General Equilibrium and Market Efficiency - Text: Old edition Ch. 16, New edition Chapter 17 Partial Equilibrium (PE) vs. General Equilibrium (GE) : - Models examined so far are all partial equilibrium models . - Partial equilibrium approach: - focus is on equilibrium in one market (or sometimes a few related markets). - limited, or no allowance, for interactions and feedbacks between the market studied and other markets. i.e. variables from other markets that affect this market are assumed to be determined independently. (reasonable if feedbacks are of secondary importance) e.g. Supply-Demand model with 1 market: equilibrium gives price and quantity. 1
Transcript
General Equilibrium and Market Efficiency
- Text: Old edition Ch. 16, New edition Chapter 17
Partial Equilibrium (PE) vs. General Equilibrium (GE):
- Models examined so far are all partial equilibrium models.
- Partial equilibrium approach:
- focus is on equilibrium in one market (or sometimes a few related markets).
- limited, or no allowance, for interactions and feedbacks between the market studied and other markets.
i.e. variables from other markets that affect this market are assumed to be determined independently.
(reasonable if feedbacks are of secondary importance)
e.g. Supply-Demand model with 1 market: equilibrium gives price and quantity.
- Shape and position of the supply and demand curves depend on factors determined in other markets:
- prices of other goods and services, prices of inputs, incomes of consumers, etc.
- these may in turn be affected by the price and quantity in the market under study.
- but supply-demand treats these variables as given (exogenous).
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- General equilibrium (GE) approach:
- Concerned with simultaneous equilibrium across markets.
- Allows for interactions, feedbacks and their effects on equilibrium.
- More complete but more complex.
- Extreme version? Arrow-Debreu model – complete set of markets.(all goods, all inputs, allows for time, uncertainty)
- Outcome in a GE model: “general equilibrium”
- supply = demand in all markets simultaneously (if competitive).
- a set of equilibrium prices that give this equilibrium.
- price system coordinates outcomes across markets (recall: Harford chapter on the role of prices)
- Underlying model of behaviour is the same in both PE and GE approaches. - Decision-makers: rational, aim to maximize their well-being.
- Chapter focuses on competitive general equilibrium (GE) models.- 1950s theoretical work suggests such an equilibrium exists under
fairly general conditions (Arrow, Debreu and McKenzie).
- GE with imperfect competition: exists in special cases. Notably: monopolistic competition (Dixit-Stiglitz Model)
- Applications: international trade theory; public finance and tax systems; macroeconomics: should macro be part of GE modelling?
- Chapter looks at GE piece by piece.- Exchange without production. - Production only.- Economy with exchange and production.
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General Equilibrium Model of a Simple Exchange Economy
- An economy of traders each with some initial allocation of each good.
i.e. no production: amount of goods fixed.
- Two persons (A and B), two goods (food and clothing).
- the model can be extended to many goods, many people.
- 2x2 case has the advantage of being easy to graph.
- can give an idea of the nature of the equilibrium outcome.
- General equilibrium:
- simultaneous equilibrium in both goods markets;
i.e. supply = demand in both markets.
- implies a set of equilibrium prices (price for each good). (see below: initially good-for-good trades, i.e. barter)
- Possible outcomes: the “Edgeworth Box”
- dimensions of the box: total amounts of clothing and food in this economy.
- lower-left corner: measure clothing and food of person A relative to this point.
- upper-right corner: measure clothing and food of person B relative to this point.
- each point in the box is a different distribution of the two goods between person A and B.
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- Starting point: initial endowment (point E below)
- each person has some food and clothing the other person has the rest.
- this endowment is a given in the exchange economy modeli.e. is not determined within the model.
- Each person has a typical set of indifference curves showing “utility” from each possible combination of clothing (C) and food (F).
- “utility” of A is rising as move northeast;
- utility of B is rising as move southwest.
- usual assumptions about indifference curves: - negatively sloped (both cloth and food are goods);
- convex shape (value of something is high when it is scarce)
- don’t cross (rational choice); higher (relative to the origin) the higher is well-being (utility).
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- slope of the indifference curves: “marginal rate of substitution” (MRS)
- measures the value of one good in terms of the other.
