Chapter 16 General Equilibrium

©2005 Pearson Education, Inc.Chapter 162 General Equilibrium Analysis To study how markets interrelate, we can use general equilibrium analysis The feedback effect is the price or quantity adjustment in one market caused by price and quantity adjustments in related markets

©2005 Pearson Education, Inc.Chapter 163 Two Interdependent Markets – Moving to General Equilibrium Scenario  The competitive markets of: DVD rentals Movie theater tickets  Changing prices in one market are likely to affect the other market

©2005 Pearson Education, Inc.Chapter 164 Two Interdependent Markets – Moving to General Equilibrium Scenario  Equilibrium price of movies is $6.00  Equilibrium price of DVD rentals are $3.00  Government places a $1.00 tax on each movie ticket  Need to look at effect of tax on Market for DVDs Feedback effects in Movie market

©2005 Pearson Education, Inc.5 Two Interdependent Markets – Movies and DVDs DVDV DMDM Price Number of Videos Price Number of Movie Tickets SMSM SVSV $6.00 QMQM QVQV $3.00 $6.35 Q’ M S* M $1 tax on each movie ticket causes supply to fall D’ V Q’ V $3.50 General Equilibrium Analysis: Increase in movie ticket prices increases demand for videos.

©2005 Pearson Education, Inc.Chapter 166 Two Interdependent Markets – Movies and DVDs Price Number of Videos Price Number of Movie Tickets DMDM SMSM $6.00 QMQM $6.35 Q’ M S* M The increase in the price of videos increases the demand for movies. D’ V DVDV SVSV QVQV $3.00 Q’ V $3.50 General Equilibrium Analysis: The Feedback effects continue. D* M $6.82 Q* M Q” M $6.75 D’ M $3.58 Q* V D* V

©2005 Pearson Education, Inc.Chapter 167 Two Interdependent Markets – Movies and DVDs Observation  Without considering the feedback effect with general equilibrium, the impact of the tax would have been underestimated  This is an important consideration for policy makers.

©2005 Pearson Education, Inc.Chapter 168 Reaching General Equilibrium Must be able to determine the equilibrium price of both movies and DVDs simultaneously  We must simultaneously find two prices that equate quantity demanded and quantity supplied in all related markets  This requires finding the solution to four equations: demand and supply for DVDs and Movies

©2005 Pearson Education, Inc.Chapter 169 The Advantages of Trade Assumptions  Two consumers (countries)  Two goods  Zero transaction costs  James & Karen have a total of 10 units of food and 6 units of clothing.

©2005 Pearson Education, Inc.Chapter 1610 The Advantage of Trade IndividualInitial Allocation TradeFinal Allocation James7F, 1C-1F, +1C6F, 2C Karen3F, 5C+1F, -1C4F, 4C

©2005 Pearson Education, Inc.Chapter 1611 The Advantage of Trade There is room for trade  James values clothing more than Karen  Karen values food more than James Actual terms of trade are determined through bargaining

©2005 Pearson Education, Inc.Chapter 1612 The Advantage of Trade From this analysis we obtain an important result: An allocation of goods is efficient only if the goods are distributed so that the marginal rate of substitution between any pair of goods is the same for all consumers.

©2005 Pearson Education, Inc.Chapter 1613 The Edgeworth Box Diagram A diagram showing all possible allocations of either two goods between two people is called an Edgeworth Box

©2005 Pearson Education, Inc.Chapter 1614 The Edgeworth Box Diagram Each point describes the market baskets of both consumers  James has 7 units of food and 1 unit of clothing – point A  Karen has 3 units of food and 5 units of clothing – point A from different axis

©2005 Pearson Education, Inc.15 Exchange in an Edgeworth Box 10F 0K0K 0J0J 6C 10F 6C James’s Clothing Karen’s Clothing James’s Food Karen’s Food 1C 5C 3F 7F A The initial allocation before trade is A: James has 7F and 1C & Karen has 3F and 5C.

