1 ya px2 py2 ya 52 22 yb 625 177 4 xa x xb xa

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Unformatted text preview: good Y. Thus, the value of YB = 6.25 is the contract curve on the interior of the box. We have said in the past that the contract curve connects the origins...and this case is no exception. Thus, the contract curve for this example has three components to it. The first is from the origin for Person B along the Y-axis for Person B up to the point where YB = 6.25. The second section moves horizontally across the box until reaching the Y-axis for Person A and the final section of the contract curve is along the Y-axis for Person A all the way to the origin for Person A. 178 YA XB ICA 6.1 3 OB 8.75 Contract Curve 6.25 Price Ratio = 2.5 ICB 1 OA 8.9 12 Y B 14 XA HOMEWORK [1] Create your own (different) example of a pure exchange economy by selecting the parameters , (1- ), , (1-), XA, YA, XB, YB, such that: Consumer A Consumer B Total GOOD X XA = ? XB = ? X = XA + XB = 1 GOOD Y YA = ? YB = ? Y = YA + YB = 1 And the consumer's utility functions are Cobb-Douglas constant returns to scale form... [a] Solve the competitive equilibrium for this pure exchange economy (i.e. find the equilibrium price vector and the equilibrium demands for each good by each consumer). [b] Represent your equilibrium solution in an Edgeworth Box diagram similar to the one presented in class. [c] Find the expression for the contract curve and (in a new Edgeworth Box) draw a diagram showing your Pareto Optimal competitive equilibrium solution. 179 ECON 301 LECTURE #11 PARETO OPTIMAL THEORY PRODUCTION ECONOMY Now let's extend our Pareto Optimal concept to a production economy... Two Goods Two Factors Two Consumers Good X Capital (K) Consumer A Good Y Labour (L) Consumer B We need to consider both the exchange efficiencies and the production efficiencies in this framework. EXCHANGE EFFICIENCY Given exogenously fixed quantities of aggregate goods endowments X and Y, the pure exchange economy provides Pareto Optimal allocations of goods X between consumers A and B. PRODUCTION EFFICIENCY Given exogenously fixed quantities of aggregate factor endowments K and L, the production side will provide Pareto...
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This note was uploaded on 05/25/2010 for the course ECON 301 taught by Professor Sning during the Spring '10 term at University of Warsaw.

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