资源环境经济学_accounting for the environment 2006

Depreciation is the amount extracted valued at the marginal product of the resource, which in this model with costless extraction is the unit rent.
We can also write:
t
Objective function:
Max
Constraints:
Kt Q Kt Ct
t 0

U CT e t dt
current-value Hamiltonian:
H Ct U Ct t Q Kt Ct
t : costate variable
C
H UC C I P S
U C , U C P Q , S R
R
H U C C I QR R NDP QR R EDP
NDP is the conventionally measured national income and EDP, national income properly measured given the use of the natural resource in production. QRR is the rent in the extraction of the resource, where the rent is the measure of the depreciation of the asset which is the resource stock.
Nobel laureate economist Robert Solow suggested that ‘an innovation in social accounting practice could contribute to more rational debate and perhaps more rational action in the economics of non-renewable resources and the approach to a sustainable economy.’
OECD (1994)
Driving Force-Pressure-State-Impact-Response Framework
The Driving Force - Pressure - State - Impact - Response Framework (DPSIR) provides an overall mechanism for analysing environmental problems.
H Ct U Ct Pt Rt t Qt Ct Pt , t : costate variables
After substituting from the PF the current-value Hamiltonian:
HCt U Ct P Rt t QKt , Rt Ct t
OECD: Towards Environmental pressure Indicators for the EU - First Edition 1998.
Important question: How to measure depreciation on natural capital?
We start with a simple economy, where one good will be produced and either consumed or added to the capital stock:
necessary conditions for optimum:
H UC 0 C H Qk K
* H ct U Ct t Kt * H ct U Ct U C Kt
maximized current-value Hamiltonian:
R R
3.) Qk 4.) P P
We can also write:
1.) t U C 2.) P P QR QR 3.) Qk 4.) P P
If we consider constant consumption, U C =0 and =U C : 3.) Q U U
Important question: How to measure depreciation on natural capital?
• if the utility function is linearlized by using U(Ct) = UCCt:
* * Hct UCCt UC Kt Hct UC Ct It
Important question: How to measure depreciation on natural capital?
current-value Hamiltonian:
H Ct U Ct t Q Kt Ct
t : costate variable
Impacts on human health and eco-systems, causing society to Respond with various policy measures, such as regulations,
information and taxes, which can be directed at any other part of the system.
Lecture
Accounting for the environment
Lecturer: Dr. Justus Wesseler, Wageningen University Literature: Perman et al. (2003), Ch.18
Why Measuring Sustainability?
or
Important question: How to measure depreciation on natural capital?
maximized current-value Hamiltonian:
* Hct U Ct UC Kt
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• Ct and dK/dt are the OPTIMAL values of the utility maximization process
remember :
We can also write:
1.) U C
H UC 0 C
P dt QR dt P QR QR P P QR P QR P 0 2.) P P Q Q (differentiating by time)
Driving forces, such as industry and transport, produce
Pressures on the environment, such as polluting emissions, which then
degrade the
State of the environment, which then
We can go back to our problem and now include a non-renewable resource:
t
Objective function:
Max
t 0

U CT e t dt
Constraints:
St Rt ,
Kt Q Kt , Rt Ct
• if we assume that capital K does not depreciate, the RHS is just net national income, and we can write:
* NDP Hct UC Ct It t
Important question: How to measure depreciation on natural capital?
EDP C I P R
• P/ is the relative (to the price of the numeraire commodity which is the consumption/capital good) price of the extracted resource, which in a model with costless extraction is the same as the price of the resource in situ. (in a fully competitive economy)
•
* H ct instantaneous national income measured in utils
• if the utility function is linearlized by using U(Ct) = UCCt:
* * Hct UCCt UC Kt Hct UC Ct It
We can differentiate the Hamiltonian by time. In this case we get for EDP:
EDP W QKW
W is the current wealth of the economy. Since the marginal product of capital is the interest rate in the economy, EDP is the return on the economy’s total stock of wealth: EDP= i W.
k C
and we also get from this: Q Q Q
R R
K
We can also linearise the Hamiltonian and using the equation of motions:
H U C PS K H U C PS K
Necessary conditions for a maximum with control variables C and R and dropping t:
H H UC 0 P QR 0 C R P H 0 P S H Qk K
HC U C P R N QK , R C GR, S F N , S
• N: additions to the known stock as the result of exploration; • F{N, S}: costs of exploration; • G{R, S}: costs of extraction; • GR: marginal extraction cost;
Measuring depreciation:
EDP C I QR R or NDP QR R EDP W QKW
This looks familiar!
In a model economy where resource extraction involves cost, and new known reserves can be established at some cost: