Intermediate Microeconomics Module 14 General Equilibrium

GENERAL EQUILIBRIUM 301 CHAPTER 14 General Equilibrium INCOME INEQUALITY IN THE UNITED STATES . 55 . 40 . SHARE OF TOP IN NATIONAL INCOME . see 1990 2000 will THE POLICY QUESTION SHOULD THE GOVERNMENT TRY TO ADDRESS GROWING INEQUALITY THROUGH TAXES AND TRANSFERS ?

Rising income inequality in the United States has received a lot of attention in the last few years . As the graph above illustrates , since 1970 , there has been a dramatic increase in the concentration of wealth at the top ofthe income distribution ( see chapter for a discussion of minimum wages ) But a more mental policy to address income inequality is a more aggressive tax and transfer policy , where a larger share ofthe income ofthe top earners is collected in taxes and then redistributed to earners through tax credits . Critics of this policy worry about the effect such a policy will have on the economy , arguing that it discourages investment and entrepreneurship and is inefficient . EXPLORING THE POLICY QUESTION . Do tax and transfer schemes necessarily lead to inefficiency ?

301 302 PATRICK EMERSON LEARNING OBJECTIVES Partial versus General Equilibrium Learning Objective Explain the difference between partial and general equilibrium , Trading Economy Box Analysis Learning Objective Draw an box for a trading economy and show how a competitive equilibrium is . Competitive Equilibrium Box with Prices Learning Objective Demonstrate how prices adjust to create a competitive equilibrium that is efficient from any allocation of goods . Production and General Equilibrium Learning Objective Draw a production possibility frontier and explain how the mix of production is determined in and how productive efficiency is guaranteed . Policy Example Should the Government Try to Address Growing Inequality through Taxes and Transfers ?

Learning Objective Show how any redistribution of resources leads to a competitive equilibrium . PARTIAL VERSUS GENERAL EQUILIBRIUM Learning Objective Explain the difference between partial and general equilibrium . In all our previous examinations of markets , we implicitly assumed that changes in other markets do not affect the market we are studying . Though we talked about complements and substitutes and price , we did not explicitly consider the interaction between markets . What we were doing is called a analysis studying the changes in a single market in isolation . This is a ful technique because it allows us to focus on one market and do comparative static analyses without having to try to figure out all the interactions with other markets . The insight gained from this sis is generally pretty accurate if a market does not have a lot of linkages . For example , the market for biodiesel type of diesel fuel produced from waste vegetable oils and animal the United States is extremely small , and a spike in production costs that increases the price of biodiesel is unlikely to have much of an impact on other markets , even automobiles . Even if a market is likely to have large spillover effects on other markets , those effects could take a while to materialize , so in the short term , partial equilibrium analyses might be reasonably accurate . However , there are other markets in which the linkages are quite large . Take , for example , the market for crude oil . Crude oil prices affect retail gasoline prices , the market for automobiles , and so on . In order to more accurately analyze these markets , in this chapter , we will relax this assumption and explicitly

GENERAL EQUILIBRIUM 303 study the interaction among markets . This is called analysis the study of how is obtained in multiple markets at the same time . We will still be working with versions of as such , we will look at several markets simultaneously , but we will not try to model all markets at once . Some economists attempt to model many markets at the same time through the use of computer simulations , but for our purposes , we will concentrate on analyses where we look only at a few closely related markets . The linkages between markets are on both the demand side and the supply side . On the demand side , substitutes like cable television and online video streaming services can cause changes in one , like the expansion of videos streaming , to affect the other , like the demand for cable television to fall . Or can be complements , and an increase in the price of bagels might decrease the demand for cream cheese , for example . On the supply side , markets can have linkages in production choices , like farmers who grow both corn and soybeans . An increase in the price of example , from the increased production of cause farmers to plant more corn and fewer soybeans , shifting the supply for soy to the left . Or the output of one industry might be an input in another . A reduction in the price of batteries could lead to a reduction in the price of cell phones and electric cars . Before we move to a full general equilibrium model , let examine the spillover effects between two related markets the crude oil market and the market for large sport utility vehicles ( that are fuel inefficient . When oil prices increase , this leads to higher gasoline prices and reduces the demand for and vice versa . Let examine the effect of a significant event in the crude oil market on equilibrium in that market and the market for large in the United States . Suppose the members of ( Organization of Petroleum Exporting Countries ) decided to dramatically cut back on oil production . Such a decision would lead to a large leftward shift ofthe ply curve , as shown in figure , where the supply curve shifts from to . This leads to a dramatic price increase from to . The price increase in oil leads to a drop in demand for as automobile consumers switch to smaller , more cars , as seen in figure , where the demand curve shifts from to resulting drop in demand lowers the price from to .

