Pareto Efficiency & Kaldor-Hicks Criterion (Eco 3 PDF)

The Pareto criterion It is a criterion for comparing alternative allocations of resources. The Pareto improvement: a reallocation of resources that makes at least one person better off without making anyone else worse off The Pareto Efficiency: an allocation of resources such that no person can be m...

The Pareto criterion It is a criterion for comparing alternative allocations of resources. The Pareto improvement: a reallocation of resources that makes at least one person better off without making anyone else worse off The Pareto Efficiency: an allocation of resources such that no person can be made better off without making another person worse off Assumptions The Pareto criterion is based on the following assumptions: Utilitarianism: Each individual is the best judge of their own wellbeing The well-being of a society is given by the sum of the well-being of the individuals that compose it The well-being of society increases if the utility of at least one individual increases without worsening that of another MRS, MRT and MRTS Marginal Rate of Substitution (MRS) The MRS between two assets measures the quantity of an asset that the individual is willing to give up in exchange for an additional unit of the other asset, for the same utility: - It measures the subjective equivalence between consumer goods - Graphically, it is the slope of the indifference curve - The MRS between goods X and Y for individual i is given by: where (∂Ui / ∂Xi) / (∂Ui / ∂Xi) is the ratio of the marginal utilities Moving along the indifference curve of the individual i towards increasing quantities of X and decreasing quantities of Y, we will have: Since along the same indifference curve the variations in utility compensate each other exactly: Exchange Efficiency: Consumer’s optimal choice Edgeworth Box 2 person / 2 good economy y Eve 0’ Fig leaves per year r v w u At “v”, how many apples and figs do Adam and Eve consume? 0 Adam s x Apples per year Indifference curves in Edgeworth Box Eve 0’ r E1 Fig leaves per year E2 E3 A3 A2 0 Adam A1 Apples per year s Beginning at Point g, how to make Adam better off without Eve becoming worse off Eve 0’ r Fig leaves per year Eg g h A Pareto Efficient Allocation p Ap Ah Ag 0 Adam Apples per year s Beginning at Point g, how to make Eve better off without Adam becoming worse off Eve 0’ r Fig leaves per year Eg g p Ep1 p1 A Pareto Efficient Allocation Ag s 0 Adam Apples per year Beginning at Point g how to make both Adam and Eve better off Eve 0’ r Fig leaves per year Eg g Pareto efficient Pareto improvement Ep2 p p2 p1 Ap2 Ag 0 Adam Apples per year s The Contract Curve Eve 0’ r Fig leaves per year Eg g The contract curve – locus of all Pareto efficient points p4 Ep2 p3 p2 p p1 Ap2 Ag 0 Adam s Apples per year Pareto Efficiency in Consumption Adam MRSaf = MRSaf Eve Where MRS: -is the rate at which an individual is willing to trade one good for another -is the absolute value of the slope of an indifference curve Exchange Efficiency The consumer maximizes his utility when, given the budget constraint, the quantity of an asset that he is willing to sell in exchange for a unit of another asset is equal to the ratio of the goods' prices. In perfect competition, the prices of goods are the same for all consumers; therefore, we will have: Exchange Efficiency: Assumptions Assets are private (rival and excludable) The marginal utility is positive and decreasing as the consumption of the good increases The inputs are available in given quantities The marginal product of the factors is positive and decreasing as the use of the factor increases Production functions (of goods) and utility functions (of individuals) are independent (between goods and between individuals) Efficiency in production - Before we were considering only the consumption and the quantity produced was given - Suppose instead that the quantities of inputs (T and L) for the two goods' production are given. What is the combination of inputs that allows an efficient Pareto production? Marginal rate of technical substitution (MRTS) The MRTS between two inputs: - measures the additional amount of an input necessary to compensate for the reduction of one unit of the other input to keep the output quantity unchanged - The MRTS between inputs T and L in the production of good X is given by: Production efficiency: best choice of the producer - An isoquant shows all combination of factors that produce a certain output - An isocost show all combinations of factors that cost the same amount. Isocosts and isoquants can show the optimal combination of factors of production to produce the maximum output at minimum cost. Production efficiency: the Edgeworth box Production efficiency The producer maximizes his profit when, given the budget constraint, the increase in one input necessary to compensate for the reduction of one unit of another input (to keep the production level constant) is equal to the input prices. In perfect competition, the prices of inputs are the same for all producers, therefore we will have: Marginal Rate of Transformation - MRT The MRT between two goods measures the additional quantity of a good that can be produced by reducing the production of the other good by one unit, for the same use of inputs The transformation curve and the MRT Also called the frontier of production possibilities. It shows the combinations of goods that can be efficiently obtained given the constraint of productive resources and technology It is the equivalent of the place of tangency points of isoquants (Edgeworth in production) Describes all efficient combinations in production The slope of the transformation curve is the MRT Fig leaves per year Production Possibilities Curve C It represents the points in the transformation curve where MRT x = MRT y │Slope│ = marginal rate of transformation w y 0 C x z Apples per year Conditions of Pareto Efficiency Efficiency in exchange (efficient allocation in the consumption of goods): It is the equality of the marginal rate of substitution (MRT) for each pair of goods among consumers Production efficiency (the efficient allocation of productive inputs): It is the equality of the marginal rate of technical substitution (MRTS) for each pair of inputs among producers Efficiency in the combination of the goods produced (the efficient composition of the product): It is the equality of the MRS, between each pair of goods for all