- shows how much of one good the individual can give up for one more unit of the other good and still be as well off.
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- Will the decision-makers (A and B) stay at the initial endowment?
- Generally no: - Let UA1 and UB1 be the indifference curves of A and B that
go through the endowment point (point E).
- A and B can usually can both do better than this.
i.e., there are a number of points between UA1 and UB1 where both A and B are better off.
(exception: not so when UA1 and UB1 are tangent at the initial endowment)
- At most endowments slopes of A and B’s indifference curves (MRSs) differ, e.g. see point E below.
- then trade can benefit both A and B.
e.g. say A’s MRS is 2 food per unit of clothing.
say B’s MRS is 1 food per unit of clothing.
A will to pay up to 2 food for another clothing
B will sell clothing for any price greater than 1 food.
- A and B will find it worthwhile to trade: - B trades clothing for food- A trades food for clothing
e.g. A trades 1.5 food for 1 clothing makes A and B better off.
- This trade moves the economy into the area between the original indifference curves:
- moves A and B to higher indifference curves
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(UA11, UB11): both better off (next page)
- A and B will have an incentive to make more trades if it is still the case that:
MRSA MRSB
- both again move to higher indifference curves as a result of mutually agreeable trades.
- Where do they end up? At a point where MRSA=MRSB
(see point T next page)
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- Trade continues until A and B reach a point between UA1 and UB1 where the two indifference curves are tangent.
- tangency: - not possible to move to another point where both A and B are both better off.
i.e., no more trades that benefit both parties.
- MRS’s of A and B are the same so no difference in A and Bs valuations of the two goods. (see point T in diagram)
- The new outcome (point T) is “Pareto optimal” or “Pareto efficient”.
Pareto optimal: no change can be made which will make one person better off without making someone worse off.
- The outcome is pareto superior to the endowment point since everyone is better off and no one is worse off.
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- Pareto optimality and desirability of an outcome:
- in judging outcomes economists view pareto optimality as desirable.
- a move to a pareto superior outcome is typically viewed as a good thing. (there are winners but no losers)
- There are several points between UA1 and UB1 which are efficient (MRS’s equal) and both are better off than at the initial endowment.
- these are all points on the contract curve for this economy.
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- Any other endowment point in the Edgeworth box will have a different set of possible efficient outcomes associated with it.
i.e., will provide more points on the contract curve.
(entire contract curve: all allocations where MRSA=MRSB )
- Where the simple exchange economy ends up will depend on:
- initial endowments of food and clothing (determines the relevant part of the contract curve);
- preferences of the agents in the model (how they value goods), i.e. shape of indifference curves;
- bargaining skill of the two agents (determines the actualequilibrium point on the relevant part of the contract curve).
(Relevant? Between the indifferences curve that go through the endowment point.)
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Markets and the Exchange Economy Equilibrium:
- Discussion above: A and B trade among themselves.
- Imagine instead that markets determine prices of clothing and food and that A and B trade based on these prices.
e.g. an auctioneer (“the market”) calls out prices.
- if supply does not equal demand at the prices stated the prices change (rise if excess demand, fall if excess supply).
i.e., prices adjust as in the supply-demand model.
- process continues until prices are found where supply and demand are equal.
- Let: Pc = price of clothing per unit Pf = price of food per unit.
- given the prices persons A and B each face a budget constraint:
- straight line going through the endowment point.
- person moves along the budget constraint by selling one good and buying the other
so: Pc C + Pf F = 0
C = change in clothing from endowment (>0 buying, <0 selling)
F = change in food from endowment (>0 buying, <0 selling)
- income to buy one good is obtained by selling from the endowment of the other good.
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- Budget line slope:
F/C = -Pc/Pf (if Clothing is on horizontal and Food on the vertical axis)
i.e., shows the rate at which the person can trade clothing for food.
e.g. Pc = $2 and Pf=$1 can get 2 food for 1 clothing.
- Both A and B face the same prices and buy or sell relative to the endowment: in box same line represents A and B’s budget line.
- Given the budget constraint persons A and B will choose the point that puts them on the highest indifference curve.
i.e., tangency: MRS = Pc/Pf
- usual outcome in consumer theory: - tradeoff in preferences equals tradeoff in market prices.
