Lecture 12. Welfare Economics (welfare economics)
Recommended reading : 【Microeconomics】 Microeconomics Table of Contents
1. Efficiency
2. Equity
1. Efficiency (efficiency)
⑴ Overview
① Definition : Achieving the maximum effect with the minimum cost
② In other words, the economic resources that exist within an economy are not wasted at all and are utilized in the best possible way
③ The evaluation criterion for efficiency is Pareto efficiency
⑵ Feasible allocation (feasible allocation)
① Definition : An allocation that does not exceed the endowment of resources in the economy
② (Allocation of good X to A) + (allocation of good X to B) ≤ (total amount of good X in the economy)
⑶ Pareto efficiency : Also called Pareto optimality
① Definition : A state in which it is impossible to move to a new allocation without decreasing anyone’s utility level
○ That is, the most efficient state of resource allocation
○ Reason : Because all opportunities are being exploited
○ Here, “utility” means ordinal utility : it is assumed that the utilities of different people cannot be compared
② Pareto improvement : A change that benefits at least one person without harming anyone
③ Type 1. Pareto efficiency in exchange
○ Definition : Within the given quantities of goods, allocating them well so as to maximize the utilities of two people
○ Edgeworth box (Edward box) : also called an Edgeworth box
Figure. 1. Edgeworth box]
○ Every point inside the Edgeworth box employs (uses) all given economic resources
Figure. 2. Contract curve]
○ Contract curve (contract curve) : the curve connecting Pareto-efficient allocation points
○ In general, indifference curves are assumed to be convex to the origin
○ A point on the contract curve such as point G is a tangency point of a common tangent line to iA and iB
④ Type 2. Pareto efficiency in production
○ Definition : Using the given factors of production well to produce as much output as possible
○ As in Pareto efficiency in exchange, an Edgeworth box can be drawn
○ (Reference) Production possibility curve (production possibility curve; PPC)
○ By mapping (moving) points on the contract curve, one can obtain the production possibility curve
○ Overview
○ Simple definition : A curve showing combinations of goods that can be produced to the maximum in an economy
○ Precise definition : A graph showing combinations of two goods that can be produced under full employment in a society
○ Drawn in the first quadrant
○ Points farther from the origin than the PPC : impossible
○ Points closer to the origin than the PPC : inefficient
○ Law of increasing opportunity cost (law of increasing opportunity cost)
○ Meaning 1. In reality, the PPC is concave to the origin
○ Meaning 2. As the output of one good increases, the opportunity cost of that good increases
○ Meaning 3. The slope of the PPC increases (in absolute value)
○ Tip. The slope of the PPC represents opportunity cost
○ (Reference) If opportunity cost increases → concave to the origin; if constant → straight line; if decreasing → convex to the origin
○ Fundamental reason : As production increases, less efficient factors are brought into production, so opportunity cost rises
⑤ Type 3. Overall (comprehensive) Pareto efficiency (ref)]
○ For the economy-wide allocation of resources to be efficient, both consumption and production must achieve Pareto efficiency
○ 1st. For each point on the PPC, there is a corresponding Edgeworth box
○ 2nd. For each Edgeworth box, one can draw a contract curve
○ 3rd. Along the contract curve inside each Edgeworth box, one can draw a utility-possibility curve
○ 4th. If all utility-possibility curves are gathered and smoothly connected (as an envelope), one can find the utility possibility frontier
○ Utility possibility frontier (utility possibility frontier; UPF)
○ The boundary between efficient allocations and inefficient allocations
○ Every point on a utility-possibility curve satisfies Pareto efficiency in consumption
○ Because only one point on the contract curve satisfies MRS = MRT, only that point lies on the utility possibility frontier
⑥ Limitations of Pareto efficiency
○ Using Pareto efficiency yields infinitely many solutions, so another criterion is needed to choose an “optimal” point
○ It cannot judge equity
⑷ First Fundamental Theorem of Welfare Economics
① Assumptions
○ Every consumer’s preference system satisfies strong monotonicity
○ No externalities exist in the economy
② Conclusion : In a competitive (general competition) market, a Pareto-efficient allocation of resources is achieved automatically
○ A modern interpretation of Adam Smith’s “invisible hand”
③ Limits of the market
○ The market does not guarantee equity in distribution
○ Sometimes problems arise even in terms of efficiency of resource allocation : due to imperfect competition or the existence of externalities
⑸ Second Fundamental Theorem of Welfare Economics
① Assumptions
○ Initial endowments are appropriately distributed
○ Everyone’s preferences are continuous, strongly monotonic, and convex
② Conclusion : A Pareto-efficient allocation can be realized as a competitive general equilibrium
○ This corresponds to the converse of the First Theorem
2. Equity (equity)
⑴ Overview
① How equitably resources in the economy are distributed among members of society
② It is impossible to find an objective standard of equity
⑵ Measuring inequality
① Inequality index (inequality index) : based on the premise that equalization implies equality
○ Income decile (income decile) : income groups consisting of people in 10% segments
○ Mean household income (mean household income) : the average income across all households
○ Median household income (median household income) : the household income of the median in the income distribution
○ Deciles distribution ratio (deciles distribution ratio)
○ Definition : (income of the bottom 40%) divided by (income of the top 20%)
○ Ranges from 0 to 2; the smaller the value, the more unequal the distribution
○ Quintile ratio
○ Definition : (income of the top 20%) divided by (income of the bottom 20%)
○ Takes values from 1 to ∞, like the deciles distribution ratio with numerator/denominator swapped
○ Poverty rate
○ Poverty line (poverty line) : an income level below which a household is judged to be in absolute poverty
○ Poverty rate (poverty rate) : the proportion of households whose income is below the poverty line in the total population
○ The poverty line is also called the minimum cost of living
○ Methods for estimating the minimum cost of living : Rowntree, Leyden, or a fixed proportion of mean or median income
○ Poverty indices : the Sen index, etc.
