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