304 PATRICK EMERSON Price , per barrel of oil 011 , billion barrels per year Figure General equilibrium in markets GENERAL EQUILIBRIUM 305 Price Figure equilibrium in SUV markets This drop in the price of will cause automobile manufacturers to shift production away from and into more compact cars and electric hybrids . This leads to a shift in SUV supply from to in figure , and the final price and quantity will be at and . Finally , this shift to more cars , along with other consumption changes , will lower the demand for crude oil , shifting the demand from to in panel a and resulting in a final price and quantity that will be at and . From this example , we can see how markets that are connected influence each other in significant ways . When we ignore these linkages , as we do in partial equilibrium analysis , we can miss significant effects , and our conclusions can be biased . TRADING ECONOMY BOX ANALYSIS Learning Objective Draw an box for a trading economy and show how a competitive equilibrium is efficient . Though the example introduces the idea of how equilibrium in one market adjusts to changes in another , it is still only a partial analysis . In this section , we will build a simple economy from the most fundamental of starting initial endowment of resources for members of the we will then show how , through trade in the form of barter , they are able to make themselves better off . In fact , we will show how free trade will lead to a outcome one where it is not possible to make one person better off without hurting another person . In the next section , we will add currency prices and show how prices adjust to achieve equilibrium in the supply and demand ofall and show again that the outcome is efficient .

306 PATRICK EMERSON To construct our trading economy , we need to start with an initial state of the world . To keep matters simple and tractable , our model will assume that there are only two people in this world and two resources . As with all such models in economics , the results are generalizable to many individuals and many goods . Imagine that two people from the same sea voyage are shipwrecked on two uninhabited tropical islands , separated by a small stretch of call them and Mary Ann . The only things the islands have for them to consume are the bananas and coconuts growing in the trees on both islands . Immediately after the shipwreck , they both take an inventory of the bananas and coconuts available to them . We call this initial allocation of goods their endowments . finds that he has 60 coconuts and 60 bananas . Mary Ann has 40 coconuts and 90 bananas . The total amount of resources available to both of them is 100 ( 60 40 ) coconuts and 150 ( 60 , 90 ) bananas . As In chapter , we can draw a graph for both and Mary Ann that shows their initial bundle and their indifference curves through those bundles , as in figure . Mary Ann Coconuts Coconuts 60 40 Mary 50 Bananas 90 Bananas ) Bananas Mary Ann Bananas Figure and Mary Ann initial endowments and curves The question for this chapter Is , What happens when and Mary Ann discover each existence ?

More specifically will they trade with each other ?

Will it improve their ?

To answer these questions , we can begin by implementing a graphical technique called an box ( named after the English economist Francis ) and shown in figure . The box has dimensions that equal the total resources In the economy . In our case , its height is measured in coconuts , and since there are 100 coconuts total , the height of the box is 100 . The width of the box is measured in bananas , and since there are 150 bananas in total , the width is 150 . In this way , the dimensions ofthe box represent the total endowment ofthe economy . We measure resources from the origin In the southeast corner of the box , labeled OG . In contrast , we measure Mary Ann resources from the northeast corner of the box , labeled OM .

GENERAL EQUILIBRIUM 307 Mary Bananas ( 150 OM 100 ?

60 40 Eu 100 60 150 a , Bananas Bananas Figure The box for and economy Now each of their initial endowments can be expressed by a single point , marked . Note that at his point , has sixty coconuts . Since there are one hundred coconuts in total , that leaves exactly forty for Mary Ann . This is the distance from sixty to the top of the box . We measure Mary endowment of coconuts from the top of the box down to her endowment point , Her having forty coconuts leaves sixty for . The same is true for bananas we measure from left to right starting at , and we measure Mary Ann bananas from right to left starting at OM . In fact , any spot in the box represents a full distribution ofall the combined is the clever trick of the box . It also means that nothing is wasted there are no leftover resources available at any spot in the box . As in figure , we can draw indifference curves through the initial endowment point for both ple . is identical to the one in figure . Mary Ann indifference curve is identical as well in relation to the new origin for her , OM . The trick to understanding the box is to imagine taking Mary Ann graph from figure and rotating it 180 degrees and then sliding it over until the endowment points for both are on the same spot . This is illustrated in figure .

308 PATRICK EMERSON ( Coconuts 017 ) 60 Bananas ) Bananas Figure Creating the box from two individual endowments and indifference curves In the box in figure , better consumption bundles for are to the northeast of his initial indifference curve , or in the areas labeled and this is called the preferred set for gan . Better bundles for Mary Ann are now to the southwest of her initial indifference curve , in the areas labeled and this is the preferred set for Mary Ann . Note that area is the one area that is the preferred set for both and Mary Ann . This area is called the lens . Now we have to ask the next question When and Mary Ann become aware of each other and make contact , should they trade ?

