Saku Aura Department of Economics - University of Missouri 1 / 28
Normative (welfare) economics Analysis of efficiency (and equity) in: resource sharing production in any situation with one or more economic/social actors with well-defined objectives Not covered in detail in the textbook Supplementary reading: Pindyck and Rubinfeld, Chapter 16 (8th edition). 2 / 28
Analysis of resource sharing Pure Exchange Economy Two goods, two individuals Our running example: Bob - Anne Food - Clothing 3 / 28
Edgeworth box Anne s preferences Food Clothing 4 / 28
Edgeworth box Resource constraints Available Food Food Bob's clothing Bob's origin Anne's Food A Clothing Anne's origin Anne's Clothing Available Clothing 5 / 28
Edgeworth box Bob s preferences Food Utility Increases Clothing 6 / 28
Edgeworth box An allocation example Food Bob's Indifference Curve Anne's Indifference Curve A Clothing 7 / 28
Pareto improvement A Pareto Improvement is a situation where at least one person is made better off without hurting anyone else. Food Allocations better than A Bob's Indifference Curve Anne's Indifference Curve A Clothing 8 / 28
Pareto efficiency An allocation is Pareto efficient (or efficient, optimal or Pareto optimal ) if No Pareto improvements are possible In plain English: It is impossible to rearrange the allocation and make at least one person better off without hurting someone else No free lunches: just trade offs 9 / 28
Efficiency and tangency Tangency (or non-crossing) of indifference curves required for efficiency (in an interior allocation) Food 1: Better for Anne, worse for Bob 2 1 2,3: Worse for both 4: Better for Bob, worse for Anne 4 B 3 Clothing 10 / 28
Boundary point C is an efficient point Food C Bob cares almost solely about clothing in this example Clothing 11 / 28
Formal proof of the tangency condition Assign one of the individuals (say Bob) a fixed level of utility u b (f b, c b ) = ū. Maximize the utility of Anne subject to Bob s utility constraint and the total resource constraints For simplicity let there be 10 units of both food and clothing each In our 2 person, 2 good case there is only one degree of freedom 12 / 28
Math of the tangency condition max u A (f A, c A ) {f A,c A,f B,c B } Subject to u B (f B, c B ) = ū f A + f B = 10 c A + c B = 10 13 / 28
Math continued Substituting in the resource constraint we have a LaGrangian: ( ) max {f A,c A } u A (f A, c A ) + λ u B (10 f A, 10 c A ) ū Taking the first-order conditions and rearranging gives: u A f u A c = ub f u B c 14 / 28
Example Ann: Perfect substitutes u A (f, c) = f + c. Bob: Cobb-Douglas U B (f, c) = log f + log c. Efficiency: MRS A = MRS B 1 = cb f B f B = c B In this example, Bob should always consume equal amounts of food and clothing 15 / 28
Contract curve Contract curve = the set of efficient points Pareto optimality is satisfied by many points Without altruism: Giving everything to one person is optimal Food Clothing 16 / 28
Production economy: partial equilibrium Reminders: consumer surplus, producer surplus, total surplus Producer Surplus=Variable Profits Total Surplus= Producer Surplus+ Consumer Surplus Price S P* Consumer surplus Producer surplus D Q* Quantity 17 / 28
Optimality of the market equilibrium Price Positive surplus S Negative surplus D Under production Q* Over Quantity production 18 / 28
Optimality of the market equilibrium With production, efficiency requires equality of demand and supply Using inverse demand and inverse supply curves: Marginal Willingness to Pay = Marginal Cost 19 / 28
First welfare theorem Huge significance for the classical liberal (conservative) school of thought Goes back to Adam Smith Under certain conditions: markets deliver first-best (Pareto-Efficient) outcomes 20 / 28
First welfare theorem intuition In a market equilibrium prices decentralize the need for information: All the relevant information about scarcity and production cost; and all the relevant information about consumer preferences and needs; is in the prices 21 / 28
Sketch of a proof for the first welfare theorem Consumers Partial equilibrium with production Pareto Optimality Equality of the MRS between cons Demand=Supply 22 / 28
First welfare theorem requires no market failures Market Failures (examples): 1 Market power 2 Externalities 3 Public goods 4 Informational problems: Moral Hazard Adverse Selection Market failures are a potential reason for a government intervention 23 / 28
Equity Another reason for interventions Food Potential market outcome Bob's origin Anne's origin Clothing 24 / 28
Equity Under very specialized conditions the Second Welfare Theorem holds This says that the only intervention needed is costless redistribution of income/wealth Not relevant for practice: costless redistribution not possible The equity-efficiency trade off a key to understanding policy 25 / 28
Utilitarianism and the social welfare function In order to represent equity-efficiency trade offs mathematically economists often rely on a Social Welfare Function The form usually used is the sum of individual utilities Social Welfare W = u A + u B One justification: For policy analysis we need to be able to compare individual utilities Provides a reasonable presentation of the relevant equality-efficiency trade offs for a particular (small) policy change Can be justified through Veil of Ignorance experiments (Rawls, Harsanyi) 26 / 28
Utilitarianism: background Historically an English-speaking school of moral philosphy Part of the consequentialist school of moral philosophy: the end result is all that matters Contrast with proceduralism: fair process is all that matters 27 / 28
Utilitarianism: some criticisms Remember your micro: Utility is an ordinal concept. Here we are (through value judgements) forcing cardinality Choice of welfare function is subjective Arrow s Impossibility Theorem limits the domain of applicability Without other constraints can lead to paradoxical conclusions: Mankiw/Hamermesh: height tax, beauty tax Population ethics: repugnant conclusions Further (very optional reading): collected works of Amartya Sen, a textbook by Peter Lambert ( The Distribution and Redistribution of Income ) 28 / 28