THE EFFICIENCY OF PERFECT COMPETITION

THE EFFICIENCY OF PERFECT COMPETITION
Chapter 17 THE EFFICIENCY OF PERFECT COMPETITION MICROECONOMIC THEORY BASIC PRINCIPLES AND EXTENSIONS EIGHTH EDITION WALTER NICHOLSON Copyright ©2002 by South-Western, a division of Thomson Learning. All rights reserved.

Smith’s Invisible Hand Hypothesis
Adam Smith believed that the competitive market system provided a powerful “invisible hand” that ensured resources would find their way to where they were most valued Reliance on the economic self-interest of individuals and firms would result in a desirable social outcome

Smith’s Invisible Hand Hypothesis
Smith’s insights gave rise to modern welfare economics The “fundamental theorem” of welfare economics suggests that there is a close correspondence between the efficient allocation of resources and the competitive pricing of these resources

Pareto Efficiency An allocation of resources is Pareto efficient if it is not possible (through further reallocations) to make one person better off without making someone else worse off The Pareto definition identifies allocations as being “inefficient” if unambiguous improvements are possible

Efficiency in Production
An allocation of resources is efficient in production (or “technically efficient”) if no further reallocation would permit more of one good to be produced without necessarily reducing the output of some other good Technical efficiency is a precondition for Pareto efficiency but does not guarantee Pareto efficiency

Efficient Choice of Resources for a Single Firm
A single firm with fixed inputs of labor and capital will have allocated these resources efficiently if they are fully employed and if the RTS between capital and labor is the same for every output the firm produces

Assume that the firm produces two goods (X and Y) and that the available levels of capital and labor are K’ and L’ The production function for X is given by X = f (KX, LX) If we assume full employment, the production function for Y is Y = g (KY, LY) = g (K’ - KX, L’ - LX)

Technical efficiency requires that X output be as large as possible for any value of Y (Y’) Setting up the Lagrangian and solving for the first-order conditions: L = f (KX, LX) + [Y’ – g (K’ - KX, L’ - LX)] L/KX = fK + gK = 0 L/LX = fL + gL = 0 L/ = Y’ – g (K’ - KX, L’ - LX) = 0

From the first two conditions, we can see that This implies that RTSX (K for L) = RTSY (K for L)

Efficient Allocation of Resources among Firms
Resources should be allocated to those firms where they can be most efficiently used the marginal physical product of any resource in the production of a particular good should be the same across all firms that produce the good

Suppose that there are two firms producing X and their production functions are f1(K1, L1) f2(K2, L2) Assume that the total supplies of capital and labor are K’ and L’

The allocational problem is to maximize X = f1(K1, L1) + f2(K2, L2) subject to the constraints K1 + K2 = K’ L1 + L2 = L’ Substituting, the maximization problem becomes X = f1(K1, L1) + f2(K’ - K1, L’ - L1)

First-order conditions for a maximum are

These first-order conditions can be rewritten as The marginal physical product of each input should be equal across the two firms

Efficient Choice of Output by Firms
Suppose that there are two outputs (X and Y) each produced by two firms The production possibility frontiers for these two firms are Yi = fi (Xi ) for i=1,2 The overall optimization problem is to produce the maximum amount of X for any given level of Y (Y*)

The Lagrangian for this problem is L = X1 + X2 + [Y* - f1(X1) - f2(X2)] and yields the first-order condition: f1/X1 = f2/X2 The rate of product transformation (RPT) should be the same for all firms producing these goods

Firm A is relatively efficient at producing cars, while Firm B is relatively efficient at producing trucks Cars Cars 100 100 50 Trucks 50 Trucks Firm A Firm B

If each firm was to specialize in its efficient product, total output could be increased Cars Cars 100 100 50 Trucks 50 Trucks Firm A Firm B

Theory of Comparative Advantage
The theory of comparative advantage was first proposed by Ricardo countries should specialize in producing those goods of which they are relatively more efficient producers these countries should then trade with the rest of the world to obtain needed commodities if countries do specialize this way, total world production will be greater

Suppose that this is the marginal cost data for England and Portugal for the production of wine and cloth

In Ricardo’s analysis, marginal costs were assumed to be constant If we let total resource costs be fixed for each country at 100, the production possibility frontier for England is 8W + 4C = 100 and for Portugal it is 2W + 2C = 100

The RPTs differ between these countries:

Although Portugal has an absolute advantage in the production of both goods, both countries could benefit from trade wine is relatively less costly in Portugal Portugal has a comparative advantage in wine cloth is relatively less costly in England England has a comparative advantage in cloth

Suppose that, prior to trade, each country devotes half its resources to each good For England: W = 50/8 = 6.25 C = 50/4 = 12.5 For Portugal: W = 50/2 = 25 C = 50/2 = 25