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- Say that at the starting prices:
Person A: F<0 and C>0 (sell food, buy clothing)
Person B: F<0 and C>0 (sell food, buy clothing)
(like Figure 16-7 old edition. 17-7 new edition)
- this is not an equilibrium:
- both demand clothing, no one sells it (excess demand)
- both sell food, no one supplies it (excess supply).
- Persons A and B cannot carry out their plans.
- Now new prices are announced: Pf falls (due to excess supply), Pc rises (due to excess demand).
- Budget constraint becomes steeper: pivots around the
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endowment point.
- Each person finds his/her new best choice. - if still have excess demand or excess supply prices
change again.
(Could have shown excess supply of clothing and excess demand for food at starting prices and endowment: then Pf rises and Pc falls)
- Equilibrium:
- set of prices (Pc, Pf) where there are no excess demands or supplies.
i.e., one person demands just as much food as the other supplies. (FA + FB =0 )
one person demands just as much clothing as the other supplies. (CA + CB =0 )
both people satisfy their budget constraints.
- at such a point:
MRS = Pc/Pf for each person
MRS of A and B are equal
UA and UB are tangent to one another (MRS’s are equal at the same point in the Edgeworth box).
- see text Figure 16-8 (17-8) for example.
- This outcome will be just like the trader outcome earlier.
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(Walras’ Law: if we know that all markets but one are in equilibrium then the remaining market is in equilibrium.
e.g. Budget constraints imply:
For A: Pf FA + Pc CA = 0 For B: Pf FB + Pc CB = 0
adding them together gives:
Pf (FA +FB) + Pc (CA +CB) = 0
so if: (FA +FB) = 0 then (CA +CB) = 0 )
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- Comment on the Market Outcome: an equilibrium in “relative prices”
- The outcome determines equilibrium relative prices: ratio of Pc to Pf but not the actual money prices.
e.g. if Pc/Pf = 3 in equilibrium this is consistent with: Pc = $6 and Pf = $2
or Pc = $9 and Pf = $3or Pc = $1800 and Pf = $600 etc.
i.e. key is the implied tradeoff between pairs of goods
(price: important only relative to other prices)
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Fundamental Theorems of Welfare Economics:
(1) A competitive equilibrium exhausts all possible gains from exchange.
- Market outcome is Pareto optimal (efficient).- “Invisible hand” result.
(Aside: note parallels between this idea of efficiency and efficiency defined as maximizing combined consumer
and producer surplus, i.e., all gains from exchange are realized)
(2) Any allocation on the contract curve can be sustained as a competitive equilibrium.
- Take an arbitrary point on the contract curve.
- Set equilibrium relative price equal to MRS of A and B at that point: this gives the budget constraint.
- Any point on this budget constraint is an endowment point that would give this equilibrium.
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- Implications of the second theorem?
- Redistribution can allow you to obtain any efficient (Pareto optimal) outcome.
- Efficiency and distribution can be separated.
- choose best distribution.
- market forces will still give efficiency.
- Limits to the argument: this assumes redistribution does not alter the total amount of output available.
(Recall Harford’s Chapter 3: discussed Kenneth Arrow and the “head-start” theorem --- the ‘head-start’ idea is rooted in the second theorem! )
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Production Efficiency and Market Outcomes:
- Production efficiency in an economy:
i.e., what is an efficient allocation of inputs (resources) between different uses?
- Definition: the allocation of inputs is efficient if it is not possible to reallocate inputs and raise the output of one good without lowering the output of some other good.
i.e. efficient if you can’t reallocate and get something for nothing!
- similar concept to pareto optimality in the exchange economy.
- for an economy’s outcome to be pareto optimal need production efficiency too.
Why? if the outcome is not production efficient you can reallocate inputs and raise combined output.
- this extra output could be used to make someone better off without making anyone else worse off !
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- Simple case: 2 firms (a clothing and a food producer) that use capital (K) and labour (L) to produce output.
- say that the economy has total amounts of K and L of (L*, K*);
- these amounts are the dimensions of an Edgeworth production box (K on the vertical and L on the horizontal axis).
- measure amounts of K and L used by clothing producers from lower left corner and amounts of K and L used by food producers from upper right corner.