Assuming nothing compels them to trade , they will only engage in trade if they can be made better off because otherwise , they will just keep their initial endowment . Assuming that and Mary Ann are utility , as usual , we have already identified a set of alternate of resources that make both better off the feasible bundles in the lens . They are feasible because they represent a complete distribution of the available resources , as does any spot in the box . They make both people better off because they cause both to achieve a higher indifference curve and therefore a higher utility . The movement from allocation to allocation is shown in figure . Note that at both gan and Mary Ann are on higher indifference curves moves from ( to , and Mary Ann moves from to ?

As long as there is a lens , there is a mutually beneficial trade to be made , so only where the two indifference curves just touch each other or are tangent to each other does the lens disappear . One such point is point GENERAL EQUILIBRIUM 309 Mary Bananas 100 ' 610 35 65 ' 100 00 Banana Bananas Figure ' trade to a ' allocation Point isn better for both it is also efficient there is no way to reallocate resources from that point without making one of the people worse off ( on a lower indifference curve ) So what is the trade that gets and Mary Ann from to ?

trades coconuts to Mary Ann in exchange for forty bananas . goes from having sixty bananas to having one hundred and from sixty coconuts to . Mary Ann goes from having ninety bananas to having fifty and from forty coconuts to . Why is point both efficient and optimal ?

We know it is the point at which both and Mary Ann indifference curves are tangent . This means that the marginal rates of substitution ( of both are equal at Recall that the of an agent is the rate at which they would trade one good for the other and be just as well off . When they are equal , there is no more incentive to trade . For example , if both parties are willing to trade one coconut for one banana , neither would be made better off trading . Note at the optimal bundle , On the other hand , if could trade two coconuts for one banana and be just as well off ( his is ) and Mary Ann could trade one coconut for two bananas and bejust as well off ( her is ) then if traded one of his coconuts for one banana from Mary Ann , it will make better off ( he only had to give up one coconut when he could give up two and be as well off ) and Mary Ann better off ( she only had to give up one banana when she could give up two and be as well off ) This is to the situation at point where is greater than Mary Ann , so trades coconuts for bananas .

310 PATRICK EMERSON Mary Ann Bananas ( 150 50 OM 100 ) 60 35 65 El 100 100 150 , Bananas Bananas Figure Tangent , equal latex ?

and the allocation But point is not the only efficient allocation possible . In fact , there are an infinite number of efficient allocations , as the space is filled with an infinite number of indifference curves for both and Mary Ann , and therefore , for each indifference curve for one person , there is a point of tangency with an indifference curve of the other . The contract curve is the line that connects all these points of efficiency . Note that the contract curve begins and ends at the corners that represent the complete absence of goods for , and Mary Ann , OM . This is a allocation as well because if has nothing and Mary Ann has all the coconuts and bananas , it is not possible to give some without taking away from Mary Ann and making her worse off . The same logic applies at OM .

GENERAL EQUILIBRIUM 311 Bananas ( 150 50 OM . 100 Contract Curve 35 65 100 06 100 150 , Bananas Bananas Figure The contract curve We know that there will always be an incentive to trade as long as the marginal rates of substitution are not equal and that from the initial allocation ( they will trade to some point within the lens . We also know that is a allocation within the lens and is one such point . But the contract curve shows us that there are many allocations in the lens . The portion of the contract curve that lies within the lens is the core and is shown in figure .

312 PATRICK EMERSON Mary Ann Bananas ( a ! 40 Contract Curve 100 60 150 , Bananas Bananas Figure The contract curve , the , and the core Mathematical Extension We have described two conditions that define allocations . First , they are feasible . We have ensured feasibility with technique of the bo allocations within the box are feasible . Mathematically , a feasible allocation is one that meets the two following 12 ?

where is the total amount of bananas , is gan share of bananas , and is Mary Ann share of bananas . where is the total amount of coconuts , is gan share of bananas , and is Maw Ann share of coconuts . Second , at allocations , the marginal rates of substitution are equal . Mathematically , the marginal rate of substitution latex ( is So while we can not predict precisely which allocation and Mary Ann will end up on once they discover each other and decide to trade , we know that it will be somewhere on the core . Note that through barter , the als reach a outcome , but this outcome depends critically on the initial allocation . The initial allocation determines the lens or the range of outcomes given the initial tion . Our policy example asks about tax and transfer schemes that address inequality . From this analysis , it is clear that an unequal initial allocation will lead to outcomes that are also relatively unequal . So there is nothing within the barter economy that addresses or acts as a corrective for inequality . The barter economy is a great duction to general equilibrium and critical insight into how voluntary trade makes both parties better off and

