Social Choice in Practice

Cullis and Jones: Chapter 2

Stiglitz: Chapter 5

• The government attempts to identify and measure the net benefits (benefits minus costs) received by different groups

• Second whether the project is a Pareto improvement, every one is better off.

• If Pareto improvement is not met, government makes judgment based on summary statistics of efficiency and equity.

• Efficiency is sum of losses or gains by individuals.• Equity is measured by some measure of inequality.

• There are cases where trade off between equity and efficiency have to made.

• Example: More a tax redistribute income , the greater the inefficiencies are introduced.

Measuring Benefits

• The benefits of a program to a particular individual is measured by willingness to pay (which reflects preferences), which is different from what from what he has to pay (market price).

• The willingness to pay concept (keeping the individual at the same level of utility) is used to construct demand curve called compensated demand curve.

• For Marshallian demand curve we need to know how much units of a commodity bought at each price.

• If the price falls the individual the cheaper goods for other goods called the substitution effect. If the individual is better off and buy the same amount of good with less money and have some money left over, it is called income effect.

• If we take away this extra money, we have the compensated demand curve, we eliminate the income effect.

• So the compensated demand curve reflect only the substitution effect

Consumer Surplus

• The difference between what an individual is willing to pay and what he has to pay is called consumer surplus.

• The consumer surplus is area under the compensated demand curve and the price line.

• Aggregate social benefits measured by adding up the benefits received by all individual.

• The net benefit or efficiency of a project is difference between total willingness to pay and total cost.

• How much the individual is willing to give up to have the inefficiency eliminated.

• Example inefficiency caused by cigarette tax because it causes individual to forego more preferred consumption to less preferred consumption. So eliminating the cigarette tax and imposing a lump sum tax leaves the individual welfare unchanged. The difference between the revenue raised by lump sum tax is called the deadweight loss or excess burden.

Distributional effects

• The Poverty index measures the fraction of population whose income lies below a critical threshold income level.

• Poverty gap measures how much income we give to poor to bring them up to the poverty thresholds.

Social Choices

• The compensated Principle

• Trade-off across measures

• Weighted net benefit

Consumer Surplus: Measuring Welfare Effect

• Individual consumer surplus as the excess of the price which he would be willing to pay rather go without the thing over which he actually does pay.

• The individual demand curve for good X presents quantity per unit that would be chosen at different prices.

• Demand curve can be interpreted in terms of prices that individuals are willing to pay for successive increase in quantity of particular good per period, that is estimate of the value of good to the individual are worth area under the demand curve.

• Difference between what an individual is willing to pay and the market price individual actually does pay is used to estimate consumer surplus.

• At price P3 consumer actually pays OP3BQ3 that is P3 per unit, triangle AB P3 equals consumer surplus.

• If the price of good falls the consumer surplus increases by P3 BC P4 .

• If the government reduces the price of the good by the subsidy of P3P4, this would worth P3 BC P4 to the consumer. The consumer surplus is used to evaluate the welfare effect of this government measure. Individual would be willing to give up P3 BC P4

• If the government introduces a change that improved conditions for tax-payers, if they are asked how much they would pay for such a change, maximum they pay no positive income effect associated with price fall, as real income will be maintained.

• A fall in price increases the real income of the individual. It enable individual to purchase more of all goods.

• Individual buys more of a good because as the price falls there is substitution effect in favor of cheaper good. For normal good he also buys more because as real income increases, there is income effect.

• If the government is considering a change that improved tax-payers, how much the tax-payer will pay for such a change, if they pay maximum, then there could be no income effect associated with price fall.

• When money income is held constant the individual demand curve is D. Holding real income constant we get compensated demand curve C1 which lie inside the Marshallian demand curve. The curve C2 by asking what is the maximum sum that individual pay for an additional unit of the good holding real income constant

• When the price falls from P1 to P2• According to D the individual would pay P1ABP2and holding

real income constant he is willing to payP1ACP2 a smaller sum, called price compensating variation.

• Price compensating variation, that is the maximum sum that individual would be prepared to give up for a favorable change

• The price fall shift the budget line the shift from AB to AC, and consumer maximizing welfare point shift from B* to C*,.

• If we shift the budget line parallel to AC we maintain the relative prices but reduce the real income of the individual.

• The amount of income we have taken from the individual is AD equal to P1ACP2 in figure a...

• If the price fall is proposed but not fall actually.• If the price fall, the individual will be on a higher level of real income

and compensated demand curve is C2 Indifference curve IC2. • The amount given to the individual if the price had fallen is E by

drawing budget line parallel to AB, The amount of money P1DBP2 is called price equivalent variation.

• The price compensating variation is not equal to price equivalent variation. The maximum sum of money that individual give up holding real income constant to experience fall in prices of good X is typically less than the amount of money he would require to make him as well off as if the price of good had fallen by same amount.

Equity and Willing to Pay

• The rationale of the ability to pay approach is that individual tax payer should make an equal sacrifice when they pay their tax

• Income is used as measure of ability to pay. What tax system proportional, regressive or progressive is consistent with ability to pay,

• The extent to which unequal be treated equally called vertical equality.

• The equal treatment of equals is called horizontal equity.

• In the figure A and B are assumed to have same marginal utility. A is assumed to be rich and B is poor, so YA is greater than YB.

• Horizontal equity is met when with the same income pay the same tax.

• The vertical equity depends both on the form that MU of income take and on equal sacrifice rule.

• Equal absolute sacrifice involves A and B losing the same amount of utility, so that after tax income YAa and YBb for A and B respectively involve their losing utility area YAABYAa equal to YBCDYBa. The amount of tax paid equal to (YA-YAa)+(YB-YBa).

• With diminishing utility of income, tax liability increases with income’

• However, proportionality, progression and regression depends whether the elasticity of MU of income w.r.t. income is equal, less than or greater than unity

• Equal proportional sacrifice require the proportion of utility lost by A and B to be the same for A and B

• The tax paid is (YA-YAp)+(YB-YBp)

• Equal marginal sacrifice involve A paying YA-YAm and B paying YB-YBm so that the marginal utility associated with the post-tax income is YAmF=YBmH.

• In this case any decreasing marginal utility implies a progressive income tax.

• Equal absolute sacrifice=U(Y)-U(Y-T).

• Elasticity of the marginal utility of income is less than unity.

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• Equal proportional sacrifice=

• U(Y)-U(Y-T)/U(Y)

• Demising but straight line marginal utility of income.

• Equal marginal sacrifice

• Any decreasing marginal utility.

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