World output can be increased if England was to produce less wine and more cloth and Portugal was to produce more wine and less cloth Suppose that England decided to devote all of its resources to the production of cloth W = 0/8 = 0 C = 100/4 = 25

Suppose that Portugal decided to devote 70% of its resources to the production of wine, with the remaining 30% used to produce cloth W = 70/2 = 35 C = 30/2 = 15 World output of wine has increased from to 35, and cloth output has risen from 37.5 to 40

Efficiency in Product Mix
Technical efficiency is not a sufficient condition for Pareto efficiency demand must also be brought into the picture In order to ensure Pareto efficiency, we must be able to tie individual’s preferences and production possibilities together

The condition necessary to ensure that the right goods are produced is that the marginal rate of substitution for any two goods must be equal to the rate of product transformation of the two goods MRS = RPT the psychological rate of trade-off between the two goods in people’s preferences must be equal to the rate at which they can be traded off in production

Suppose that we have a one-person (Robinson Crusoe) economy and PP represents the combinations of X and Y that can be produced P Output of Y Any point on PP represents a point of technical efficiency Output of X

Only one point on PP will maximize Crusoe’s utility U1 U2 U3 Output of Y At the point of tangency, Crusoe’s MRS will be equal to the technical RPT P Output of X P

Assume that there are only two goods (X and Y) and one individual in society (Robinson Crusoe) Crusoe’s utility function is U = U(X,Y) The production possibility frontier is T(X,Y) = 0

Crusoe’s problem is to maximize his utility subject to the production constraint Setting up the Lagrangian yields L = U(X,Y) + [T(X,Y)]

First-order conditions for an interior maximum are

Combining the first two, we get or

Competitive Prices and Efficiency
Attaining a Pareto efficient allocation of resources requires that the rate of trade-off between any two goods be the same for all economic agents In a perfectly competitive economy, the ratio of the prices of the two goods provides the common rate of trade-off to which all agents will adjust

In minimizing costs, a firm will equate the RTS between any two inputs (K and L) to the ratio of their competitive prices (w/v) this is true for all outputs the firm produces RTS will be equal across all outputs

A profit-maximizing firm will hire additional units of an input (L) up to the point at which its marginal contribution to revenue is equal to the marginal cost of hiring the input (w) PXfL = w

If this is true for every firm, then with a competitive labor market PXfL (for firm 1) = w = PXfL (for firm 2) fL (for firm 1) = fL (for firm 2) Every firm that produces X has identical marginal productivities of every input in the production of X

Recall that the RPT (of X for Y) is equal to MCX /MCY In perfect competition, each profit-maximizing firm will produce the output level for which marginal cost is equal to price Since PX = MCX and PY = MCY for every firm, RTS = MCX /MCY = PX /PY

Thus, the profit-maximizing decisions of many firms can achieve technical efficiency in production without any central direction Competitive market prices act as signals to unify the multitude of decisions that firms make into one coherent, efficient pattern

The price ratios quoted to consumers are the same ratios the market presents to firms This implies that the MRS shared by all individuals will be equal to the RPT shared by all the firms An efficient mix of goods will therefore be produced

X* and Y* represent the efficient output mix X* Y* Output of Y Only with a price ratio of PX*/PY* will supply and demand be in equilibrium P U0 Output of X P

Laissez-Faire Policies
The correspondence between competitive equilibrium and Pareto efficiency provides some support for the laissez-faire position taken by many economists government intervention may only result in a loss of Pareto efficiency

Departing from the Competitive Assumptions
The ability of competitive markets to achieve efficiency may be impaired because of imperfect competition externalities public goods

Imperfect Competition
Imperfect competition includes all situations in which economic agents exert some market power in determining market prices these agents will take these effects into account in their decisions Market prices no longer carry the informational content required to achieve Pareto efficiency

Suppose that there are two goods that are produced (X and Y) X is produced under imperfectly competitive conditions MRX < PX Y is produced under conditions of perfect competition MRY = PY

The profit-maximizing output choice is that combination of X and Y for which This will result in a nonoptimal choice of outputs less X and more Y will be produced than would be optimal

Imperfect competition in the market for X will result in less X and moreY produced than is Pareto efficient X’ Y’ Output of Y Production is efficient and supply and demand are in equilibrium, but the outcome is not Pareto efficient Y* U2 U1 Output of X X*

Externalities An externality occurs when there are interactions among firms and individuals that are not adequately reflected in market prices With externalities, market prices no longer reflect all of a good’s costs of production there is a divergence between private and social marginal cost

Public Goods Public goods have two properties that make them unsuitable for production in markets they are nonrival additional people can consume the benefits of these goods at zero cost should their prices be zero? they are nonexclusive extra individuals cannot be precluded from consuming the good consumers will become free riders

Market Adjustment and Information
The efficiency properties of a competitive price system may be affected by the level of information in the market

Establishing Competitive Equilibrium Prices
What market signals do suppliers and demanders use to move toward equilibrium? Suppose that the competitive market price for a good starts at P0 We know that under certain circumstances there exists an equilibrium price (P*) such that D(P*) = S(P*) How does the market move from P0 to P*?