GENERAL EQUILIBRIUM leads to outcomes . ever , in the real world , most transactions happen not by barter but through the use of money . In the next chapter , we will expand our model to a competitive setting with the use of money and where there are prices and are price takers . COMPETITIVE BOX WITH PRICES Learning Objective how prices adjust to create a equilibrium that is efficient any initial allocation of goods . Much of the trade in the real wo Id occurs in markets that use some sort currency as the medium of exchange a where the prices are posted . Take , example , a supermarket where food a other goods are displayed on shel with prices listed . There is no you either buy or do buy a good at the price shown . To make our simple model more realistic , we need to add a market and prices . The idea that two people stranded on tropical islands would sider themselves to be price takers might seem a little odd , but we will maintain this assumption to keep the analysis ple . In reality , we are applying this model to situations where there are many ers and example , think of a large farmers market where there are many different sellers of the same and many buyers as well . So now , instead of exchanging bananas for coconuts , and Mary Ann exchange them for dollars . For example , if Mary Ann wants more coconuts , she has to sell some bananas to earn money and then use the money earned to buy coconuts . With only two goods , it is the relative price that matters because it is the relative price that ?

SEM ( for ) MUM , for ) Let consider a specific example . We have the total bananas ( 150 ) and coconuts ( I 00 ) in the economy . 313 ( BUG ace ' 250 and so ' BUM So the condition is equivalent to BUG aUM ab 3110 2901 is equivalent to ( Now let return to Band Given our resources , these become the following 150 150 100 100 Substituting equations ( and ( into ( 141 ) yields the following expression of the ta condition This is the equation of the contract curve . In this simplified example , the contract curve the diagonal of the rectangular box .

314 PATRICK EMERSON mines the rate of exchange . For example , if the price of bananas is and the price of coconuts is , then the rate of exchange of bananas to coconuts is , or . It takes two bananas to get one coconut . This is true if the price of bananas was 100 and the price of coconuts was 200 would still take two bananas to get one coconut . To start , let consider the price of bananas to be and the price of coconuts to be . At the initial distribution of goods , the bounty of island is worth 180 ( per banana 60 bananas per coconut 60 coconuts ) and the resources on Mary Ann island are worth 170 ( 90 40 ) Now suppose would like to trade he knows , because of the prices , that he can trade at a rate of two bananas for one coconut . He could , for example , sell all his bananas for 60 and then buy 30 coconuts with the money earned . This would leave him with bananas and 90 coconuts . Alternatively , he can sell 45 coconuts to buy 90 bananas and could then have all 150 bananas on the two islands , which would leave him with 15 coconuts . He could also end up with any other bundle that represents a one trade of bananas and coconuts . This set of available bundles at these prices is illustrated in figure and called the price line . Bananas 32 00150 90 90 a 60 40 Price Line 85 100 05 60 150 , Bananas Bananas Figure The initial endowment and the price line Mary Ann has equivalent choices she can sell 90 bananas to earn 90 and then spend that money on 45 coconuts , leaving her with bananas and 85 coconuts . Or she could sell 30 coconuts and buy 60 bananas , leaving her with all 150 of the bananas on the two islands and 10 coconuts . Therefore , the price line resents all the points in the box at which and Mary Ann could end up , given the initial distribution of resources and the prices . These prices do not allow and Mary Ann to get to a outcome , however . Each of them maximizing their utility leads to two optimal bundles that are not feasible together , they want too many bananas ( more than the two islands have ) and too few coconuts . This situation is shown in figure .

GENERAL EQUILIBRIUM 315 Mary Bananas 32 100150 70 90 a 50 40 85 100 100 150 Bananas Figure 74 . 71 equilibrium in the product markets As we can see in figure , optimal consumption bundle is at point , where his indifference curve is tangent to the price line , and Mary Ann optimal consumption bundle is at point , where her indifference curve is tangent to the price line . At these bundles , would like to consume 100 bananas and 40 coconuts , and Mary Ann would like to consume 70 bananas and 50 coconuts . The total demand for bananas , 170 , is greater than the total amount available , 150 , and the total demand for coconuts , 90 , is less than the total amount available , 100 . Thus there is excess demand for bananas and excess supply of coconuts . We know from previous chapters that excess demand causes prices to rise and excess supply causes the process to fall , so banana prices should rise , coconut prices should fall , and therefore , the relative price of bananas to coconuts should rise . What is equilibrium in this market ?

Equilibrium is a set of prices , or a price ratio , where the number of bananas demanded by both and Mary Ann exactly equals the total number available and the number of coconuts demanded by both and Mary Ann exactly equals the total number available . In our case , the price ratio does exactly that .

