Welfare Economics
and
Sustainability
Terms & Concepts
• Resources, Market commodities and
services, Externalities, Public Goods,
Policies
• Production, Consumption, Cost, Profit,
Economic Surplus, Utility, Welfare
• Indifference curve, possibility frontier
Production Economics
• Profit maximization  Cost minimization
• Efficiency implies
– Using a given amount of resources, one
cannot produce more of one good without
producing less of at least some other good
• All possible efficient production decisions
form the production possibility frontier
Normal Production Function
X2
Production
Factor 2
Y = f(X1,X2)
YA > YB > YC
Y=YA
Y=YC
Y=YB
X1 Production Factor 1
Leontief Production Function
X2
Production
Factor 2
Y=Min(X1/a,X2/b)
Y = YB
Y = YA
X1 Production Factor 1
Cost function
X2
Production
Factor 2
C = r2*X1+r1*X1
X2 = C/r2-(r1/r2)*X1
X1 Production Factor 1
Normal Production Function
X2
Production
Factor 2
Y = f(X1,X2)
YA > YB > YC
Y=YA
Y=YC
Y=YB
X1 Production Factor 1
Leontief Production Function
X2
Production
Factor 2
Y=Min(X1/a,X2/b)
Y = YB
Y = YA
X1 Production Factor 1
Production Possibility Frontier
Y2
Production
Good 2
Y = (Y1,Y2) = f(X1,X2) = f(X)
YA = f(XA)
YB = f(XB)
YC = f(XC)
Y1 Production Good 1
Production Possibility Frontier
Y2
Production
Good 2
Leontief Production Function
YA = f(XA)
YB = f(XB)
YC = f(XC)
Y1 Production Good 1
Revenue (R)
Y2
Production
Good 2
R = p1*Y1+p2*Y2
Y2 = R/p2-p1/p2*Y1
Y1 Production Good 1
Optimal Production Level
Y2
Production
Good 2
Y2*
Y1*
Production
Good 1
Optimal Production Level
Y2
Production
Good 2
Leontief Production Function
Y1 Production Good 1
Utility Economics
• Utility (U) function of a person can be
measured and depends on consumption
(C) of goods and services
– market and non-market goods
• Social welfare (SW) function can be
measured and depends on utility of all
people in a society
– may include expected utility of future people
Utility (U) Indifference Curves
Consumption
Good 2
U = U(C1,C2)
U = UA
U = UB
U = UC
Consumption Good 1
Budget (B) Constraint
Consumption
Good 2
p1*C1+p2*C2 ≤ B
B/p2
C2 ≤ B/p2-(p1/p2)*C1
B/p1
Consumption
Good 1
Optimal Consumption Levels
Consumption
Good 2
U = UA
C2*
U = UB
U = UC
C1*
Consumption
Good 1
Utility Possibility Frontier (UPF)
• Shows the maximum utility of agents for a
given amount of outputs
• Combining all utility possibility frontiers
yields the grand utility possibilities frontier
(GUPF)
Pareto Efficiency / Optimality
• No pareto improvement (PI) possible
• No change in the allocation of goods and
services can improve the utility of at least
one person without decreasing the utility of
at least another person
• Vilfredo Federico Damaso Pareto (1848
1923) was an Italian engineer, sociologist,
economist, and philosopher
Pareto Optimality
• Strong: no alternative allocation of goods
where at least one is better and no one is
worse off
• Weak: no alternative allocation of goods
where all are better off
• Actual: true PI without compensation
• Potential: compensation possible
• Kaldor-Hicks Criterion: judge policy
efficiency using potential PI
Social Welfare Function
• represents the joint utility of several (many, all)
people
• includes implicitly or explicitly equity (fairness)
considerations
• developed by Abram Bergson (1938,1948,
1954), Paul Samuelson (1947, 1950, 1956),
Gerhard Tintner (1946) and Jan de Van Graaff
(1957)
• "Bergson-Samuelson" social welfare function
SW = SW(U1, U2, ..)
