicator of resourcescarcity
I Sincep = λ+ cq ,
clearly p and λ can have opposite signs
Scarcity
I An economic de�nition of scarcityI Must depend on demand (price) and extraction costsI A resource becomes more scarce if demand (price) increasesand less scarce if demand decreases
I Economic scarcity is decreasing if extraction costs increaseand prices don�t
I The shadow price λ (the di¤erence between price andmarginal cost) is regarded as the correct measure of economicscarcity
I A trend in the shadow price is the best indicator of resourcescarcity
I Sincep = λ+ cq ,
clearly p and λ can have opposite signs
Scarcity
I An economic de�nition of scarcityI Must depend on demand (price) and extraction costsI A resource becomes more scarce if demand (price) increasesand less scarce if demand decreases
I Economic scarcity is decreasing if extraction costs increaseand prices don�t
I The shadow price λ (the di¤erence between price andmarginal cost) is regarded as the correct measure of economicscarcity
I A trend in the shadow price is the best indicator of resourcescarcity
I Sincep = λ+ cq ,
clearly p and λ can have opposite signs
Scarcity
I An economic de�nition of scarcityI Must depend on demand (price) and extraction costsI A resource becomes more scarce if demand (price) increasesand less scarce if demand decreases
I Economic scarcity is decreasing if extraction costs increaseand prices don�t
I The shadow price λ (the di¤erence between price andmarginal cost) is regarded as the correct measure of economicscarcity
I A trend in the shadow price is the best indicator of resourcescarcity
I Sincep = λ+ cq ,
clearly p and λ can have opposite signs
Rent capture
I Economic pro�ts � resource rent
I Government may try to capture (some) rent for society�sbene�t
I Common charges are taxes on revenues/quantities (severancetax) or pro�ts (royalty)
I With a revenue tax τ the �rm maximisesZ T
0[[p � τ] q � c (q, x)] e�rtdt
I E¤ect similar to an increase in the costs of extraction:extraction ceases earlier and more resource is left in theground
I A revenue tax is distortionary
Rent capture
I Economic pro�ts � resource rentI Government may try to capture (some) rent for society�sbene�t
I Common charges are taxes on revenues/quantities (severancetax) or pro�ts (royalty)
I With a revenue tax τ the �rm maximisesZ T
0[[p � τ] q � c (q, x)] e�rtdt
I E¤ect similar to an increase in the costs of extraction:extraction ceases earlier and more resource is left in theground
I A revenue tax is distortionary
Rent capture
I Economic pro�ts � resource rentI Government may try to capture (some) rent for society�sbene�t
I Common charges are taxes on revenues/quantities (severancetax) or pro�ts (royalty)
I With a revenue tax τ the �rm maximisesZ T
0[[p � τ] q � c (q, x)] e�rtdt
I E¤ect similar to an increase in the costs of extraction:extraction ceases earlier and more resource is left in theground
I A revenue tax is distortionary
Rent capture
I Economic pro�ts � resource rentI Government may try to capture (some) rent for society�sbene�t
I Common charges are taxes on revenues/quantities (severancetax) or pro�ts (royalty)
I With a revenue tax τ the �rm maximisesZ T
0[[p � τ] q � c (q, x)] e�rtdt
I E¤ect similar to an increase in the costs of extraction:extraction ceases earlier and more resource is left in theground
I A revenue tax is distortionary
Rent capture
I Economic pro�ts � resource rentI Government may try to capture (some) rent for society�sbene�t
I Common charges are taxes on revenues/quantities (severancetax) or pro�ts (royalty)
I With a revenue tax τ the �rm maximisesZ T
0[[p � τ] q � c (q, x)] e�rtdt
I E¤ect similar to an increase in the costs of extraction:extraction ceases earlier and more resource is left in theground
I A revenue tax is distortionary
Rent capture
I Economic pro�ts � resource rentI Government may try to capture (some) rent for society�sbene�t
I Common charges are taxes on revenues/quantities (severancetax) or pro�ts (royalty)
I With a revenue tax τ the �rm maximisesZ T
0[[p � τ] q � c (q, x)] e�rtdt
I E¤ect similar to an increase in the costs of extraction:extraction ceases earlier and more resource is left in theground
I A revenue tax is distortionary
Rent capture contd.
I With a pro�ts tax τ the �rm�s objective function isZ T
0[1� τ] [pq � c (q, x)] e�rtdt
I The tax does not change pro�t-maximising behaviour andhence is not distortionary
I But, a pro�ts tax reduces the present value of the resourceI Government may (also) sell extraction or prospecting rightsI Or, in some cases, the resource itself
Rent capture contd.
I With a pro�ts tax τ the �rm�s objective function isZ T
0[1� τ] [pq � c (q, x)] e�rtdt
I The tax does not change pro�t-maximising behaviour andhence is not distortionary
I But, a pro�ts tax reduces the present value of the resourceI Government may (also) sell extraction or prospecting rightsI Or, in some cases, the resource itself
Rent capture contd.
