WELFARE ECONOMICS Positive Economics: What “is” Concerned with understanding and predicting economic behaviour. Normative Economics: What “ought to be” Focus on using resources optimally so as to achieve maximum well-being for individuals in society.
SimilarityPropositions are logical deductions from a set of definitions and assumptions, realistic or not. • DifferenceEconomic "welfare" is not an observable variable. Welfare status of an individual is formally given by his/her utility level, which is unobservable.
UtilityA term generally used synonymously with happiness or satisfaction.Ui = U(qi1, qi2, ..., qin) Basic PropositionUtility increases as the amount of goods consumed increases.
Assumptions • a. Each consumer has exact and full knowledge of all information relevant to his consumption decisions : knowledge of the goods and services available and of their technical capacity to satisfy his wants, of market prices, and of his money income.
b. Ranking Assumptions 1. If A provides more satisfaction than B, then A is preferred to B. If B provides more satisfaction than A, then B is preferred to A. If both provide the same satisfaction, then the consumer is indifferent between A and B. • If A is preferred to B and B is preferred to C, then A is preferred to C. Preference is transitive. 3. If A is larger than B, then A is preferred to B.
Testing of Theory • Positive: Test the conclusions. • Normative: Examine the assumptions.
CONTROVERSIESIN WELFARE ECONOMICS Old Welfare Economics • 1. Accepts the principle that social gains are maximized by competitive markets. Therefore recommend policy measures that eliminate distortions.
2. Employs the technique of partial-equilibrium analysis in developing recommendations. • 3. Holds that the triangle-like area to the left of demand curve and above price is a serviceable money measure of utility to the consumers in a market. Similarly, the triangle-like area to the left of the supply curve and below price is an adequate money measure of welfare for producers in a market.
Criticisms by New Welfare Economists • P. A. Samuelson (1942):Consumer surplus is not well defined, i.e. consumer surplus is not generally a unique money measure of utility. Alternative money measures of welfare : compensating and equivalent variations
2. Pareto (1896), Kaldor (1939) and Hicks (1939):Pareto PrincipleSociety is better off when some people are made better off and no one is made worse off. • 3. Lipsey and Lancaster (1956-57):The partial approach to welfare economics may not be appropriate. There are circumstances under which distortions in one market imply that distortions must also exist in other sectors in order to make everyone as well off as possible.
PARETO OPTIMALITY Allocation: Specific consumption levels for each consumer and specific input and output levels for each producer. An allocation is Pareto-optimal if production and distribution cannot be reorganized to increase the utility of one or more individuals without decreasing the utility of others.
Conditions Necessary for the Attainment of Pareto Optimality • Second-order conditions are satisfied for each consumer and producer. • No consumer is satiated. • No external effects in either consumption or production.
PARETO OPTIMALITY FOR CONSUMPTION Utility functions: U1(q11, q12), U2(q21, q22) Constraints: q11 + q21 = q1o q12 + q22 = q2o
Problem Maximize utility of consumer I subject to these constraints and the utility of consumer II at U2o = constant.
U1* = U1(q11, q12) + [U2(q1o - q11, q2o - q12) - U2o] FOC's U1*/q11 = U1/q11 - U2/q21 = 0 U1*/q12 = U1/q12 - U2/q22 = 0 U1*/ = U2(q1o - q11, q2o - q12) - U2o = 0
U1/q11U2/q21----------- = -----------U1/q12U2/q22 MU11 MU21------- = -------MU12 MU22 MRS1 = MRS2
02 q2 U2o A • U1o B U1’ q1 01
Utility Possibilities Frontier U2 UPF U1 0
In perfectly competitive market MU11 MU21 p1------- = ------- = ----MU12 MU22 p2 Each utility-maximizing consumer equates his MRS for Q1 and Q2 to their price ratio
q2 • A p1 Uo p2 q1 0
PARETO OPTIMALITY FOR PRODUCTION Production functions: q1 = f1(x11, x12), q2 = f2(x21, x22) Constraints: x11 + x21 = x1o x12 + x22 = x2o
Problem Maximize output of good I subject to these constraints and the output of good II at q2o = constant.
L = f1(x11, x12) + [f2(x1o - x11, x2o - x12) - q2o] FOC's L/x11 = f1/x11 - f2/x21 = 0 L/x12 = f1/x12 - f2/x22 = 0 L/ = f2(x1o - x11, x2o - x12) - q2o = 0
f1/x11f2/x21--------- = -----------f1/x12f2/x22 MP11 MP21------- = -------MP12 MP22 MRTS1 = MRTS2
02 x2 q2o A • q1o B q1’ x1 01
Production Possibilities Frontier q2 PPF q2o U2o U2’ U1’ U1o q1 q1o 0
In perfectly competitive marketMP11 MP21 r1------- = ------- = ----MP12 MP22 r2 Each profit-maximizing producer equates his MRTS for x1 and x2 to their factor price ratio
x2 • A r1 qo r2 x1 0
PARETO OPTIMALITY IN GENERAL Utility Functions:Ui = Ui(qi1*, ..., qis*, xi1o - xi1*, ..., xino - xin*) i = 1, ..., m
where qik* is the quantity of Qk consumed by the ith consumer xijo is the consumer's fixed endowment of the jth primary factor xij* is the amount that the consumer supplies to producers, and xijo - xij* is the amount that he consumes.