- each point in the production box is an allocation of K and L between the two producers.
- Both producers have a set of isoquants showing the combinations of K and L that produce a given amount of output.
- Define: MPL = marginal product of labour
MPK = marginal product of capital.
- isoquants: usual shape.
- downward sloping (K and L are substitute inputs);
- higher isoquant (vs. own origin) means higher output;
- convex shape: assumes diminishing returns.
- Slope of an isoquant: Marginal rate of technical substitution (MRTS).
MRTS = amount of K the firm needs to keep output constant if it gives up a unit of L.
= MPL/MPK
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Why?
- a small change in L (L) changes output by: MPL∙L
- a small change in K (K) changes output by: MPK∙K
- along an isoquant K and L change but output is constant so:
MPL∙L = - MPK∙K
Slope of isoquant: K/∙L = -MPL/MPK
- Start the economy at some initial allocation of K and L.i.e. any point in the production box.
- Usually the isoquants of the two firms will intersect at this initial allocation.
- slopes will not be equal.
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- When MRTS differs between firms:
- the allocation is inefficient: reallocation can raise output of both firms.
(diagram: area between the initial isoquants – both firms are on higher isoquants)
e.g., Clothing firm: - MRTS of clothing firm is 2- to keep output constant firm needs 2 K for each
unit of L it gives up.
Food firm: - say MRTS is 1- to keep output constant firm needs 1 K for each
unit of L it gives up.
- Now: Shift 1 unit of L from Food firm to Clothing firm.
Shift 1.5 units of K from Clothing to Food firm.
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Result?- output of both clothing and food rises!
(food firm gets more K than it needs to compensate for the loss of 1 L; clothing firm gives up less K than it needs to
hold output constant given it gets 1 more)
- What is required for a (production) efficient outcome?
- full employment: all K and L are used in production;
- all inputs must be used: else some output is foregone.
- isoquants of clothing and food firms tangent (see point 2 in diagram above);
- so MRTS equal in the two firms:
- if so firms can’t trade inputs and raise combined output.
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- as in the exchange economy can identify a contract curve of efficient allocations: all allocations where MRTS same across firms.
- Market outcomes and production efficiency:
- As in exchange economy input prices are market determined.
- excess demand: input price rises
- excess supply: input price falls.
- input prices adjust until supply=demand for inputs (so full employment)
- all producers face the same market determined input prices.
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- Each firm aims to minimize costs (this maximizes profits):
- Cost minimization requires: MRTS = w/r
w = price of labour (wage);r = rental price of capital.
i.e. firms chooses K, L combination that lets it produce a level of output at the lowest possible cost.
e.g. if MRTS =1 and w/r = 2:
- firm can lower L by 1, raise K by 1 and have same output but since labour costs twice as much as capital costs will be lower.
- generally if: MRTS w/r
firms can change K, L mix and reduce costs.
(Note can also show this using isocost lines: K,L combinations with same cost level.
C0 = wL + r K isocost for cost level C0.
- slope: -w/r
- higher isocost means higher cost level.
- firm produce any give output level at least cost:
- choose K, L combination where the isocost line is tangent to the isoquant for that output level.
i.e. slopes same so: MRTS = w/r )
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- Same result is suggested by factor (input) demand models: competitive firms hire inputs until:
MRPL = w
MRPK = r
MRPL = MR x MPL = MPL = MRTS = w MRPK MR x MPK MPK r
- Each firm faces same input prices (w, r) so:
MRTSClothing = w/r = MRTSFood
- So production efficiency results.
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Efficiency of the Product Mix:
- Even if output is produced efficiently (MRTSClothing = MRTSFood) and is exchanged efficiently (MRSA= MRSB) the outcome could still be inefficient.
i.e., it may be possible to switch to a different mix of output and make at least one person better off without making anyone worse off.
- What is necessary to ensure the efficient mix of output?
- Take the Edgeworth Production Box.
- all production efficient allocations of inputs are on the contract curve.
- each point on the contract curve identifies a given output of clothing and an output of food.
- plotting these output levels (food on vertical and clothing on the horizontal axis) gives the Production Possibility Frontier (PPF).
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- Production Possibility Frontier (PPF):
- Shows the set of all possible production-efficient output combinations.