Walrasian Price Adjustment
Changes in price are motivated by information about the degree of excess demand at any particular price The Walrasian adjustment mechanism specifies that the change in price over time is given by dP/dt = k[D(P) - S(P)] = k[ED(P)] k > 0

Price will rise if there is positive excess demand and fall if there is negative excess demand This mechanism is called a tâtonnement process

ED > 0 P If excess demand is positive, price will rise. Price S ED < 0 P If excess demand is negative, price will fall. P* This equilibrium price (P*) will be stable because the forces will move price toward P* D Quantity

ED > 0 P If excess demand is positive, price will rise. Price ED < 0 P If excess demand is negative, price will fall. P* This equilibrium price (P*) will not be stable because the forces will move price away from P* S D Quantity

The Walrasian price adjustment procedure is a differential equation We can use a Taylor approximation of the form dp/dt = k[ED’(P*)](P - P*) This is called a first-order differential equation

An important theorem in the study of first-order differential equations is that their solutions have the same stability properties as do the nonlinear equations they approximate

The general solution to this type of problem will be of the form P(t) = (P0 - P*)ekED’(P*)t + P* where P0 represents the initial price at t = 0 for this system to be stable, it must be the case that ED’ (P*) < 0 an increase in price must reduce excess demand a fall in price must increase excess demand

Marshallian Quantity Adjustment
A somewhat different picture of the adjustment process was suggested by Marshall individuals and firms should be viewed as adjusting quantity in response to imbalances in quantity demanded and quantity supplied price changes follow from these changes in quantity

Marshallian Quantity Adjustment
Let D -1(Q) represent the price that buyers are willing to pay for each quantity Let S -1(Q) represent the price that suppliers require for each quantity The Marshallian adjustment mechanism can be represented by dQ/dt = k[D -1(Q) - S -1(Q) ] = k[ED -1(Q)] k > 0

Transactions and Information Costs
To develop a behaviorally oriented theory of market adjustment, one must examine the costs involved in reaching market equilibrium and illustrate how economic actors will seek to minimize these costs Will market adjustments be primarily of the Walrasian or Marshallian type?

Transactions and Information Costs
If prices can be easily changed and if information about price changes is readily disseminated among buyers and sellers, Walrasian price adjustment may dominate If prices are difficult to alter and if the quantity traded can be changed with little cost, markets are more likely to exhibit Marshallian quantity adjustment

Disequilibrium Pricing and Expectations
The traditional model pictures supply and demand decisions as being made simultaneously The theory offers no guidance on how demanders or suppliers act in disequilibrium situations If the simultaneity assumption could be relaxed, this problem would be simplified

Assume that demand responds to the current market price which is known with certainty Demand is given by QtD = c - dPt

However, suppliers can respond only to what they expect the market price to be Therefore, supply is given by QtS = a + bE(Pt) where E(Pt) is what suppliers expect the market price to be at time t

The behavior of this model will depend on how suppliers form price expectations If suppliers always expect the price in period t - 1 to prevail in period t E(Pt) = Pt - 1 In this case, the model would become a cobweb model

The Cobweb Model Initially, price is set at P0, and Q1 will be produced P0 Q1 Price S Demanders will bid for Q1 thus establishing the market price at P1 P1 At a price of P1, suppliers will choose to produce Q2 which will lead to a price of P2 P2 Q2 D Quantity

The Cobweb Model The process is repeated until price works its way to the equilibrium price (P*) Price S P0 P2 Before reaching equilibrium, a number of disequilibrium (and inefficient) outcomes occur P* P1 D Quantity Q2 Q1

Rational Expectations
A separate hypothesis about the formation of price expectations was proposed by Muth in the early 1960s In his model, expectations are made on a “rational” basis by incorporating all available information about the market in question

A supplier who know the precise forms of the demand and supply curves could calculate the equilibrium price This value could then be used to form the price expectation

Using this expected price, supply will be at its equilibrium level the market will be free of the inefficient fluctuations observed in the cobweb model In the absence of any other information or transactions costs, equilibrium will be established instantly

Price Expectations and Market Equilibrium
Suppose the demand for handmade violins is given by QtD = Pt Because producing a violin takes longer than one period, makers base their decision on what they expect the price to be QtS = 2 + E(Pt)

In equilibrium E(Pt) = Pt P* = 2 Q* = 4

With adaptive expectations, other price-quantity combinations might be observed Suppose that E(Pt) = Pt -1