consumers, and of the marginal rate of transformation (MRT) Overall Pareto efficiency where T denotes the transformation function (technological constraint): that is, the possible combinations of the two goods X and Y when the inputs are used efficiently Limits of the Pareto criterion Individualistic view, the rational individual is the best judge of himself (ethical individualism): - Does the individual always have all the relevant information to assess his well-being correctly? - Are individual preferences given, or can they evolve and depend on (endogenous) situations? It does not admit meritorious different needs to protect from those expressed by individuals: - Are there goods whose individual consumption could be considered desirable even if the individual does not express a need for them? Limits of the Pareto criterion It does not allow for the possibility of inter-personal comparisons: - it is not possible to compare different allocations along the efficiency frontier (i.e., other optimal allocations) It does not allow for the possibility of compensation between individuals: - If the individual utilities are incomparable, it is impossible to reasonably identify a monetary amount that compensates for any loss of utility (unless the subject himself establishes it, but in this case, it is again an exchange). Interpersonal comparisons We avoid academic debate by accepting Amartya Sen's reasonable objection: “We may be able to make interpersonal comparisons to some extent, but not in every comparison, nor of every type, nor with tremendous exactness” We may, for example, have no great difficulty in accepting that Emperor Nero's utility gain from the burning of Rome was smaller than the sum-total of the utility loss of all the other Romans who suffered from the fire.... There may, thus, be room for demanding 'partial comparability' -denying both the extremes: full comparability and no comparability at all.... It can also be shown that there may be no general need for terribly refined interpersonal comparisons for arriving at definite social decisions. A. Sen, Nobel Lecture (1998) Why is efficiency important? In microeconomics The market (by itself) produces efficient outcomes In economic policy In the presence of market failures, it is necessary to know what is efficient in order to intervene. On the Pareto criterion A Pareto improvement implies a change in the economy that leaves at least one part more satisfied and all the others no less satisfied. All achievable Pareto improvements should be voluntarily pursued by individuals. Once the exchanges that can be obtained voluntarily are exhausted, is there more to be done? And what if the subjects cannot voluntarily trade? An example - Two neighboring apartments: an old professor and a student. - The student wants to organize a party that generates a utility of € 50 for the student and a disutility of € 100 for the neighboring professor. - Each of the 30 guests would also have a utility of € 5 Is the organization of the party a Pareto improvement? Yet the total value generated by the party (€ 50 + € 150) is higher than the disutility of the elderly.... The Kaldor-Hicks criterion - Informally: a Kaldor-Hicks improvement is a change in the economy that increases the total "value" achieved by society as a whole. - Cf with the Pareto improvement... - The "value" that each gets is measured in monetary terms as the willingness to pay for it - K-H improvement may not be achievable voluntarily but requires external intervention The Kaldor-Hicks criterion - The improvement of K-H may involve winners and losers - As long as the winners earn more than the losers lose, society generates a net gain that can be redistributed. - There is the possibility of compensating - In the example: the student can pay € 40 and each guest € 3 to the senior teacher. - The professor earns (€ 40 + € 90) -100 € = € 30 - Students earn (€ 50-€ 40) + € 2 × 30 = € 70 The Kaldor-Hicks criterion - The professor earns (€ 40 + € 90) -100 € = € 30 - Students earn (€ 50-€ 40) + € 2 × 30 = € 70 in this case we can speak of potential Improvement. Pareto In almost all situations of "public choice," we face situations in which the possible Paretian exchanges are already exhausted, and there are potential improvements of KaldorHicks to be exploited. The «price" of Kaldor-Hicks “As long as the winners earn more than the losers lose...” - It is possible to use the K-H criterion if we accept that we can compare and sum the utilities of different individuals: we must in fact be able to compare the winners 'gains with the losers' losses... - The implicit hypothesis is that the utility is measurable through the willingness to pay... (we said that the party creates a disutility equal to € 100) Formal definition of a Kaldor-Hicks improvement - A change to the economy is a Kaldor-Hicks improvement if it could be turned into a Pareto improvement with monetary transfers - K-H improvements also called potential Pareto improvements ⬥ I get your car for free ⬥ If we combined this change with me giving you €3,500… ⬥ …then it would be a Pareto improvement ⬥ So even without the transfer, it’s a K-H improvement ⬥ we will call a change to the economy efficient if it is a Kaldor-Hicks improvement ⬥ A law A is more efficient than law B if moving from B to A is a Kaldor-Hicks improvement ⬥ and we’ll say a situation is efficient if there are no available Kaldor-Hicks improvements ⬥ an efficient situation is when there’s no way to make some people better off, without making some others worse off by more ⬥ we’re already getting maximal value out of all available resources Pareto efficiency vs KaldorHicks efficiency Pareto efficiency no available Pareto improvements impossible to help someone without hurting someone else kind of useless for comparing different policies efficiency no available K-H improvements impossible to help someone without hurting someone else more (impossible to increase total payoffs realized by everyone) One more example: is it efficient for me to drive to work instead of taking the metro? ⬥ Metro to LUMSA campus from where I live is 3€ ⬥ Driving is more convenient, but costs me €4 (gas) ⬥ Driving also imposes costs on other people: there’s more traffic, less parking, more pollution ⬥ Suppose when I drive to work, it makes 1,000 other people worse off by €0.01 each ⬥ By driving to work, I create €14 of total costs ⬥ what is privately efficient? ⬥ what is socially efficient?