文档介绍：Environment and Natural Resource Economics Course
Nanjing Agriculture University
September 4 to September 30, 2006
Lecturers: Volker Beckmann, Humboldt University Max Spoor, ISS, The Hague
Justus Wesseler, Wageningen University
Lecture 5 and 6
The efficient and optimal use of natural
resources
Lecturer: Dr. Justus Wesseler, Wageningen University
Objective for the two morning lectures are:
to develop a simple economic model built around a production function in which natural resources are inputs into the production process;
to identify the conditions that must be satisfied by an economically efficient pattern of natural resource use over time;
to establish the characteristics of a socially optimal pattern of resource use over time in the special case of a utilitarian social welfare function.
The economy and its production function:
The simple optimal resource depletion model
Production function with two inputs
For example Cobb-Douglas PF
For example CES PF
The natural resource R is essential, if Q = Q(K,R=0) = 0.
Elasticity of substitution, , between capital and resource:
Proportional change in the ratio of capital to the resource in response to a proportionate change in the ratio of the marginal products of capital and the resource, conditional on total output remaining constant.
Elasticity of substitution, , ranges between zero and infinity.
Production function isoquant is the locus of binations of inputs which, when used efficiently, yield a constant level of output:
= 0: no input substitution possible, (Leontief PF)
= : perfect substitution possible
0 < < : imperfect substitution possible
The social welfare function and an optimal allocation of natural resources
General social welfare function (SWF):
Utilitarian SWF:
Utility in each period a concave function of consumption level in that period, Ut = U(Ct):
In continuous time:
Objective: what properties for natural resource allocation must be satisfied, that the allocation maximi