- All points on the PPF are production efficient.
(all inputs are used and are efficiently allocated between food and clothing firms)
- Slope of the PPF:
- negative: as move along the contract curve more of one good and less of the other is produced.
i.e. reallocating inputs between firms in the production box.
- Absolute value of the slope is the Marginal Rate of Transformation (MRT).
- MRT shows the rate at which the economy can efficiently transform clothing into food.
i.e. efficiently reallocate K and L between the food and clothing industries.
- In the example MRT becomes larger as move down the PPF:
- true if there are decreasing returns in food and clothing industries.
- Efficient outcome must be on PPF.
- if below PPF: production is inefficient,- can reallocate inputs and have more of both
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outputs.
- can’t be above PPF: not enough inputs given technology for these points to be attainable.
- Product mix efficiency requires:
MRT = MRS of persons A and B
- Say instead: MRT > MRS
e.g. MRT =2 and MRS =1
- MRS=1 means: giving up 1 clothing to get 1 food leaves person A or B at same utility level.
- MRT=2 means: economy can transform 1 clothing into 2 food.
- So reducing clothing by 1 and producing 2 more food makes it possible to make someone better off without making anyone worse off.
i.e. when MRT > MRS the product mix is inefficient.
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- Say instead: MRT < MRS
e.g. MRT =2 and MRS =4
- MRS=4 means: giving up 4 food to get 1 clothing leaves the person at same utility level.
- MRT=2 means: economy can transform 2 food into 1clothing.
- So reducing food by 2 and producing 1 more clothing makes it possible to make someone better off without making anyone worse off.
i.e. when MRT < MRS the product mix is inefficient.
- Say MRT = MRS:
e.g. MRT =2 = MRS
- Tradeoff between clothing and food for the consumer (MRS) is same as for the economy in production (MRT).
- can’t change the output mix to make anyone better off without making someone worse off.
- Competitive markets and product mix efficiency:
- Will competitive markets yield product mix efficiency?
- We know that the best choice for consumers is when:
MRS = Pc/Pf (budget line and indifference curves
tangent)
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- And that for product mix efficiency:
MRS = MRT
- So need: MRT = Pc/Pf if competitive markets will give efficiency.
- Will this happen?
- say that producing the marginal unit of clothing costs $200 (cost of extra K and extra L): this is marginal cost of clothing (MCC);
- say that producing the marginal unit of food costs $100 (cost of extra K and extra L): this is marginal cost of clothing (MCF);
- so: it costs $200 of K and L to produce clothing and $100 of K and L to produce food.
- So reducing clothing production by 1 frees up $200 which will produce 2 food ($100 each).
- So: MRT = MCC / MCF
- In competitive markets: Pc = MCC and Pf = MCF
So: MRT = Pc/Pf = MRS
- Output mix will be efficient!
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Efficiency of equilibrium in a competitive economy:
- Competitive outcome: -a set of prices where supply=demand in output and input markets.
- decision-makers buying and selling decisions based on these prices.
- Competitive market outcomes will be efficient satisfying:
(1) Exchange efficiency: MRS equal for all consumers = Pc/Pf
(2) Production efficiency: MRTS equal across all goods = w/r
(3) Product mix efficiency: MRT = MRS = Pc/Pf
- This is a modern version of Adam Smith’s “invisible hand” result.
- individual decision-makers acting in their own self-interest can produce an outcome with desirable features.
Generalizing the General Equilibrium Results:
- Above illustrated competitive outcome for 2 consumers, 2 goods, 2 firms and 2 inputs.
- Do the results generalize to larger numbers of consumers, firms, goods and inputs?
- Yes! Arrow-Debreu model is a general version of our model.
(however it also indicates specific “market failures” that will prevent efficiency)
- in general model competitive equilibrium gives a set of output and input prices that set supply = demand is all markets.
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- at this equilibrium:
- consumer’s MRS equal price ratios for each pair of goods.
- MRTSs equal ratio of factor prices for each pair of factor prices.
- MRS for any pair of goods equals MRT for that pair of goods.
Pareto optimality (efficiency) as a criterion for judging outcomes
- An outcome is better if at least one person is better off and no one is worse off.