©2005 Pearson Education, Inc.Chapter 1616 Exchange in an Edgeworth Box 10F 0K0K 0J0J 6C 10F 6C James’s Clothing Karen’s Clothing James’s Food Karen’s Food 1C 5C 3F 7F A The allocation after trade is B: James has 6F and 2C & Karen has 4F and 4C. 4F 6F +1C -1F 2C4C B

©2005 Pearson Education, Inc.Chapter 1617 Efficient Allocations A trade from A to B makes both Karen and James better off If James’s and Karen’s MRS are the same at B the allocation is efficient.

©2005 Pearson Education, Inc.Chapter 1618 Efficient Allocations We can see both parties are better off at point B since they both end up on a higher indifference curve Although a trade might make both parties better off, the new allocation is not necessarily efficient

©2005 Pearson Education, Inc.Chapter 1619 A: U J 1 = U K 1, but the MRS is not equal. All combinations in the shaded area are preferred to A. Karen’s Clothing Karen’s Food UK1UK1 James’s Clothing James’s Food UJ1UJ1 Efficiency in Exchange 10F 0K0K 0J0J 6C 10F 6C Gains from trade A

©2005 Pearson Education, Inc.Chapter 1620 Efficiency in Exchange Karen’s Clothing Karen’s Food James’s Clothing James’s Food 10F 0K0K 0J0J 6C 10F 6C UK1UK1 UJ1UJ1 A Point B is on higher IC but is not efficient UJ2UJ2 UK2UK2 B At point C, MRSs are equal and allocation is efficient UK3UK3 C D is also a possible efficient allocation depending on bargaining UJ3UJ3 D

©2005 Pearson Education, Inc.Chapter 1621 Efficiency in Exchange Any move outside the shaded area will make one person worse off (closer to their origin). B is a mutually beneficial trade--higher indifference curve for each person. Trade may be beneficial but not efficient. MRS is equal when indifference curves are tangent and the allocation is efficient. A Karen’s Clothing Karen’s Food UK1UK1 UK2UK2 UK3UK3 James’s Clothing James’s Food UJ1UJ1 UJ2UJ2 UJ3UJ3 B C D 10F 0K0K 0J0J 6C 10F 6C

©2005 Pearson Education, Inc.Chapter 1622 Efficiency in Exchange The Contract Curve  To find all possible efficient allocations of food and clothing between Karen and James, we would look for all points of tangency between each of their indifference curves.  The contract curve shows all the efficient allocations of goods between two consumers, or of two inputs between two production functions

©2005 Pearson Education, Inc.Chapter 1623 The Contract Curve 0J0J James’s Clothing Karen’s Clothing 0K0K Karen’s Food James’s Food E F G Contract Curve E, F, & G are Pareto efficient.

©2005 Pearson Education, Inc.Chapter 1624 Contract curve All points of tangency between the indifference curves are efficient.  MRS of individuals is the same  No more room for trade The contract curve shows all allocations that are Pareto efficient.  Pareto efficient allocation occurs when further trade will make someone worse off.

©2005 Pearson Education, Inc.Chapter 1625 Consumer Equilibrium in a Competitive Market We can show opportunities for trade for many consumers  When prices of food and clothing are equal, we can show the price line, PP’ with a slope of –1  James buys 2 clothing for 2 food: A to C  Karen buys 2 food for 2 clothing: A to C  Both increase satisfaction

©2005 Pearson Education, Inc.Chapter 1626 Consumer Equilibrium in a Competitive Market Price Line 10F 0K0K 0J0J 6C 10F 6C James’s Clothing Karen’s Clothing Karen’s Food James’s Food C A Begin at A: Each James buys 2C and sells 2F moving from Uj1 to Uj2, which is preferred (A to C). Begin at A: Each Karen buys 2F and sells 2C moving from UK1 to UK2, which is preferred (A to C). P P’ UJ2UJ2 UJ1UJ1 UK1UK1 UK2UK2

©2005 Pearson Education, Inc.Chapter 1627 Consumer Equilibrium in a Competitive Market The amount of clothing that Karen wanted to sell is equal to the amount of clothing that James wanted to buy An equilibrium is a set of prices at which the quantity demanded equals the quantity supplied in every market  Also called competitive equilibrium