316 PATRICK EMERSON 50 100 50 . 90 60 40 35 65 100 , 60 100 150 , Bananas Bananas Figure Competitive equilibrium in the island economy As can be seen in , at the price ratio of , wants to sell coconuts at a coconut , and with the 50 he earns from that sale , he will buy forty bananas at a banana . At the same time , Mary Ann wants to sell forty bananas at a banana , and with the 50 she earns , she wants to buy coconuts . Equilibrium is achieved because the number of bananas gan wants to buy is exactly equal to the number of bananas Mary Ann wants to sell and the number of coconuts wants to buy is exactly equal to the number of coconuts Mary Ann wants to sell . Since this is the case , the condition that characterizes the equilibrium point is In other words , both indifference curves and the price line all have the same slope at the optimal point , point This guarantees that the competitive equilibrium lies on the contract curve , which guarantees that it is efficient . We call this result the first theorem of welfare economics . First Theorem of Welfare Economics Any competitive equilibrium is There is a second theorem that is closely related to the first . It concerns the ability Mathematical Extension of a social planner to select a particular equilibrium point along the contract We have described two conditions that define allocations in curve . Is it possible to reallocate an exchange economy in the previous section ( they have to be feasible , and resources to achieve equilibrium at a desired point ?

The answer is yes . the marginal rates need to be equal . With a market economy , we now have to incorporate the price system into our analysis . What we know is that the price line connects the initial allocation Second Theorem of Welfare GENERAL EQUILIBRIUM Economics Any competitive is achievable through the reallocation One implication of the second rem is that society can address inequality through transfers of resources without any efficiency loss . Any efficient tion on the contract curve can be achieved through a redistribution of the initial endowment . Note that this does not have to be on the contract curve it is any initial endowment that lies on the equilibrium price line connecting the point on the contract curve . PRODUCTION AND GENERAL EQUILIBRIUM Learning Objective Draw a duction possibility frontier and explain how the mix of production is determined in equilibrium and how productive is guaranteed . In the example economies above , we have ignored bananas and coconut were simply there , endowed to the inhabitant of the island . Now we are going to add the final piece of complexity by adding production . Instead ofa pile of coconuts and bananas available to the inhabitants , the inhabitants must produce them through the use of their labor to harvest them from trees on the islands . We will of assume that both banana trees and coconut trees grow on both islands but that and Mary Ann differ in how many coconuts and bananas they can harvest in a day . Banana trees are not tall , and their fruit is easy to reach without climbing , while coconut trees are very tall and require a lot of climbing to reach their fruit . It turns out that while they are both 317 and the equilibrium point this means that the equilibrium has to be affordable , and is determined by the initial allocation and the prices selves . Let the initial allocation of bananas be given by be where is the total amount of bananas , is share of bananas , and is Mary Ann share of bananas . The initial allocation of coconuts is given by where is the total amount of coconuts , is share of bananas , and is Maw Ann share of coconuts . In terms of initial wealth , has This is how much can earn from selling his endowment . Similarly , has Any potential equilibrium has to be affordable these constraints are ( Mary Ann ) where the hats on top of the and the represent equilibrium amounts . These constraints state that the total amount of money spent on the allocations has to equal the amount earned from selling the initial tion . These constraints , along with the equality of the marginal rates of tion and the price ratio , characterize the competitive equilibrium BUG BUM ab av BUM ( 360 Note , however , that the nominal prices do matter at all only relative prices matter , since the nominal values do not affect the ability to exchange allocated goods for new goods . So we can set one price , to .

318 Lets consider the same example from the previous section . We have the total bananas ( inthe UG and ( is 2179 ) And the contract curve is given as , be Thus A The demand functions for these preferences are A 50191 50 A ( 50 ) Thus the equilibrium quantities and prices are the following 125 ea 42 ( after im ding ) ISM 25 ( EM 58 A PATRICK EMERSON more than capable of harvesting both fruits , is more adept at finding ) and IS re harvesting If ing if collecting hundred . between the banana and bananas , while Mary Ann better at climbing trees and coconuts . spends his entire day 1125 , he can collect one he spends his entire day bananas , he can collect two He can also split his time two activities . If we call of the time he spends on , then is the time he spends on coconut harvesting . So in one day , will harvest two hundred bananas plus one hundred ( co to one , we . By varying zero can find all the points in gan production possibility frontier ( I ine that shows all the possible combinations of bananas and coconuts can harvest in a single day . This is shown in .