I With a pro�ts tax τ the �rm�s objective function isZ T
0[1� τ] [pq � c (q, x)] e�rtdt
I The tax does not change pro�t-maximising behaviour andhence is not distortionary
I But, a pro�ts tax reduces the present value of the resource
I Government may (also) sell extraction or prospecting rightsI Or, in some cases, the resource itself
Rent capture contd.
I With a pro�ts tax τ the �rm�s objective function isZ T
0[1� τ] [pq � c (q, x)] e�rtdt
I The tax does not change pro�t-maximising behaviour andhence is not distortionary
I But, a pro�ts tax reduces the present value of the resourceI Government may (also) sell extraction or prospecting rights
I Or, in some cases, the resource itself
Rent capture contd.
I With a pro�ts tax τ the �rm�s objective function isZ T
0[1� τ] [pq � c (q, x)] e�rtdt
I The tax does not change pro�t-maximising behaviour andhence is not distortionary
I But, a pro�ts tax reduces the present value of the resourceI Government may (also) sell extraction or prospecting rightsI Or, in some cases, the resource itself
Dynamic optimisation: the Hamiltonian
I De�ne an instantaneous pro�t function
π (q (t) , x (t)) � pq (t)� c (q (t) , x (t))
I The (social planner�s) problem is to
maxq
Z T
0π (�) e�rtdt
s.t. x = f (x (t) , q (t)) , x (0) = x0
I De�ne a Lagrangian function
L �Z T
0
�π (�) e�rt + µ (t) [f (�)� x ]
dt
whereµ (t) � λ (t) e�rt
Dynamic optimisation: the Hamiltonian
I De�ne an instantaneous pro�t function
π (q (t) , x (t)) � pq (t)� c (q (t) , x (t))
I The (social planner�s) problem is to
maxq
Z T
0π (�) e�rtdt
s.t. x = f (x (t) , q (t)) , x (0) = x0
I De�ne a Lagrangian function
L �Z T
0
�π (�) e�rt + µ (t) [f (�)� x ]
dt
whereµ (t) � λ (t) e�rt
Dynamic optimisation: the Hamiltonian
I De�ne an instantaneous pro�t function
π (q (t) , x (t)) � pq (t)� c (q (t) , x (t))
I The (social planner�s) problem is to
maxq
Z T
0π (�) e�rtdt
s.t. x = f (x (t) , q (t)) , x (0) = x0
I De�ne a Lagrangian function
L �Z T
0
�π (�) e�rt + µ (t) [f (�)� x ]
dt
whereµ (t) � λ (t) e�rt
Dynamic optimisation contd.
I De�ne a (present value) Hamiltonian
H (�) � π (�) e�rt + µ (t) f (�)
so that
L =Z T
0H (q, x , µ, t) dt �
Z T
0µ (t) xdt
I Integrate the �nal term by parts to obtainZ T
0µ (t) xdt = µ (T ) x (T )� µ (0) x0 �
Z T
0µx (t) dt
Dynamic optimisation contd.
I De�ne a (present value) Hamiltonian
H (�) � π (�) e�rt + µ (t) f (�)
so that
L =Z T
0H (q, x , µ, t) dt �
Z T
0µ (t) xdt
I Integrate the �nal term by parts to obtainZ T
0µ (t) xdt = µ (T ) x (T )� µ (0) x0 �
Z T
0µx (t) dt
Dynamic optimisation contd.
I Rewrite the Lagrangian as
L �Z T
0fH (�) + µxg dt + µ (0) x0 � µ (T ) x (T )
I Di¤erentiate w.r.t. q and x to get the FOCs
Lq = Hq = πqe�rt + µfq = 0
Lx = Hx + µ = πx e�rt + µfx + µ = 0
I Hence we require
πqe�rt = �µfq ) πqe�rt = µ
given f (�) � g (x)� q and hence fq = �1I This is equivalent to the familiar current period condition
πq = λ
Dynamic optimisation contd.
I Rewrite the Lagrangian as
L �Z T
0fH (�) + µxg dt + µ (0) x0 � µ (T ) x (T )
I Di¤erentiate w.r.t. q and x to get the FOCs
Lq = Hq = πqe�rt + µfq = 0
Lx = Hx + µ = πx e�rt + µfx + µ = 0
I Hence we require
πqe�rt = �µfq ) πqe�rt = µ
given f (�) � g (x)� q and hence fq = �1I This is equivalent to the familiar current period condition
πq = λ
Dynamic optimisation contd.
I Rewrite the Lagrangian as
L �Z T
0fH (�) + µxg dt + µ (0) x0 � µ (T ) x (T )
I Di¤erentiate w.r.t. q and x to get the FOCs
Lq = Hq = πqe�rt + µfq = 0
Lx = Hx + µ = πx e�rt + µfx + µ = 0
I Hence we require
πqe�rt = �µfq ) πqe�rt = µ
given f (�) � g (x)� q and hence fq = �1
I This is equivalent to the familiar current period condition
πq = λ
Dynamic optimisation contd.