©2005 Pearson Education, Inc.Chapter 1628 Consumer Equilibrium in a Competitive Market In a general equilibrium setting where all markets are perfectly competitive, we can show the same result  Best example of Adam Smith’s invisible hand  Economy will automatically allocate all resources efficiently without need for regulatory control

©2005 Pearson Education, Inc.Chapter 1629 Consumer Equilibrium in a Competitive Market Competitive equilibrium 1.Because the indifference curves are tangent, all MRSs are equal between consumers 2.Because each indifference curve is tangent to the price line, each person’s MRS is equal to the price ratio of the two goods

©2005 Pearson Education, Inc.Chapter 1630 Consumer Equilibrium in a Competitive Market Difficult for efficient allocation with many consumer and producers unless all markets are perfectly competitive Efficient outcomes can also be achieved by centralized system

©2005 Pearson Education, Inc.Chapter 1631 Equity and Efficiency Although there are many efficient allocations, some may be fairer than others The difficult question is what is the most equitable allocation? There is no reason to believe that efficient allocation from competitive markets will give an equitable allocation

©2005 Pearson Education, Inc.Chapter 1632 The Utility Possibilities Frontier From the Edgeworth box we showed a two person exchange The utility possibilities frontier represents all allocations that are efficient in terms of the utility levels of the two individuals

©2005 Pearson Education, Inc.Chapter 1633 The Utility Possibilities Frontier James’ Utility Karen’s Utility E F G OKOK L OJOJ H O J – James has zero utility O K – Karen has zero utility E, F, G – points on contract curve H – inefficient – can do better in shaded area L - unobtainable

©2005 Pearson Education, Inc.Chapter 1634 The Utility Possibilities Frontier James’ Utility Karen’s Utility E F G OKOK OJOJ H Are all efficient points equitable? Efficient points E or F make both persons better off without making one worse off from H If only possible points are H and G, can argue that one is more equitable to James and one to Karen

©2005 Pearson Education, Inc.Chapter 1635 The Utility Possibilities Frontier From previous example, we can see that an inefficient allocation might be more equitable than an efficient one. But how do we define an equitable allocation?

©2005 Pearson Education, Inc.Chapter 1636 Four Views of Equity Egalitarian All members of society receive equal amount of goods Rawlsian Maximize the utility of the least-well- off person Utilitarian Maximize the total utility of all members of society Market - Oriented The market outcome is the most equitable

©2005 Pearson Education, Inc.Chapter 1637 Equity and Perfect Competition A competitive equilibrium can occur at any point on the contract curve depending on the initial allocation. Since not all competitive equilibriums are equitable, we rely on the government to help reach equity by redistributing income.  Taxes  Pubic services

©2005 Pearson Education, Inc.Chapter 1638 Efficiency in Production We can extend to the efficient use of inputs used for production. Assume:  Two fixed inputs: capital and labor  Produce same two goods: food and clothing  Many consumers own inputs to production and earn income from selling them  Income allocated between goods

©2005 Pearson Education, Inc.Chapter 1639 Efficiency in Production Using the Edgeworth box diagram, we can show efficient use of inputs in production  Labor on horizontal axis  Capital on vertical axis  50 hours of labor and 30 hours of capital available

©2005 Pearson Education, Inc.40 Production in an Edgeworth Box 50L 0C0C 0F0F 30K 50L 30K Capital in Food Production Capital in Clothing Production Labor in Food Production Labor in Clothing Production 5K 25K 15L 35L A The initial allocation is A. Every combination of labor and capital used to produce two goods is represented as point in box

©2005 Pearson Education, Inc.Chapter 1641 Production in an Edgeworth Box Can use production isoquants to show levels of output produced with each combination of inputs  3 isoquants representing 50, 60 and 80 units of food  3 isoquants representing 10, 25 and30 units of clothing

©2005 Pearson Education, Inc.42 Production in an Edgeworth Box 50L 0C0C 0F0F 30K 50L 30K Capital in Food Production Capital in Clothing Production Labor in Food Production Labor in Clothing Production 5K 25K 15L 35L 3 isoquants representing food production 3 isoquants representing clothing production 10C 60F 50F 25C B 30C 80F A

