Competitive Equilibrium and International TradeNo nation was ever ruined by trade.Benjamin Franklin1. Preliminaries2. The Advantages of Trade3. The Edgewood Box Diagram4. Competitive Equilibrium5. Efficiency in Production6. Opening up an Economy to Trade7. Comparative Advantage8. Changing the Terms of Trade1Preliminaries• Focus on sections 16.2, 16.4-16.8• On Friday, April 21, Marzena Rostek’s sections (which usually meet inWLH) will meet in SA80, 107.2The Advantages of Trade• Some definitions– An exchange economy is a market in which two or more consumerstrade two good among themselves.– A Pareto efficient allocation is an allocation of goods in which noone can be made better off without making someone else worse off.• In order for two parties to engage in a voluntary exchange, both partiesmust be better off. In the language of the policy world it must be“win-win”.3• Consider the book’s example of James and Karen with food and cloth-ing.• Initial allocationIndividual allocation MRS of food for clothingJames 7 food, 1 clothing 1/2Karen 3 food, 5 clothing 3• James is currently willing to trade 1/2 a unit of clothing to get 1 unitof food. In other words, he is willing to give up 2 units of food to getone unit of clothing.• Karen is currently willing to trade 3 units of clothing for one unit offood. In other words, she is willing to give up 1/3 a unit of food to getone unit of clothing.4• Are there gains to trade here? Yes.– Karen is willing to give up 3 units of clothing for 1 unit of food.James is willing to give up 1 a unit of food for 1/2 unit of clothing.– If James gives Karen one unit of food and receives one unit of cloth-ing in return, both are better off.– James gets one more unit of clothing which he values more than theone unit of food he gave up.– Karen gets one more unit of food which she values more than theone unit of clothing she gave up.• Trade will continue until James and Karen equate marginal rates ofsubstitution.• An allocation of goods is efficient only if the goods are distributed sothat the MRS between any pair of goods is the same for all consumers.5The Edgewood Box Diagram• Among the two consumers, James and Karen, there are 10 units of foodand 6 units of clothing.• We can view trade between these two people in an Edgewood box dia-gram.• An Edgewood box diagram shows all possible allocations of either twogoods between either two people.• Figures 16.3 - 16.6• Since the total supply of food is fixed at 10 and the total supply ofclothing is fixed at 6, for every unit of clothing James gains, Karenmust give up one unit.6• Consider an initial allocation.• Gains to trade, but even if a trade from an inefficient allocation makesboth people better off, the new allocation is not necessarily efficient.• An efficient allocation is one in which the MRSs of James and Karenare equated. That is where their indifference curve are tangent.• The contract curve is the curve showing all efficient allocations of goodsbetween two consumers.– It is all the points of tangency between each of their indifferencecurves.– These allocations are efficient because there is no way to reallocatethe goods to make someone better off without making someone elseworse off.– Karen and James have strong incentives to move (via trade) to apoint on the contract curve.7Competitive Equilibrium• For a competitive equilibrium we need two things1. Consumers should be maximizing their utility given prices.2. Markets should clear. That is supply should equal demand.• What prices are consistent with a competitive equilibrium?• Recall from consumer demand theory, that consumer optimization im-plies thatMRS =MUFMUC=PFPC• Recall we argued, if everyone faces the same relative prices for the twogoods, and everyone is optimizing ... then everyone must have the samemarginal rate of substitution for food and clothing• The market is offering everyone the same rate of exchange for foodand clothing, and everyone is adjusting consumption of the goods untiltheir “internal” marginal valuation of the two goods equals the market’s“external” valuation of the two goods.8• So we know from consumer demand theory, thatMRS =MUFMUC=PFPCmust hold in equilibrium for all consumers.• But do markets clear at these prices?• Yes, whenMRS =MUFMUC=PFPCholds for all consumers, no wants to engage in any more trade. All theincentives for additional trade are used up. So markets have cleared.9• RECAP: In equilibrium:– Because the indifference curves are tangent, all marginal rates ofsubstitution between consumers are equal.– Because each indifference curve is tangent to the price line, eachperson’s MRS between two goods is equal to the ratio of prices ofthe two goods.• FormallyMRSJF,C=PFPC= M RSKF,C• I believe there is a typo in equation 16.1 in the book.• If everyone trades in the competitive marketplace, all mutually bene-ficial trades will be completed and the resulting equilibrium allocationof resources will be economically efficient.10Efficiency in Production• Edgewood box• Analogous to what we did above expect with inputs (capital and labor)and isoquants.• Capital and labor each in fixed supply.• Technical efficiency is when firms combine inputs to produce a givenoutput as inexpensively as possible.• Production contract curve is shows all the technically efficient alloca-tions of capital and labor.• From these tangency points we can determine the relative price of laborand capital.• Recall from our discussion of theory of the firm that cost minimizationoccurs whenslope of isoquant = slope of isocost line−MRT S = −wrMP LMP K=wrratio of marginal products = ratio of input prices11• Recall from our discussion of theory of the firm that cost minimizationoccurs whenslope of isoquant = slope of isocost line−MRT S = −wrMP LMP K=wrratio of marginal products = ratio of input prices• We can rewrite this optimality condition as:MP Lw=MP Kr• This condition tells us that at the cost minimizing input combination,the additional output per dollar spent on labor equals the the additionaloutput per dollar spent on capital. Thus the firm is getting equal “bangfor the buck” from each input.• We can display the production contract curve as a production possibilityfrontier.• We are back were we started in January.12A Two Good Model of Trade• Start with a small closed economy.– Closed means that it doesn’t trade