MIT14_03F10_lec10

MIT14_03F10_lec10 - Lecture Note 10 General Equilibrium in...

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Lecture Note 10: General Equilibrium in a Pure Exchange Economy David H. Autor, Massachusetts Institute of Technology 14.03/14.003, Microeconomic Theory and Public Policy, Fall 2010 1
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1 Motivation To now, we’ve talked about one market at a time: labor, sugar, food, etc. But this tool is a convenient fiction. Not always a badly misleading fiction. But still a fiction. Markets are always interrelated: Reduce sugar tariffs reduce sugar prices Drop in employment of sugar cane farmers • → Cane workers apply for other farm jobs, depress wages for farm workers generally • → Arable land is freed for other uses • → Gives rise to new crop production • → Prices of other farm products fall • → Real consumer incomes rise • → Rising consumer income increases demand for sweets, a luxury good • → The dessert market grows and the café sector booms • → Starbucks buys up all urban real estate in four major cities • → ...there is literally no end to this chain of events. Viewed from this perspective, the notion of the market for a single good is a convenient fiction; all changes in quantities or prices ultimately feed back into the demand and/or supply for all other goods through several channels: Income effects Substitutability/complementarity of goods whose prices rise/fall Changes in the abundance/scarcity of resources To understand this richer story, we need a model that can accommodate the interactions of all markets simultaneously and determine the properties of the grand equilibrium. What we need to develop is a general equilibrium model, in contrast to the partial equilibrium models we’ve used thus far this term. 2
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2 The Edgeworth Box We need to reduce the dimensionality of the ‘all markets’problem to something analytically tractable. But we need to retain the essence of the problem. The Edgeworth Box (after Jevons Edgeworth) allows us to do this. It turns out that we only need two markets to see the entire problem: 2 goods 2 people Pure exchange. Perfect expression of the economic concept of opportunity costs. Simple as this model is, it can be used to demonstrate two of the most fundamental results in economics: the 1st and 2nd welfare theorems. [Note: We will not model or analyze the production of goods in this model, only pure exchange. The extension of the GE model to production is fascinating in its own right and well worth mastering, but I have decided that it needs to yield space to other topics in 14.03/14.003. If you would like to know something about GE with production, please ask for my GE lecture notes from 14.03/14.003 Spring 2003.) 2.1 Edgeworth box, pure exchange —Setup Two goods: call them food F and shelter S. Two people: call them A and B . The initial endowment: F A S A E A = ( E , E ) F B S B E B = ( E , E ) Their consumption: F A , X S A X A = ( X ) X B = ( X F B , X S B ) 3
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Without trade: X A = E A X B = E B With trade, many things can happen, but the following must be true: X F A F B F A + E F B + X E = X S A S B S A + E S B + X E = Note the elements of this figure: All resources in
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