class5_GE_

# class5_GE_ - Econ 51 Winter 2011 Class 5 PS#1 due Friday...

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1 Econ 51, Winter 2011 Class 5 • PS #1 due Friday. See posts at Piazzza. PS #2 posted on Thursday, due a week from Friday (January 28 th ). • Today: Continue with GE.

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2 General Equilibrium (without production) • Last time we motivated why we need to think about general, rather than partial, equilibrium. • Today we’ll see some formal analysis.
3 Rob and Tom on an island GE (w/o prod.) From the last class: Rob and Tom were stranded on a deserted island. Rob has 4 bananas and no apples. Tom has 7 apples and no bananas. Both of them like both apples and bananas and have utility; u R (a,b)=u T (a,b)=log(a)+log(b) What kind of trade will happen?

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4 Some definitions GE (w/o prod.) The goods owned by people before trade takes place are called initial endowments : Rob has an initial endowment of e R =(0,4) and Tom has an initial endowment of e T =(7,0) . Aggregate endowments are the sum of all individual endowments: e=e R +e T =(7,4) . This is all the stuff available on the island. A feasible allocation is a collection of consumptions for each agent which add up to aggregate endowments. A feasible allocation is (c R ,c T ) such that c R +c T =e.
5 The Edgeworth Box GE (w/o prod.) At their initial endowments, Rob and Tom are unhappy. They hate only one type of food - they want a fruit salad! They will trade: Rob will give Tom some of his bananas and will receive some apples in return. What can we say about the resulting allocation? An Edgeworth box is a useful visual tool. Rob is in the origin, Tom is upside down. Each point in the box is a feasible allocation

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6 Edgeworth Box GE (w/o prod.) An Edgeworth box. Rob is at the origin, Tom is upside down. Each point in the box represents a feasible allocation.
7 Indifference curves in an Edgeworth box Rob’s indifference curves look normal. Tom’s indifference curves are up side down.

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8 Pareto Efficiency GE (w/o prod.) If Rob and Tom do a good job, they are likely to trade to an allocation from which they cannot both improve. Such an allocation is called Pareto Efficient.
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class5_GE_ - Econ 51 Winter 2011 Class 5 PS#1 due Friday...

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