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# Handout #3 Econ326 Spring 2012 Instructor: Ginger Jin In-class example of Edgeworth Box Edgeworth box is used to describe two-good two-person...

Hello, Can you please explain to me how the equation Px/Py=(Ya-5)/(5-Xa) was got. And how equation 5 and 6 was gotten also. Thank you.

Handout #3 Econ326 Spring 2012 Instructor: Ginger Jin 1 In-class example of Edgeworth Box Edgeworth box is used to describe two-good two-person economy. Consider a close economy with two individuals (A and B) and two goods (X and Y). At the start, A and B are each endowed with 5 units of x and 5 units of y. So in total there are 10 units of X and 10 units of Y. The utility function of A is U A =X A *Y A , the utility function of B is U B =X B 2 *Y B . (1) At the endowment, compute the marginal rate of substitution for A and B separately. Are they equal? Is there any room for trade? 5 1 5 XA A YA MU Y MRS MU X 2 22 2*5 2 5 X B B B B Y B B MU X Y Y MRS MU X X The two MRS are not equal: A is willing to trade one X for one Y, but B is willing to trade one X for two Ys. Since B thinks X is more valuable than A does, both could be better off if B gives away some Y for X. In other words, there will be room for trade. (2) At what price will A and B trade? How many X and Y will A have at the end of the trade? How many X and Y will B have at the end of trade? Suppose the allocation after trade is (X A ,Y A ) for A and (X B ,Y B ) for B. The two individuals must divide the existing resources, so Equation 1: 10 AB XX  Equation 2: 10 AB YY  In the following Edgeworth box, the trading price is the slope of the short red line that links endowment to the final allocation, this implies: 5 5 XA YA PY PX
Handout #3 Econ326 Spring 2012 Instructor: Ginger Jin 2 The allocation after trade must reflect the optimal choices of A and B. We know when A maximizes her utility, her MRS is equal to price; when B maximizes her utility, her MRS is also equal to price. This amounts to: Equation 3: 5 5 X A X A A Y A Y A MU Y P Y MRS MU X P X Equation 4: 25 5 X B X A B Y B Y A MU Y P Y MRS MU X P X Now we have four equations (1-4) to solve four unknowns (X A , Y A , X B , Y B ), which yields a unique solution. There are many ways to go through the algebra. Below is one of them: Rewrite Equation 3, we have Equation 5: 2 5 5 A A A A X Y X Y  . U B U A Endowment MRS A =1 at Endowment MRS B =2 at Endowment Allocation after trade A B 10 10
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The attachment says:
In the following Edge worth box, the trading price is the slope of the short red line that links
endowment to the final allocation,
So the given equation is the equation for...

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