Intertemporal Allocation of Natural Resources by yurtgc548

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									                         Part II
              Intertemporal Allocation of
               Nonrenewable Resources:
                  a Global Perspective
               Content
          • A Ramsey Approach
          • Sustainability I: Basic Considerations
          • Sustainability II: Concepts and Applications

Gunter Stephan - Intertemporal Allocation of Natural Resources 2008   1
                                           Motivation

   Points of departure
   • So far the analysis was focused on resource markets
     only
   • So far the interaction with the rest of the economy
     was almost completely neglected
   • So far important variables such as the interest rate
     have been taken as exogenously given

Gunter Stephan - Intertemporal Allocation of Natural Resources 2008   2
                                           Motivation

   Consequences of the
   approach used so far
   • Gap-type Economy:
     - no price effects
     - agents do not learn and
       change behavior
   • Elephant–rabbit -Paradox:
       Interaction between
       sectors of the economy
       misrepresented

Gunter Stephan - Intertemporal Allocation of Natural Resources 2008   3
                                           Motivation




Gunter Stephan - Intertemporal Allocation of Natural Resources 2008   4
                                           Motivation

   Questions, we intend to answer
   • How to use nonrenewable resources socially
     optimal over time?
   • How to realize an optimal allocation of
     nonrenewable resources within a decentralized
     market economy?
   • Does the finiteness of nonrenewable resource
     stocks limit economic growth?

Gunter Stephan - Intertemporal Allocation of Natural Resources 2008   5
                                           Motivation
   Further questions to be answered
   • Can economic development be sustainable in case
     of nonrenewable resources?
   • How does the allocation of resources affect welfare
     and intergenerational equity?
   • Which aspects must be part of a general equilibrium
     analysis of the intertemporal allocation of
     nonrenewable resources?


Gunter Stephan - Intertemporal Allocation of Natural Resources 2008   6
                                Essential Aspects

   Important to consider
         There are different ways of affecting the well being
         of future generations
   Examples
   • Investment into physical capital
   • Investment into human capital and technological
     knowledge
   • Investment into environmental capital

Gunter Stephan - Intertemporal Allocation of Natural Resources 2008   7
                                Essential Aspects

   Competition exists
   • with respect to gross output:
     the option exists to consume or to invest GDP
   • with respect to investment:
     the option exists to invest into tangible capital or
     environmental capital



Gunter Stephan - Intertemporal Allocation of Natural Resources 2008   8
                                 A Working Horse

    The Ramsey model: A basic approach to the
    economic analysis of growth



                                                     Franck Ramsey
                                                     1904 –1930




Gunter Stephan - Intertemporal Allocation of Natural Resources 2008   9
                                 A Working Horse

    Factors, which affect growth

                                                                      Investing into tangible
                                                                      capital is of great
                                                                      importance
                                                                      It allows to shift the
                                                                      service of non-durable
                                                                      factors into the future


Gunter Stephan - Intertemporal Allocation of Natural Resources 2008                             10
                                 A Working Horse

    Capital - concrete time (labor)
                                                                      Fish can be caught by
                                                                      hand or by using a
                                                                      net, which rises
                                                                      productivity of labor
                                                         no net       Producing a net
                                                        available     consumes labor,
                                                                      which then is not
                            Consumption today                         available for catching
                                                                      fish
Gunter Stephan - Intertemporal Allocation of Natural Resources 2008                            11
                                 A Working Horse

    Investment - a source of economic growth
                           Capital accumulation


                          K t1  (1  β ) K t  it



         Capital stock                                                Investment
                                         Depreciation rate


Gunter Stephan - Intertemporal Allocation of Natural Resources 2008                12
                                 A Working Horse

   Production
                                Production function
                                       y t  f ( Lt , K t )


                 Output                                               capital
                                                   labor

   Marginal productivity of factors is positive, but decreasing


Gunter Stephan - Intertemporal Allocation of Natural Resources 2008             13
                                 A Working Horse

  Material balance
                                       y t  c t  it

                 Output               Consumption                     Investment


                         f (L t ,K t )  c t  K t 1  (1  β)K t
                                                    
                                                                it

  Capital might be consumed

Gunter Stephan - Intertemporal Allocation of Natural Resources 2008                14
                                 A Working Horse

   Welfare maximization
   Ramsey Planer, representative Household


                    W  W ( c0 ,...,cT )                              More and more
                                 T
                                                                      applied
                                        t
                     W   δ u( c t )
                               t 0

                                  T
                                         t
                     W  δ                   ln( c t )
                                t 0                                        : discount rate

Gunter Stephan - Intertemporal Allocation of Natural Resources 2008                            15
                                 A Working Horse

    Problem
           T t                                                                  
       max  δ u(c t ) t : L t  Wt , c t  f(L t , K t )  K t 1  (1  β)K t 
          t 0                                                                   