Social Optimum
• First Fundamental Welfare Theorem:
every competitive equilibrium is Paretooptimal.
• Second Fundamental Welfare Theorem:
every Pareto-optimal allocation can be
achieved as a competitive equilibrium after
a suitable redistribution of initial
endowments.
Social Welfare (SW) Function, 1
Utility
Person 2
SW Indifference Curves
45°
SW = SWB
SW = SWA
Utility Person 1
Social Welfare (SW) Function, 2
Utility
Person 2
SW = SWB
SW = SWA
Utility Person 1
Social Welfare (SW) Function, 3
Utility
Person 2
SW = SWB
SW = SWA
Utility Person 1
Social Optimum
Utility
Person 2
Grand Utility
Possibility Frontier
SW = SWB
SW = SWA
Utility Person 1
Externality – Definition, 1
Definition in terms of effects :
“an externality is present whenever some
economic agent (say A’s) welfare (utility
or profit) is affected by real (ie. nonmonetary) variables whose values are
chosen by others without particular
attention to the effects on A’s welfare”
Externality – Definition, 2
Definition in terms of cause:
“an externality is present whenever there
is insufficient incentive for a potential
market to be created for some good and
the non-existence of the market leads
to a non Pareto optimal equilibrium”.
Externality and Property
Rights
• Private property rights absent for
external goods (transaction cost higher
than private benefits from
internalization)
• Without property rights there is no
market
• Without market, allocation of good is
not efficient (Market failure)
Examples
• a construction company trucking
through a private garden
• a farmer polluting ground water through
excess fertilization
Similar events but different outcomes.
Externality Types
• positive (beneficial) or negative
(harmful)
• consumption or production related
• depletable (private) or non-depletable
(public)
• stock or flow related
• point or not point source
Agricultural Externalities
• are often negative (water, air, and soil
pollution, biodiversity, habitat reduction,
erosion)
• can be positive (open landscape, emission sink)
• relate to production
• are mostly non-depletable
• arise from non-point sources
• local (odor), regional (water), or global (GHG)
Pesticide Externality, 1
Use of pesticides by farmer A wipes out pests
that might affect farmer B.
• positive?
• production externality
• primarily a flow externality (plus a possible
stock effect by reducing the breeding pool)
• local
• depletable (private)
Pesticide Externality, 2
Use of pesticides by farmer A increases
pesticide resistance, reducing
effectiveness of pesticides available to
other farmers.
• negative
• a production externality
• a stock effect (resistance arises through
cumulative use)
• mutual (farmer A is affected too)
• wider-than-local, potentially global
• non-depletable?
Fertilizer Externalities
• Decrease in species diversity, promotion
of few fast growing grasses
• Eutrophication/Hypoxia (Fish killing)
• Increase leaching of potassium and
calcium (mobilizing aluminum)
• Human health effects (nitrite poisoning
of babies)
Fertilization: Costs and Benefits
Value
social cost
yield function
social net benefit
0
Fertilizer Amount
Value
Marginal Effects
200
Value
150
social cost
social net benefit
private benefit
100
50
0
0
-50
-100
-150
-200
-250
Marginal private benefit
= Marginal social cost
Marginal private
benefit = marginal
private cost
Fertilizer Amount
Fertilizer Externality Effects
• Social and private marginal costs of
fertilization differ - so prices reflect
private costs, not social costs.
• Individual profit maximizing behavior
leads to Pareto inefficiency.
Leakage
• unintended flows of economic activities
across space, time, and/or sectors and
their consequences for non-market goods
and services
• relates to commodity trade and can be
couteracted through trade policies, i.e. socalled border tax adjustments
Scope of Sustainability Efforts
• Time
• Space
(Current period – Entire Future)
(Local – Global – Universal)
• Commodities (Individual – All)
• Resources (Individual – All)
• Externalities (Individual – All)
Scope of Sustainability Efforts
Leakage
• Time
• Space
High
Low
(Current period – Entire Future)
(Local – Global – Universal)
• Commodities (Individual – All)
• Resources (Individual – All)
• Externalities (Individual – All)