GENERAL EQUILIBRIUM 319 a ) a ) Mary Ann Coconuts 200 Coconuts 100 100 50 100 200 Bananas Bananas Figure 74 . 73 frontiers Similarly , if Mary Ann spends her entire day collecting coconuts , she can collect two hundred if she spends her entire day collecting bananas , she can collect one hundred . She can also split her time between the two activities . If we call the fraction of the time she spends on banana harvesting , then is the time she spends on coconut harvesting . So in one day , Mary Ann will harvest one hundred bananas plus two hundred ( coconuts . By varying from zero to one , we can find all the points in Mary Ann production possibility frontier . This is shown in figure . Marginal Rate of Transformation The slope of the is the marginal rate of transformation ( the cost of production of one good in terms ofthe foregone production ofanother good . This is the opportunity cost of producing that good . In this case , the is the number of coconuts that can be collected if the collection of bananas is reduced by one banana . For , every banana he chooses not to collect leads to enough time to collect more coconuts , or put in another way , for every bananas he gives up , he can collect more coconut . Thus his is , which is the same as the slope of his . Similarly , for Mary Ann , if she reduces her banana collecting by one banana , she can collect coconuts . So her is , which is the same as the slope of her . Comparative Advantage This leads directly to the concept of comparative advantage a person has a comparative advantage in the production of a good if they have a lower opportunity cost of production than someone else . In our case , has a lower opportunity cost of producing ( collecting ) bananas , as he gives up only coconut per banana . It must be the case in this world that Mary Ann has a comparative in collecting coconuts , as she gives up only a banana to collect a coconut ( while would have to give up ) As the name suggests , this is a comparative concept it is only relative to someone else . And it does not have anything to do with absolute productivity . To see this , suppose that Mary Ann could collect bananas and coconuts in a day . She would still have the same , and thus the same opportunity cost of bananas . If they combined their outputs , they would have a joint , as shown in figure .

320 PATRICK EMERSON Coconuts 200 200 300 Bananas Figure 14 . production By producing based on their comparative advantage and trading , both and Mary Ann can be made better off . To see this , imagine that both and Mary Ann do not trade and spend half their time on each collecting activity . From figure , we can see that collects one hundred bananas and fifty coconuts , while Mary Ann collects fifty bananas and one hundred coconuts . Now suppose that each spends all their time collecting the good in which they have a comparative advantage . will collect only bananas and harvest two hundred , and Mary Ann will collect only coconuts and harvest two hundred . By sharing harvest with each other , they will end up with one hundred of each , or fifty more in total . This is the lesson of trade based on comparative advantage all parties can benefit . As we add producers , this adds segments to the . For example , suppose another person , whom we will call , arrives on the islands , and his ability to collect bananas is 150 per day if he spends all his time collecting bananas and 150 coconuts if he spends his entire day collecting coconuts . is shown in figure .

GENERAL EQUILIBRIUM 321 Coconuts 150 75 75 150 Bananas Figure 74 . 75 production is , and if he spends half his day collecting bananas and half his day collecting coconuts , he will collect 75 of each . When we add to the group , or the joint production , we have to think about the most effective way for the group to collect both bananas and coconuts . Starting from a position of all three spending their entire time collecting coconuts and thus collecting 450 coconuts and no bananas , we need to ask , Who is the best person to start collecting bananas if they want to add bananas to their collection ?

The answer , based on having the lowest opportunity cost , is . But can only collect ZOO bananas if he devotes his entire day to the endeavor . What if the group wants to collect even more ?

The next best person is , whose opportunity cost of collecting bananas is , which is lower than Mary Ann , which is . Thus the second segment in the joint is , therefore , followed by Mary Ann , as is shown in figure .

322 PATRICK EMERSON Coconuts 350 200 200 300 450 Bananas Figure latex As we add more and more producers to this economy , two things will happen . One , we will add their production to thejoint , which will shift the out as more goods are being produced all . Two , we will add more and more segments of the joint , each with its own slope , and the joint will become more and more kinks in the curve will become less and less evident until eventually it will appear as a smooth curve , as shown in green in figure .

GENERAL EQUILIBRIUM 323 Curves 5000 Price Line 6000 Bananas Figure 7477 The optimal product ' The concave shape of the leads to an that is constantly changing . The slope becomes steeper as we move down the , and therefore , the increases in absolute value . The more bananas they produce , the more coconuts they have to give up per banana . The tells us the cost of producing one extra banana in terms of the marginal cost of producing another good in this case , the is the ratio ofthe marginal cost of bananas and the marginal cost of coconuts Every point on the is efficient there are no wasted is at its maximum and feasible . Now we want to know , among all ofthe possible points , what is the optimal mix of bananas and coconuts ?