    Maximizing the Lagangian gives
               T                    T                                         T
                     t
        L   δ u(c t )   pt {f (L t ,K t )  c t  K t 1  (1  β)K t }   w t ( Wt  L t )
              t 0                 t 0                                      t 0




Gunter Stephan - Intertemporal Allocation of Natural Resources 2008                                16
                                 A Working Horse

     First Order Conditions
                  dL              u( c t )
     (1)                0  δ t            pt  0
                  dc t             c t



                   dL             f              
     (2)                 0  pt        (1  β )   pt-1  0
                   dK t           K t            




Gunter Stephan - Intertemporal Allocation of Natural Resources 2008   17
                                      A Working Horse

    Ramsey-Rule

                                                        1   u( c t )  f             u( c t 1 )
                                                    δ                       (1  β )  
                                                              c t  K t                 c t 1
         Consumption tomorrow




                                Consumption today
Gunter Stephan - Intertemporal Allocation of Natural Resources 2008                                18
                           A Ramsey Approach

   • Time                                        T+1 periods t=0,...,T
   • Agents                                      Ramsey (Central) Planer
   • Commodities                                 Stock R of nonrenewable,
                                                 producible yt which can be
                                                 consumed ct or invested it
                                                 into capital formation kt
   • Markets                                     none
   • Property rights                             none

Gunter Stephan - Intertemporal Allocation of Natural Resources 2008           19
                           A Ramsey Approach

                                                                       T
                                                                                t
   • Objective function                                                (1  δ ) ut ( c t )
                                                                      t 0



   • Material balance                                                   yt  c t  it


   • Productions function                                               yt  f ( kt , xt )


Gunter Stephan - Intertemporal Allocation of Natural Resources 2008                           20
                           A Ramsey Approach

   • Investment (tangible capital)
                                  kt 1  kt  it

   • Resource constraint
                                             T
                                    R   xt
                                           t 0

   • Optimization
                     T                                                          T
                                   t
          max{  (1  δ ) ut ( c t ) / f ( kt , xt )  c t  ( kt 1  kt ), R   xt }
                   t 0                                                        t 0


Gunter Stephan - Intertemporal Allocation of Natural Resources 2008                       21
                             A Ramsey Approach
                              T
                      L   ( 1  δ ) t ut ( c t ) 
                             t 0
                       T                                                      T
                        pt [ f ( kt , x t )  c t  ( kt 1  kt )]  w( R   x t )
                      t 0                                                   t 0

                                            t   ut
  (1)                        (1  δ )                 pt  0
                                                 ct
                                  f
 ( 2)                          pt      pt  pt 1  0
                                  kt
                                     f
  ( 3)                            pt     w 0
                                     xt
Gunter Stephan - Intertemporal Allocation of Natural Resources 2008                     22
                           A Ramsey Approach

   Ramsey-Condition
                                                                      ct+1

     f           
               1 
     kt 1       
               ut ( c t ) ut 1( c t 1 )
    ( 1  δ )[            /                 ]
                  c t        c t 1


   Marginal rates of substitution
   are identical                                                             ct


Gunter Stephan - Intertemporal Allocation of Natural Resources 2008               23
                           A Ramsey Approach

   Solow-Stiglitz Condition

                      f   f       f
                 (1     )        
                      kt x t 1   x t

   The marginal productivity of extracting resources today
                                              equals
   the return of investing the output of extracting an additional
   unit of resources yesterday

Gunter Stephan - Intertemporal Allocation of Natural Resources 2008   24
                           A Ramsey Approach

     Solow (1974)
     “It is very easy to substitute other factors for natural
     resources, then there is in principle no ‚problem‘. The
     world can, in effect, get along without natural resources ...“

     Georgescue-Roegen (1975)
     “One must have a very erroneous view of the economic
     process as a whole not to see that there are no material
     factors other than natural resources. To maintain further
     that ‘the world can, in effect, get along without natural
     resources’ is to ignore the difference between the actual
     world and the Garden of Eden “

Gunter Stephan - Intertemporal Allocation of Natural Resources 2008   25
                           A Ramsey Approach

    Why is it that neoclassical production                            …until now,…, mass balance has not been a
    functions do not satisfy the condition of mass                    controlling factor in the growth of industrial
    balance?                                                          economies
    Must production be interpreted as a kind of                       This is – no doubt – one aspect of
    physical transformation?                                          production
    Are economies embedded in a larger                                Certainly, and any attempts to model the
    environment, and totally dependent on it as                       dependence in a transparent way, so that it
    both source and sink for matter/energy                            can be incorporated in aggregative
    transformed by economic activity.                                 economics, are well-come


    Do you agree that the matter/energy                               No doubt everything is subject to the
    transformations required by economic activity                     entropy law, but this is of no immediate
    are constrained by the entropy law?                               practical importance for modeling



Gunter Stephan - Intertemporal Allocation of Natural Resources 2008                                                26

								
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