I Rewrite the Lagrangian as
L �Z T
0fH (�) + µxg dt + µ (0) x0 � µ (T ) x (T )
I Di¤erentiate w.r.t. q and x to get the FOCs
Lq = Hq = πqe�rt + µfq = 0
Lx = Hx + µ = πx e�rt + µfx + µ = 0
I Hence we require
πqe�rt = �µfq ) πqe�rt = µ
given f (�) � g (x)� q and hence fq = �1I This is equivalent to the familiar current period condition
πq = λ
Dynamic optimisation contd.
I We also requireµ = �πx e�rt � µfx
I From µ (t) � λ (t) e�rt we can �nd
µ =�λ� rλ
�e�rt
I Hence, in current value terms, we have
λ = �πx � λ [fx � r ]
I For a non-renewable resource, fx = g 0 (x) = 0 and so
λ = λr � πx
I Or, without resource-dependent costs,
λ = λr
Dynamic optimisation contd.
I We also requireµ = �πx e�rt � µfx
I From µ (t) � λ (t) e�rt we can �nd
µ =�λ� rλ
�e�rt
I Hence, in current value terms, we have
λ = �πx � λ [fx � r ]
I For a non-renewable resource, fx = g 0 (x) = 0 and so
λ = λr � πx
I Or, without resource-dependent costs,
λ = λr
Dynamic optimisation contd.
I We also requireµ = �πx e�rt � µfx
I From µ (t) � λ (t) e�rt we can �nd
µ =�λ� rλ
�e�rt
I Hence, in current value terms, we have
λ = �πx � λ [fx � r ]
I For a non-renewable resource, fx = g 0 (x) = 0 and so
λ = λr � πx
I Or, without resource-dependent costs,
λ = λr
Dynamic optimisation contd.
I We also requireµ = �πx e�rt � µfx
I From µ (t) � λ (t) e�rt we can �nd
µ =�λ� rλ
�e�rt
I Hence, in current value terms, we have
λ = �πx � λ [fx � r ]
I For a non-renewable resource, fx = g 0 (x) = 0 and so
λ = λr � πx
I Or, without resource-dependent costs,
λ = λr
Dynamic optimisation contd.
I We also requireµ = �πx e�rt � µfx
I From µ (t) � λ (t) e�rt we can �nd
µ =�λ� rλ
�e�rt
I Hence, in current value terms, we have
λ = �πx � λ [fx � r ]
I For a non-renewable resource, fx = g 0 (x) = 0 and so
λ = λr � πx
I Or, without resource-dependent costs,
λ = λr
Dynamic optimisation contd.
I What does the Hamiltonian represent?
I The present value Hamiltonian is
H (�) � π (�) e�rt + µ (t) f (�)
I Or, in current value terms
Hc (�) � π (�) + λ (t) f (�)
I The Hamiltonian measures the total rate of increase in thevalue of the resource
I π (�) is the net �ow of returns from the resourceI λ (t) f (�) is the increase in the value of the stock
Dynamic optimisation contd.
I What does the Hamiltonian represent?I The present value Hamiltonian is
H (�) � π (�) e�rt + µ (t) f (�)
I Or, in current value terms
Hc (�) � π (�) + λ (t) f (�)
I The Hamiltonian measures the total rate of increase in thevalue of the resource
I π (�) is the net �ow of returns from the resourceI λ (t) f (�) is the increase in the value of the stock
Dynamic optimisation contd.
I What does the Hamiltonian represent?I The present value Hamiltonian is
H (�) � π (�) e�rt + µ (t) f (�)
I Or, in current value terms
Hc (�) � π (�) + λ (t) f (�)
I The Hamiltonian measures the total rate of increase in thevalue of the resource
I π (�) is the net �ow of returns from the resourceI λ (t) f (�) is the increase in the value of the stock
Dynamic optimisation contd.
I What does the Hamiltonian represent?I The present value Hamiltonian is
H (�) � π (�) e�rt + µ (t) f (�)
I Or, in current value terms
Hc (�) � π (�) + λ (t) f (�)
I The Hamiltonian measures the total rate of increase in thevalue of the resource
I π (�) is the net �ow of returns from the resourceI λ (t) f (�) is the increase in the value of the stock
Dynamic optimisation contd.
I What does the Hamiltonian represent?I The present value Hamiltonian is
H (�) � π (�) e�rt + µ (t) f (�)
I Or, in current value terms
Hc (�) � π (�) + λ (t) f (�)
I The Hamiltonian measures the total rate of increase in thevalue of the resource
I π (�) is the net �ow of returns from the resource
I λ (t) f (�) is the increase in the value of the stock
Dynamic optimisation contd.
I What does the Hamiltonian represent?I The present value Hamiltonian is
H (�) � π (�) e�rt + µ (t) f (�)
I Or, in current value terms
Hc (�) � π (�) + λ (t) f (�)
I The Hamiltonian measures the total rate of increase in thevalue of the resource
I π (�) is the net �ow of returns from the resourceI λ (t) f (�) is the increase in the value of the stock