To answer this , we need to know about the preferences of the consumers of the two goods . To keep things simple , assume that we can represent the preferences of every consumer in this economy with a single indifference curve , perhaps because every consumer has identical preferences . The optimal sion then is the point on the that allows the consumers to achieve the highest indifference curve possible . In , point I is on the but leads to an indifference curve that is below the one that includes point a . Point a is the one point that allows the consumers the most utility from the mix . It is also the one that isjust tangent to the at point This means that we have a familiar condition that characterizes the optimal mix of goods . We know from chapter that utility maximizing consumers choose a bundle of a good for which their marginal rate of substitution equals the slope of the budget negative of the price ratio . If all consumers face the same price ratio , they will all pick a consumption bundle where they all have the same . This is true even if their preferences differ because prices are common to all consumers , and a condition of the optimal consumption bundle is that equals the negative of relative prices . Because all consumers have the same , no trades will happen there are no mutually beneficial

324 PATRICK EMERSON trades to be had . This is called consumption efficiency it is not possible to redistribute goods to make one person better off without making another person worse off . This also indicates that the consumption bundle lies on the contract curve . Suppose that rather than being traded , bananas and coconuts are sold by competitive firms . In a competitive environment , each firm sells a quantity of each good so that their marginal cost of duction equals the price MOB We divide one equation by the other to get ( From , we know that MOB , so . 146 ) This has an intuitive explanation . Consider an of what this means is that they can trade off production one for one . They can produce one more banana by producing one less coconut . Now pose that the price of bananas is and the price of coconuts is , so the price ratio is . Should the firm adjust output ?

Yes . By producing one more banana , they earn more they have to produce one less coconut to do so , but they only forgo in earnings , so their net gain is . Only where Po do these potential gains disappear . Since we know the optimal consumption bundle is where equals the negative of the price ratio , we know ( Equation ( is illustrated in figure , the price line , and the indifference curves all have the same slope at point ( Competition ensures that equals , and this means that the economy has achieved productive efficiency there is no other mix of output levels that will increase the firm earnings . We can combine the ?

and the box in the same graph by noting that each point on the defines the dimensions ofan box . In figure , firms produce 150 bananas and 100 coconuts , point a on the . This is the dimension of the box drawn inside of the . The prices that consumers pay are the same as the prices producers receive , so the price line in the box has the same slope as the price line that touches the .

GENERAL EQUILIBRIUM 325 Price Line Mary Arm Bananas Coconuts ) Price Line 100 150 ( Bananas Figure 7418 equilibrium In equilibrium , the price line is tangent to the consumers indifference curves at point as well as to the at point a . Thus a competitive equilibrium is reached . Consumers are maximizing their utilities at point producers are maximizing their returns at point a , and supply equals demand in both markets consumes 100 bananas and 35 coconuts Mary Ann consumes SO bananas and 65 coconuts and the combined demand for both , 150 bananas and 100 coconuts , exactly equals the supply . POLICY EXAMPLE SHOULD THE GOVERNMENT TRY TO ADDRESS GROWING INEQUALITY THROUGH TAXES AND TRANSFERS ?

Learning Objective Show how any redistribution of resources leads to a tive equilibrium . Income inequality is the outcome of markets and society . An unequal distribution of societal resources can be represented in the abstract through the use of box analysis . Though an box represents only two people and two goods , the insight to many people and many goods . We can represent inequality by an initial distribution of societal resources that gives most of them to only one person , as shown in figure .

326 PATRICK EMERSON ( 02 01 QA Figure tax and transfer scheme to address initial Figure shows an economy where there are two people , and , and two goods , A and . The initial allocation is at A , where person has most of both goods . The competitive equilibrium that is obtained from this allocation is at , which is still highly unequal . To address this , a tax and transfer scheme could be implemented by taking away some of the initial allocation of A and from and transferring them to . This is shown in figure as the movement from allocation ( to the tion it . The government that does this is not able to know all the societal preferences and thus is unable to know where the competitive do not know the contract curve . So their tax and transfer scheme does not get them directly to a competitive equilibrium . However , the first and second welfare theorems ensure that the competitive equilibrium is efficient and that any allocation can be obtained through a redistribution ofthe initial endowment . So we can see in the figure that the new allocation will lead to the outcome . This suggests that there is no efficiency loss from a tax and transfer scheme . Person is worse before the taxes and transfers , and person is better off . Inequality has been addressed , but whether society is better off because of it is something that would require additional analyses . What we can say is that there are no wasted societal is no inefficiency . This assumes , however , that the tax and transfer scheme itself is costless , while we know that in reality , such a program would require a lot of bureaucratic costs . We also have not analyzed what a tax and transfer scheme would do to the incentive to produce . If the rich were not able to enjoy the full benefit of their labor because of an income tax , economic theory suggests that they might not work as hard , and society would produce less . How would this reveal itself ?