If P0 = 1, supply in period 1 is Q1 = 2 + P0 = 3 and P1 is determined by the demand curve 3 = 10 - P1 P1 = 7/3 Proceeding in this way yields the following prices and quantities over time:

Information and Inefficient Equilibria
The proof of the efficiency of competitive prices assumed that these equilibrium prices were known to all economic actors If some actors are not fully informed about prevailing prices or product quality, inefficient allocations may result

Asymmetric Information and the Lemons Model
Assume that used cars come in a number of qualities (n) each of these qualities has a price associated with it (P1,…,Pn) representing the value these cars would have to buyers and sellers in a fully informed situation Sellers know precisely the value of their car

Buyers have no way of knowing a car’s quality until they own it and base their evaluation of cars on the average quality of all cars available (P’) equilibrium price must be P’ this is what demanders will pay for a car of average quality

At a price of P’, quantity supplied will be where Si s the supply of cars of quality Pi and the sum is taken over qualities less than P’ For cars with better quality (Pi > P’), the seller will choose to hold on to the car

In this situation, buyers will be unsatisfied because the quality of used cars is lower than they expect this situation will deteriorate even further over time The inefficiency in this market occurs because sellers have no way to convince buyers that their cars are not lemons

Distribution Although there are forces in competitive price systems that direct resources toward efficent allocations, there are no guarantees that these allocations will exhibit desirable distributions of welfare among individuals

Distribution Assume that there are only two people in society (Smith and Jones) The quantities of two goods (X and Y) to be distributed among these two people are fixed in supply We can use an Edgeworth box diagram to show all possible allocations of these goods between Smith and Jones

Distribution OJ UJ4 UJ3 UJ2 UJ1 Total Y US4 US3 US2 US1 OS Total X

Distribution Any point within the Edgeworth box in which the MRS for Smith is unequal to that for Jones offers an opportunity for Pareto improvements both can move to higher levels of utility through trade

Distribution OJ OS Any trade in this area is an improvement over A UJ1
US4 US3 US2 US1 UJ2 UJ3 Any trade in this area is an improvement over A UJ4  A OS

Contract Curve In an exchange economy, all efficient allocations lie along a contract curve points off the curve are necessarily inefficient individuals can be made better off by moving to the curve Along the contract curve, individuals’ preferences are rivals one may be made better off only by making the other worse off

Distribution OJ Contract curve UJ1 US4 US3 US2 US1 UJ2 UJ3 UJ4 A  OS

Distribution Suppose that the two individuals possess different quantities of the two goods at the start it is possible that the two individuals could both benefit from trade if the initial allocations were inefficient

Distribution Neither person would engage in trade that would leave him worse off Only a portion of the contract curve shows allocations that may result from voluntary exchange

Distribution Suppose that A represents the initial endowments OJ OS
 A Suppose that A represents the initial endowments UJA USA OS

Distribution OJ Neither individual would be willing to accept a lower level of utility than A gives UJA A  USA OS

Distribution OJ Only allocations between M1 and M2 will be acceptable to both M1  M2 UJA A  USA OS

Distribution If the initial endowments are skewed in favor of some economic actors, the Pareto efficient allocations promised by the competitive price system will also tend to favor those actors voluntary transactions cannot overcome large differences in initial endowments some sort of transfers will be needed to attain more equal results

Important Points to Note:
Pareto’s definition of an efficient allocation of resources -- the point at which no one person can be made better off without making someone else worse off -- provides the basis for normative welfare theory

Productive or technical efficiency is a necessary though not sufficient condition for Pareto efficiency achieving technical efficiency requires that three marginal conditions hold: equality of rates of technical substitution across different outputs equality of marginal productivities among firms equality of rates of product transformation across firms

Pareto efficiency requires productive efficiency and efficiency in the choice of output mix this latter goal can be attained by choosing that technically efficient output for which the rate of product transformation between any two goods is equal to individuals’ marginal rate of substitution for these goods

Reliance on competitive equilibrium prices will yield a technically efficient allocation of resources because profit-maximizing firms will make choices consistent with the three marginal allocation rules existence of competitive equilibrium prices for outputs will also result in an efficient output mix the correspondence between Pareto efficiency and competitive equilibrium is complete

Violations of the competitive assumptions may distort the allocation of resources away from Pareto efficiency imperfect competition externalities existence of public goods

Imperfect information may affect the speed with which markets achieve equilibrium, perhaps yielding inefficient disequilibrium outcomes over the short term informational asymmetries may also affect the Pareto efficiency of competitive equilibria

Distributional outcomes under competitive markets may sometimes be considered undesirable from the perspective of equity initial endowments may constrain the range of outcomes achievable through voluntary transactions

THE EFFICIENCY OF PERFECT COMPETITION

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