©2005 Pearson Education, Inc.Chapter 1643 Production in an Edgeworth Box To find efficient production, we must find different combinations of inputs used to produce the two outputs An allocation of inputs is technically efficient if the output of one good cannot be increased without decreasing the output of another goods

©2005 Pearson Education, Inc.44 Production in an Edgeworth Box 50L 0C0C 0F0F 30K 50L 30K Capital in Food Production Capital in Clothing Production Labor in Food Production Labor in Clothing Production 5K 25K 15L 35L Can move from A to B or C which increases efficiency. 10C 60F 50F 25C 30C C 80F D A B Any place in shaded area will increase efficiency from allocation A.

©2005 Pearson Education, Inc.Chapter 1645 Production in an Edgeworth Box Points B and C are efficient allocations and therefore lie on the production contract curve  Curve showing all technically efficient combinations of inputs.  Curve connects the origins, O F and O C  All points on curve are tangencies between two isoquants

©2005 Pearson Education, Inc.46 Production in an Edgeworth Box 50L 0C0C 0F0F 30K 50L 30K Capital in Food Production Capital in Clothing Production Labor in Food Production Labor in Clothing Production 5K 25K 15L 35L 10C 60F 50F 25C 30C C 80F D A B Production Contract Curve

©2005 Pearson Education, Inc.Chapter 1647 Producer Equilibrium – Competitive Input Markets If input markets are competitive, an efficient point will be achieved In competitive input markets  Wage rate, w, will be equal in all industries  Rental rate of capital, r, will be equal in all industries

©2005 Pearson Education, Inc.Chapter 1648 Producer Equilibrium – Competitive Input Markets If producers minimize costs, they will choose inputs to the point where the ratio of the marginal products of the two inputs is equal to the ratio of input prices:

©2005 Pearson Education, Inc.Chapter 1649 Producer Equilibrium – Competitive Input Markets Ratio of marginal products is the same as the marginal rate of technical substitution of labor for capital:

©2005 Pearson Education, Inc.Chapter 1650 Producer Equilibrium – Competitive Input Markets The MRTS is the slope of the isoquant, so competitive equilibrium exists only if:  Slopes of the isoquants are equal to one another  These also equal the ratio of the prices of two inputs Competitive equilibrium lies on the production contract curve, and the competitive equilibrium is efficient in production

©2005 Pearson Education, Inc.Chapter 1651 Production Possibilities Frontier PPF shows the various combinations of two goods that can be produced with fixed quantities of inputs. Frontier is derived from the production contract curve Points on PPF show efficiently produced levels of both goods

©2005 Pearson Education, Inc.Chapter 1652 Production Possibilities Frontier Clothing (units) Food (units) Point A is inefficient Points B, C and D are efficient All points in triangle ABC completely utilize capital and labor but distortion in labor market leads to inefficient use OFOF OCOC D C B A

©2005 Pearson Education, Inc.Chapter 1653 Production Possibilities Frontier PPF is downward sloping  In order to produce more of one good, must give up producing some of the other good PPF is concave  Slope is the MRTS which increases as the level of production of food increases

©2005 Pearson Education, Inc.Chapter 1654 Production Possibilities Frontier Marginal rate of transformation (MRT) of food for clothing is the magnitude of the slope of the frontier at each point  How much clothing must be given up to produce one additional unit of food  As we increase the production of food my moving along the PPF, the MRT increases

©2005 Pearson Education, Inc.Chapter 1655 Marginal Rate of Transformation The productivity of labor and capital differs depending on whether the inputs are used to produce more food or clothing.  Starting where only clothing is produced, MP of labor and capital are relatively low  Transferring some to food production where MP are relatively high  As we do this, MP in food decreases and MP in clothing increases

©2005 Pearson Education, Inc.Chapter 1656 Production Possibilities Frontier Clothing (units) Food (units) OFOF OCOC D  MRT = 2 B  MRT = 1 MRT < 1 MRT > 1