Production Functions:Fh(qh1, ..., qhs, xh1, ..., xhn) = 0 h = 1, ..., N where qhk is the output of Qk by the hth firm, and xhj is the amount of Xj which the firm uses.
Problem Maximize consumer I' utility subject to these constraints and the utility of all other consumers at Uio = constant.
Z = U1(q11*, ..., q1s*, x1no - x1n*) + i=2,...,mi[Ui(qi1*, ..., qis*, xino - xin*) - Uio] + h=1,...,NhFh(qh1, ..., qhs, xh1, ..., xhn) + j=1,...,nj( i=1,...,mxij* - h=1,...,Nxhj) + k=1,...,sk( h=1,...,Nqhk - i=1,...,mqik*) i, h, j and k are Lagrangian multipliers.
FOC's Z/q1k* = U1/q1k* - k = 0 Z/qik* = iUi/qik* - k = 0 Z/qhk = hFh/qhk + k = 0 Z/x1j* = U1/(x1jo - xij*) + j = 0 Z/xij* = Ui/(xijo - xij*) + j = 0 Z/xhj = hFh/xhj - j = 0 where i = 2,...,m; h = 1,...,N; k = 1,...,s; and j = 1,...,n.
Solving for j /k , jU1/q*1jUm/q*mj -- = ----------- = … = ----------- kU1/q*1kUm/q*mk F1/q1jfN/qNj= --------- = … = ------- F1/q1kfN/qNk j,k = 1,…,s
Marginal Rate of Substitution (MRS) for all consumers and the Marginal Rate of Transformation (MRT) for all producers must be equal for every pair of produced goods.
Solving for j /k , jU1/(xo1j – x*1j) Um/(xomj – x* mj) -- = -------------------- = … = --------------------- kU1/(xo1k – x*1k) Um/(xomk – x*mk) F1/x1jfN/xNj= --------- = … = -------F1/x1kfN/xNk j,k = 1,…,n
Marginal Rate of Substitution (MRS) for all consumers and the Marginal Rate of Technical Substitution (MRTS) for all producers must be equal for every pair of primary goods.
Solving for j /k, jU1/(xo1j – x*1j) Um/(xomj – x* mj) -- = -------------------- = … = ------------------- kU1/q*1kUm/q*mk F1/x1jfN/xNj = --------- = … = --------- F1/q1kfN/qNk j = 1,…,n ; k = 1,…,s
The consumers' MRS between factors and commodities must equal the corresponding producers' rates of transforming factors into commodities, i.e. their Marginal Products.
Perfect CompetitionFor ConsumersMRS = pj/pk For ProducersVMPj = pj MPj = r i.e. pj = r/MPj VMPk = pk MPk = r i.e. pk = r/MPk
Since the same prices prevail for producers and consumers under perfect competition,MRS = pj/pk = MPk/MPj = MRT
1. Pareto criterion A policy increases social welfare if it benefits some members of society (in their own judgement) without harming anyone. Limitation Because most policies will benefit some and harm others, the Pareto criterion does not go very far, and it is biased in favor of the status quo.
UB Grand Utility Possibilities Frontier B UB’ UBo C A • UA UAo UA’
2. Kaldor-Hicks criterion: (Compensation Principle) A change is an improvement if those who gain from the change can fully compensate the losers and still retain some gain. Limitation i. it is possible (though unusual) for the Kaldor-Hicks criterion to indicate that a given policy increases social welfare but also to indicate that, after the change, a movement back to the original position also increases social welfare. ii. Since compensation is not actually required, the Kaldor-Hicks criterion is based on the assumption that the gain in utility of an individual whose money income rises is greater than the loss of utility to the individual whose income falls. This line of reasoning is based on interpersonal comparisons of utility, and social welfare need not be higher.
UB Grand Utility Possibilities Frontier D B UB’ UBo C A • E UA UAo UA’
3. Scitovsky criterion: double Kaldor-Hicks test A change is an improvement if it satisfies the Kaldor-Hicks criterion, and, after the change, a movement back to the original position does not satisfy the Kaldor-Hicks criterion.
UB Grand Utility Possibilities Frontier D B UB’ UBo C A • E UA UAo UA’
4. Bergson Social Welfare Function To overcome the second limitation of the Kaldor-Hicks criterion is to squarely face the problem of interpersonal comparison of utility. A particular policy can be said to increase social welfare it it puts society on a higher social indifference curve. Limitation A social welfare function is extremely difficult or impossible to construct by democratic vote (Arrows Impossibility Theorem).