In this case , the would shrink , and so would the size ofthe box , and since we assume more is better , then the opposite must also be is worse . So both the bureaucratic costs and the loss from the disincentive to work suggest that there will be a cost to this program . The benefit is a more equal distribution of income . Thus whether it is a good idea

GENERAL EQUILIBRIUM 327 to implement , such a program depends on the relative benefits ofa more equal income distribution and the costs of the program . REVIEW TOPICS AND RELATED LEARNING OUTCOMES Partial versus General Equilibrium Learning Explain the difference between partial and general equilibrium . Trading Economy Box Analysis Learning Draw an box for a trading economy and show how a competitive equilibrium is . Competitive Equilibrium Box with Prices Learning Objective Demonstrate how prices adjust to create a competitive equilibrium that is efficient from any allocation . Production and General Equilibrium Learning Objective Draw a production possibility frontier and explain how the mix of production is determined in and how productive efficiency is guaranteed . Policy Example Should the Government Try to Address Growing Inequality through Taxes and Transfers ?

Learning Objective Show how any redistribution of resources leads to a competitive equilibrium . LEARN KEY TOPICS Terms analysis Studying the changes in a single market in isolation . analysis The study of how equilibrium is obtained in multiple markets at the same time . Endowments The initial available to a or an individual , ie , when first shipwrecked , the endowment available to both and anne are 100 coconuts and 150 bananas has a personal endowment of 60 coconuts and 60 bananas , and Mary Ann has a personal endowment of 40 coconuts and 90 bananas . Contract curve The line that connects all points of . See Figures and .

328 PATRICK EMERSON Price line on a graph that illustrates the set of available bundles at any given price . See Figure 1440 . First theorem of welfare economics Any competitive equilibrium is efficient . Second theorem of welfare economics Any competitive equilibrium is achievable through the reallocation of resources . Production possibility frontier that shows all the possible combinations of outputs a can produce in a day . See Series in Graphs section below . Marginal rate of transformation The cost of production of one good in terms of the foregone production of another good . Comparative advantage A person has a comparative advantage in the production of a good if they have a lower opportunity cost of production than someone else . Consumption The point at which it is not possible to redistribute goods to make one person better off without making another person worse off . Productive The point at which there exists no other mix of output levels that will increase the firm earnings . Graphs General equilibrium in oil and SUV markets Price Figure 142 General equilibrium in SUV markers and Mary Ann initial endowments and indifference curves

GENERAL EQUILIBRIUM 329 Mary Ann Coconuts 60 40 i 50 Bananas 90 Bananas Bananas Mary Ann Bananas Figure and Mary Arm and curves The box for and Mary Ann economy Mary Ann Bananas ( 150 90 OM 100 Ca ?

60 40 Coconuts 00 60 150 , Bananas Bananas Figure The and Mar ) economy Creating the box from two individual initial endowments and indifference curves 330 PATRICK EMERSON Coconuts 017 as new 50 Bananas Bananas Figure Creating the two individual initial endowments and indifference curves Mutually trade to a allocation Mary Ann Bananas 150 90 . 50 OM 100 ) 40 35 65 100 On 60 . 100 150 ) Bananas Bananas Figure trade to allocation At the optimal point , the indifference curves are tangent , the are equal , and the allocation is .

GENERAL EQUILIBRIUM 331 Mary Ann Bananas ( 150 50 OM Coconuts ) Jew 65 Coconuts 100 On 100 150 Bananas Bananas Figure Tangent curves , equal , and the The contract curve Mary Ann Bananas ) as 65 100 On 100 150 , Bananas Bananas Figure The contract curve The contract curve , the lens , and the core

332 PATRICK EMERSON Mary Ann Bananas 100 yr 60 40 Contract Curve Eb 100 On 60 150 , Bananas Bananas Figure The ( the lens , and the ( are The initial endowment and the price line Mary Ann Bananas 150 90 100 90 er 60 00 60 150 , Bananas Bananas Figure The endowment and the i ( No equilibrium in the product markets

GENERAL EQUILIBRIUM 333 Mary Ann ! Bananas 100 90 40 Bananas Bananas Figure No if ?

the Competitive equilibrium in the island economy Mary Ann ! Bananas 150 100 60 40 35 65 100 On 150 Bananas Bananas Figure 14 . 72 Competitive in the island economy Figures , Personal production possibility 334 PATRICK EMERSON Individual production possibility frontiers a ) a ) Mary Ann Coconuts 100 50 Bananas Figure 1413 Joint production Coconuts 200 200 300 Bananas Figure 14 . production GENERAL EQUILIBRIUM production possibility frontier 335 Coconuts 150 75 75 150 Bananas Figure 14 . 75 production with Coconuts 450 350 ' 200 200 300 Figure 450 Bananas 336 PATRICK EMERSON The optimal product combination Coconuts i ( 5000 6000 Bananas Figure 1417 The optimal product combination Competitive equilibrium Price Line Mary Ann 100 ) Xu mew ' Price Lin , a 00 ( Banana Bananas Figure 1418 Competitive equilibrium A tax and transfer scheme to address initial inequality

GENERAL EQUILIBRIUM 337 Figure 14 . tax and transfer scheme to address