○ Gini coefficient (Gini coefficient)
○ Lorenz curve : a graph drawn by lining people up from poorest to richest and cumulatively plotting the share of total income
Figure. 3. Lorenz curve]
○ Let the crescent-shaped area be α, and let β be the area of the right triangle minus α; the Gini coefficient is defined as follows
○ It is 0 under complete equality and 1 under extreme inequality
○ Formula 1
○ Formula 2
○ (Distinct concept) Gini coefficient in information theory
○ Formalization
○ As the Gini coefficient moved from economics into machine learning and information theory, it came to suggest a similar “degree of inequality,” but its mathematical definition differs
○ Difference : If the distribution of variables is all identical,
○ Gini coefficient in economics : becomes extremely equal, so it takes the value 0
○ Gini coefficient in information theory : by the Cauchy–Schwarz inequality it takes its maximum value; intuitively, it is maximally disordered
○ Atkinson index : a method to measure inequality of income distribution based on society’s welfare function
○ Kuznets’ inverted-U hypothesis
② Problems : For the following reasons, it cannot fully represent inequality in living standards
○ Welfare programs (see below)
○ Life cycle of income (life cycle) : a characteristic pattern of income changes over a person’s lifetime
○ Permanent income (permanent income) : a person’s normal income, which should be distinguished from transitory income
○ Mobility between classes
⑶ Social welfare function (social welfare function; SWF) : a measure of equity
① Definition : A function that aggregates the preferences of members of society into a social preference
② Utilitarian values : the social welfare function is defined as the sum of individual utilities
③ Egalitarian values : lower weights for people with higher utility, higher weights for people with lower utility
④ Rawls (J. Rawls) : the utility of the member with the lowest utility level determines the welfare level of the society
⑤ Arrow (K. Arrow) : proved via the impossibility theorem that there is no rational criterion that can compare multiple social states
⑥ Theory of the second best : if not all efficiency conditions are satisfied, satisfying more of them does not necessarily increase social welfare
⑷ Political philosophies of income redistribution
① Egalitarianism (egalitarianism)
○ Equality is interpreted as an equal right to a minimum standard of living
② Utilitarianism (utilitarianism)
○ A political philosophy that the government should maximize the total utility of all members of society
○ Assumption : everyone has the same utility function and marginal product diminishes
○ Because marginal product diminishes, it argues that wealth should move from the rich to the poor
○ (Note) It seems, fundamentally, to distrust the market’s invisible hand
③ Liberalism (liberalism)
○ A political philosophy that the government should choose policies that a fair third party behind a “veil of ignorance” would choose
○ Based on John Rawls’s contractarian theory of justice
○ Principle 1. Maxi-min criterion (maxi-min criterion) : maximize the welfare of the poorest in society
○ Principle 2. Social insurance (social insurance) : protect citizens from the risks of disasters
④ Libertarianism (libertarianism)
○ A political philosophy that the government should only punish crime and enforce contracts, and should not redistribute income
○ Libertarians consider equality of opportunity (procedural equality) more important than equality of outcomes
⑸ Welfare programs
① In-kind transfer (in-kind transfer) : assistance provided to the poor in the form of goods or services instead of cash
② Means-tested program (means-tested program) : provides benefits when an individual or household income is below a certain level
③ Progressive taxation
④ Negative income tax (negative income tax)
○ A system in which the government pays subsidies to low-income households rather than taxing them
○ Advantage : recipients can receive benefits without stigma
○ Disadvantage : excessive cost; not a fundamental solution
⑤ Social security (social security) : provides income after retirement through payroll taxes
⑥ Unemployment insurance (unemployment insurance) : provides a portion of wages to workers who lost their jobs until they find a new one
⑦ Health insurance
○ Individuals pay a fixed cost each year and are promised payment for most of the medical expenses they will need later
○ If health insurance enrollment were completely voluntary, healthy people would not enroll, so premiums would rise
○ Compared with private health insurance, employer-based health insurance is less voluntary, so premiums become lower
○ Patient Protection and Affordable Care Act (Obamacare)
○ Also called PPACA (patient protection and affordable care act) or ACA
○ Focuses on supporting the uninsured and reducing healthcare costs
⑹ Limitations of welfare programs
① Cannot eradicate poverty at its root
② Overall decline in economic efficiency : reduced motivation of high-income earners, “welfare dependency” among low-income earners, etc.
Entered: 2020.11.23 20:21