- moving to an efficient outcome from an inefficient outcome is a “pareto improvement”: some winners, no losers.
- relies on people’s own judgment of the outcome;
- many would say it is intuitively sensible: - prefer an outcome if someone is better off there and no
one is worse off.
(but an egalitarian might disagree)
- avoids making inter-personal comparisons;
- But: Pareto efficiency can’t compare outcomes were some are better off and some are worse off.
- But in most economically interesting comparisons there will be gainers and losers when moving between outcomes.
- Compensation principle: judges a move to a new outcome as good if the gainers from the move can compensate the losers.
i.e., if gains > losses.
- note: if compensation actually occurs the new outcome is Pareto superior to the old outcome.
- but generally compensation does not occur.(the outcome is only potentially better)
- Compensation principle makes an assumption about interpersonal comparisons:
- assumes that from society’s point of view $1 to one person is of equal value of $1 to someone else.
- this is a strong assumption: distribution does not matter.
- comparing outcomes on the basis of total combined consumer and producer surplus makes this assumption.
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Market Failures: Microeconomic Causes of Departures from Efficiency
- The last set of notes suggested that competitive markets will give “Pareto efficient” or “Pareto optimal” outcomes.
- Research on general equilibrium also identifies a set of problems that will result in inefficient results, i.e. ‘Market failures’
- Market failures are circumstances where market outcomes will be inefficient for reasons other than government intervention.
- Sources of market failure:
(1) Imperfect competition or market power:
- Gives an inefficient output mix if it is market power in an output market; gives production inefficiency if market power is in an input market.
- Typically market power in the output market moves the output mix away from the competitive outcome.
e.g. Monopoly in the output market (say food):
- producer sets: MR=MC to maximize profits rather than P=MC.
i.e. restricts output in monopolized market to keep the price high.
- now: MRT = MCc/MCf = Pc / MRf ≠ Pc /Pf = MRS
- overall efficiency violated: too much clothing too little food.
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- Market power in an input market e.g. unions or monopsony
- typically alters the hiring decisions in the affected industries and moves the allocation of inputs away from the
competitive outcome.
- also gives inefficiency (production efficiency will be violated: MRTS’s will differ between industries).
e.g. union in all industries: raises ‘w’ above its market clearing level (unemployment results); union in one industry: wage will differ between industries and so will MRTS’s; monopsony: hiring decisions made on basis of marginal factor cost rather than the wage (vs. production efficiency).
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(2) Externalities:
An externality exists when an economic decision imposes costs or creates benefits for some party not involved in the decision.
i.e. it creates costs or benefits that are external to the decision-makers.
e.g. pollution (a negative externality – imposes a cost on someone other than the consumer and producer of the good creating the pollution).
- Competitive market outcomes will be inefficient since the external benefits or external costs will be ignored by the decision makers in the market (buyers and sellers).
- relative prices, MRS’s and MRT’s don’t reflect the true benefits and costs of the good to society.
(they reflect ‘private’ not ‘social’ costs and benefits)
e.g. too much of the polluting good is produced and consumed (MC is its private marginal production cost while it's true cost is higher)
- Competitive outcomes: too much production of goods with external costs, too little of goods with external benefits.
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(3) Public goods
- Public Good: a good that is non-excludable and non-rival.
(1) Non-excludable: - once provided it is available to all: exclusion is impossible.
(2) Non-rival (text: nondiminishable): - one person’s consumption of the good does not
diminish the amount available to others.
e.g. lighthouse, national defence, radio.
- Such goods are unlikely to be provided in efficient amounts.
- Why? - Externality problem: providing a unit of a public good creates a positive externality (provides it to all).
- this extra benefit will likely be ignored by an individual buyer.
- Free-rider problem: there is an incentive to let others provide the good (you can still enjoy it without having to pay for it). If all do this none is provided.
- Market prices (if the market even exists!) will not reflect the true value of the good (too low) – too little will be provided.
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(4) Asymmetric information problems: (moral hazard and adverse selection – from ECON 2017, Chapter 6)
- in some markets buyers or sellers have more information than the person(s) on the other side of the market.
- affected markets may be too small or perhaps not even exist.
i.e. too little is produced in these market, too few inputs are allocated to the affected
