Chapter 4
Welfare economics and the
environment
, Introduction
• When economists consider policy questions relating to the environment
they draw upon the basic results of welfare economics.
• We consider those results from welfare economics that are most relevant
to environmental policy problems.
Steps in our exposition:
1. State and explain the conditions required for an allocation to be (a)
efficient and (b) optimal.
2. Consideration of how an efficient allocation would be brought about in a
market economy characterised by particular institutions.
3. Market failure: situations where the institutional conditions required for
the operation of pure market forces to achieve efficiency in allocation
are not met (looked at in relation to the environment).
,Part 1 Efficiency and optimality
, The setting
• At any point in time, an economy will have access to particular quantities of
productive resources.
• Individuals have preferences about the various goods that it is feasible to produce
using the available resources.
• An allocation of resources describes what goods are produced and in what
quantities they are produced, which combinations of resource inputs are used in
producing those goods, and how the outputs of those goods are distributed
between persons.
• In Parts 1 and 2 we make two assumptions:
1. No externalities exist in either consumption or production
2. All produced goods and services are private (not public) goods
• For simplicity, strip the problem down to its barest essentials:
– economy consists of two persons (A and B);
– two goods (X and Y) are produced;
– production of each good uses two inputs (K for capital and L for labour) each available in a
fixed quantity.
, Utility functions
The utility functions for A and B:
A A A A
U = U (X , Y )
B B B B
U = U (X , Y )
Marginal utility written as and defined by
U AX U A /X A
with equivalent notation for the other three marginal utilities.
, Production functions
The two production functions for goods X and Y:
X X(KX , LX )
Y Y(K Y , LY )
Marginal product written as and defined by
MP Y/ L
Y
L
Y
with equivalent notation for the other three marginal products.
,Marginal rate of utility substitution for A:
• the rate at which X can be substituted for Y at the margin, or vice versa, while holding the
level of A's utility constant
• It varies with the levels of consumption of X and Y and is given by the slope of the
indifference curve
• Denote A's marginal rate of substitution as MRUS A
• Similarly for B
The marginal rate of technical substitution in the production of X:
• the rate at which K can be substituted for L at the margin, or vice versa, while holding
the level output of X constant
• It varies with the input levels for K and L and is given by the slope of the isoquant
• Denote the marginal rate of substitution in the production of X as MRTS X
• Similarly for Y
The marginal rates of transformation for the commodities X and Y:
• the rates at which the output of one can be transformed into the other by marginally
shifting capital or labour from one line of production to the other
• MRTL is the increase in the output of Y obtained by shifting a small amount of labour
from use in the production of X to use in the production of Y, or vice versa
• MRTK is the increase in the output of Y obtained by shifting a small, amount of capital
from use in the production of X to use in the production of Y, or vice versa
, 4.1 Economic efficiency
• An allocation of resources is efficient if it is not possible to make
one or more persons better off without making at least one other
person worse off.
• A gain by one or more persons without anyone else suffering is a
Pareto improvement.
• When all such gains have been made, the resulting allocation is
Pareto optimal (or Pareto efficient).
• Efficiency in allocation requires that three efficiency conditions are
fulfilled
1. efficiency in consumption
2. efficiency in production
3. product-mix efficiency
Welfare economics and the
environment
, Introduction
• When economists consider policy questions relating to the environment
they draw upon the basic results of welfare economics.
• We consider those results from welfare economics that are most relevant
to environmental policy problems.
Steps in our exposition:
1. State and explain the conditions required for an allocation to be (a)
efficient and (b) optimal.
2. Consideration of how an efficient allocation would be brought about in a
market economy characterised by particular institutions.
3. Market failure: situations where the institutional conditions required for
the operation of pure market forces to achieve efficiency in allocation
are not met (looked at in relation to the environment).
,Part 1 Efficiency and optimality
, The setting
• At any point in time, an economy will have access to particular quantities of
productive resources.
• Individuals have preferences about the various goods that it is feasible to produce
using the available resources.
• An allocation of resources describes what goods are produced and in what
quantities they are produced, which combinations of resource inputs are used in
producing those goods, and how the outputs of those goods are distributed
between persons.
• In Parts 1 and 2 we make two assumptions:
1. No externalities exist in either consumption or production
2. All produced goods and services are private (not public) goods
• For simplicity, strip the problem down to its barest essentials:
– economy consists of two persons (A and B);
– two goods (X and Y) are produced;
– production of each good uses two inputs (K for capital and L for labour) each available in a
fixed quantity.
, Utility functions
The utility functions for A and B:
A A A A
U = U (X , Y )
B B B B
U = U (X , Y )
Marginal utility written as and defined by
U AX U A /X A
with equivalent notation for the other three marginal utilities.
, Production functions
The two production functions for goods X and Y:
X X(KX , LX )
Y Y(K Y , LY )
Marginal product written as and defined by
MP Y/ L
Y
L
Y
with equivalent notation for the other three marginal products.
,Marginal rate of utility substitution for A:
• the rate at which X can be substituted for Y at the margin, or vice versa, while holding the
level of A's utility constant
• It varies with the levels of consumption of X and Y and is given by the slope of the
indifference curve
• Denote A's marginal rate of substitution as MRUS A
• Similarly for B
The marginal rate of technical substitution in the production of X:
• the rate at which K can be substituted for L at the margin, or vice versa, while holding
the level output of X constant
• It varies with the input levels for K and L and is given by the slope of the isoquant
• Denote the marginal rate of substitution in the production of X as MRTS X
• Similarly for Y
The marginal rates of transformation for the commodities X and Y:
• the rates at which the output of one can be transformed into the other by marginally
shifting capital or labour from one line of production to the other
• MRTL is the increase in the output of Y obtained by shifting a small amount of labour
from use in the production of X to use in the production of Y, or vice versa
• MRTK is the increase in the output of Y obtained by shifting a small, amount of capital
from use in the production of X to use in the production of Y, or vice versa
, 4.1 Economic efficiency
• An allocation of resources is efficient if it is not possible to make
one or more persons better off without making at least one other
person worse off.
• A gain by one or more persons without anyone else suffering is a
Pareto improvement.
• When all such gains have been made, the resulting allocation is
Pareto optimal (or Pareto efficient).
• Efficiency in allocation requires that three efficiency conditions are
fulfilled
1. efficiency in consumption
2. efficiency in production
3. product-mix efficiency
