Welfare Economicsand

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

X1 Production Factor 1

X2

ProductionFactor 2

Y=YA

Y = f(X1,X2)

Y=YBY=YC

YA > YB > YC

Leontief Production Function

X1 Production Factor 1

X2

ProductionFactor 2

Y = YB

Y = YA

Y=Min(X1/a,X2/b)

Cost function

X1 Production Factor 1

X2

ProductionFactor 2

X2 = C/r2-(r1/r2)*X1

C = r2*X1+r1*X1

Normal Production Function

X1 Production Factor 1

X2

ProductionFactor 2

Y=YA

Y = f(X1,X2)

Y=YBY=YC

YA > YB > YC

Leontief Production Function

X1 Production Factor 1

X2

ProductionFactor 2

Y = YB

Y = YA

Y=Min(X1/a,X2/b)

Production Possibility Frontier

Y1 Production Good 1

Y2

ProductionGood 2 YA = f(XA)

Y = (Y1,Y2) = f(X1,X2) = f(X)

YB = f(XB)

YC = f(XC)

Production Possibility Frontier

Y1 Production Good 1

Y2

ProductionGood 2 YA = f(XA)

Leontief Production Function

YB = f(XB)

YC = f(XC)

Revenue (R)

Y1 Production Good 1

Y2

ProductionGood 2

R = p1*Y1+p2*Y2

Y2 = R/p2-p1/p2*Y1

Optimal Production Level

Production Good 1

Y2

ProductionGood 2

Y2*

Y1*

Optimal Production Level

Y1 Production Good 1

Y2

ProductionGood 2

Leontief Production Function

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 1

ConsumptionGood 2

U = UB

U = UC

U = UA

U = U(C1,C2)

Budget (B) Constraint

Consumption Good 1

ConsumptionGood 2 p1*C1+p2*C2 ≤ B

C2 ≤ B/p2-(p1/p2)*C1

B/p2

B/p1

Optimal Consumption Levels

Consumption Good 1

ConsumptionGood 2

U = UB

U = UC

U = UA

C1*

C2*

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 Pareto-optimal.

• 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 1

UtilityPerson 2

SW Indifference Curves

SW = SWB

SW = SWA

45°

Social Welfare (SW) Function, 2

Utility Person 1

UtilityPerson 2

SW = SWB

SW = SWA

Social Welfare (SW) Function, 3

Utility Person 1

UtilityPerson 2

SW = SWB

SW = SWA

Social Optimum

Utility Person 1

UtilityPerson 2

SW = SWB

SW = SWA

Grand Utility Possibility Frontier

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. non-monetary) 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, 2Use 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)

Val

ue

Fertilizer Amount

social costyield function

social net benefit

Fertilization: Costs and Benefits

0

-250

-200

-150

-100

-50

0

50

100

150

200

Val

ue

Fertilizer Amount

social costsocial net benefit

private benefit

Marginal Effects

Marginal private benefit= Marginal social cost

Marginal private benefit = marginal private cost

Val

ue

0

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. so-called border tax adjustments

Scope of Sustainability Efforts

• Time (Current period – Entire Future)

• Space (Local – Global – Universal)

• Commodities (Individual – All)

• Resources (Individual – All)

• Externalities (Individual – All)

Scope of Sustainability Efforts

• Time (Current period – Entire Future)

• Space (Local – Global – Universal)

• Commodities (Individual – All)

• Resources (Individual – All)

• Externalities (Individual – All)

Leakage High Low