©2005 Pearson Education, Inc.Chapter 1657 Marginal Rate of Transformation Can also describe in terms of costs  When producing at OF the MC of food is very low and MC of clothing is very high  When MRT is low, so is the ratio of the MC of producing food to clothing  Slope of PPF measures the MC of producing one good relative to the MC of producing the other

©2005 Pearson Education, Inc.Chapter 1658 Output Efficiency For efficiency,  MRS = consumer’s WTP for additional food by consuming less clothing  MRT = cost of additional unit of food in terms of producing less clothing Efficiency means MRS = MRT

©2005 Pearson Education, Inc.Chapter 1659 Output Efficiency Clothing (units) Food (units) Indifference Curve MRS = MRT PPF

©2005 Pearson Education, Inc.Chapter 1660 Efficiency in Output Markets For perfectly competitive markets, all consumers allocate their budgets so their MRS between two good are equal to the ratio of prices Profit maximizing firms produce output to the point where price is equal to MC MRT is equal to the MRS

©2005 Pearson Education, Inc.Chapter 1661 The Gains from Free Trade We have showed gains from trade in an Edgeworth box, but what about gains from trade with two countries where one has the comparative advantage  A country has a comparative advantage over another country in the production of a good if the first country can produce the good at a lower opportunity cost than the other country

©2005 Pearson Education, Inc.Chapter 1662 The Gains from Free Trade EX: Two countries producing two goods  Holland and Italy  Cheese and Wine  Holland has comparative advantage in cheese production  Italy as comparative advantage in wine production  Trade is good for both countries

©2005 Pearson Education, Inc.Chapter 1663 The Gains from Free Trade Hours of Labor Required to Produce Cheese and Wine Cheese (1 LB) Wine (1 GAL) Holland12 Italy63

©2005 Pearson Education, Inc.Chapter 1664 The Gains from Free Trade When there is comparative advantage, free trade allows the country to consume outside their PPF Before trade  Produces at A on indifference curve U 1 where MRT and pre-trade price ratio is 2  Holland would want to export 2 pounds of cheese for 1 gallon of wine

©2005 Pearson Education, Inc.Chapter 1665 The Gains from Free Trade After trade  Suppose they choose to trade 1 gallon of wine for 1 pound of cheese  Holland will produce at the point of tangency on the 1/1 price line and PPF – point B  Consumption will occur at D, on a higher indifference curve U 2 tangent to the trade price line

©2005 Pearson Education, Inc.Chapter 1666 The Gains from Trade Cheese (lbs) Wine (gal) U1U1 Pre-Trade Prices U2U2 World Prices CBCB B WBWB A WDWD D CDCD Trade allows Holland to consume outside PPF Exports Imports

©2005 Pearson Education, Inc.Chapter 1667 Overview – Efficiency of Competitive Markets 1.Efficiency in Exchange  MRS J FC = MRS K FC  MRS J FC = P F /P C = MRS K FC 2.Efficiency in the use of inputs in production  MRTS F LK = MRTS C LK  MRTS F LK = w/r = MRTS C LK

©2005 Pearson Education, Inc.Chapter 1668 Overview – Efficiency of Competitive Markets 3.Efficiency in the output market  MRT FC = MRS PC (for all consumers)  P F = MC F, P C = MC C resulting in  MRT FC = MC F /MC C = P F /P C ; therefore  MRS FC = MRT FC

©2005 Pearson Education, Inc.Chapter 1669 Why Markets Fail Market Power  Those with market power choose the price and quantity  Less output is sold than in competitive markets  Inefficiency

©2005 Pearson Education, Inc.Chapter 1670 Why Markets Fail Incomplete Information  Consumers must have accurate information about market prices or production quality for markets to operate efficiency  Lack of information can change supply  Some markets may never develop

©2005 Pearson Education, Inc.Chapter 1671 Why Markets Fail Externalities  Consumption or production has indirect effect on other consumption or production not reflected in market prices

©2005 Pearson Education, Inc.Chapter 1672 Why Markets Fail Public Goods  Nonexclusive, nonrival good that can be made available cheaply but which, once available, is difficult to prevent others from consuming  Company thinking about researching a new technology if can’t get patent Once it’s made pubic, others can duplicate it