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4. The Problem of Exchange We consider now the development of competitive markets starting from 2-person barter exchange (direct exchange of goods) 4.1 Harvesting and Gathering: The Need for Trade property rights are respected, goods exchanged only by voluntary trade two goods A and R two agents G and E G harvest a G =8 and r G =2, E a E =2 and r E =6 total economy consists of a=10 and r=8

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4.2 Constructing the Edgeworth Box and Finding Feasible Trades Edgeworth box allows us to depict feasible allocations, possible trades and: equilibrium: outcome of trading process so that agents have no further incentive to trade horizontal dimension represents total amount of good R, vertical dimension of good A allocation to G measured from origin, allocation to E measured from top right hence each point represents one feasible allocation, i.e. possible outcome of trading process no-trade allocation: agents consume what they originally possess (Fig 4.1)

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4.3 Finding Equilibrium Trades is there a feasible allocation that both agents prefer to no- trade allocation? If not, they will remain at NTA if yes, they will trade to an equilibrium allocation where there is no further incentive to trade if equilibrium allocation is not unique, outcome has to be determined by bargaining if indiff. curves cross at NTA, trade can make both agents better off (all allocations inside lens bordered by IC’s are better for both) (Fig 4.2) an agent will block all trades that are not individually rational, i.e. that make her worse off than NTA final allocation must be efficient or Pareto-optimal: there is no other allocation where at least one agent is better off and none worse off If one agent owns everything and the other nothing, is that Pareto-optimal? Yes, because to make the second better off, the first hast to be made worse off

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whenever indiff. curves of the agents cross, there are allocations that are better for both hence in Pareto-optimal allocation IC’s have to be tangent, i.e. the MRS have to be identical otherwise G would be willing to trade at different ratio (e.g. 2:1) than E (e.g. 4:1) and hence they could find beneficial trade (e.g. trading at a ratio 3:1) contract curve links all points where IC’s are tangent, hence all efficient trades (Fig 4.3) core: set of Pareto-optimal allocations that cannot be improved upon by any individual or group of individuals together core is the part of contract curve between no-trade IC’s, represents all equilibrium allocations still leaves many possible outcomes, hence bargaining process matters

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Pareto Optima and the Contract Curve (Appendix B) finding Pareto optimum amounts to maximizing one agent’s utility holding the other’s constant in Pareto optimum thus MRS E = MRS G example: let the total amount of good X be w x and the total quantity of good Y be w y u E (x E,y E ) = x E y E and u G (x G,y G ) = x G y G then MRS E = y E / x E = y G / x G = MRS G using the constraints x E + x G = w x and y E + y G = w y we obtain y E / x E = (w y - y E )/(w x - x E ) and thus y E = x E w y / w x

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4.4 A Growing Population and the Core Assume population grows through replication, identical copies of the agents appear already with 2*2 agents trade where all gains go to one type (say E) is not possible any more (Fig 4.4) the 2 G could suggest to trade with only 1 E the G’s would then be better off due to convexity of preferences hence coalition of 2 G and 1 E would block trade core is smaller with 4 than with 2 agents core shrinks further as population grows for infinite population core consists of only one point (the competitive equilibrium allocation) where IC’s are tangent to line to NTA (Fig 4.6) all other allocations can be blocked by a sufficiently large coalition

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Competitive Behavior in large economy agents don’t bargain individually but act as price takers competitive behavior: deciding upon supply and demand taken prices as given in large economy barter trade is inefficient, use good called money agent’s budget line goes through NTA with slope = price ratio, straight because individual agent is small so does not influence prices given NTA and prices, optimal bundle is the one where the budget line is tangent to IC if at given prices G’s want to supply more of A (and buy more of R) than E’s are willing to buy (sell) there is an excess supply of A and excess demand of R

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competitive equilibrium consists of competitive prices such that supply and demand match when each agent maximizes utility resulting allocation is competitive equilibrium allocation in competitive equilibrium for all agents MRS = price ratio competitive equilibrium is the outcome both of bargaining of infinite population and price-taking behavior, hence we can assume that a market for each good exists

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