The U.S. imports lumber among other goods from Canada. The lumber has been the topic of political dialogue between the 2 countries in the past few days. So let???s take X as ???lumber??? and Y as ???other goods???.

Suppose the Canadian lumber and other exportable goods are produced with the following production Possibilities frontier (PPF):

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?????????????? X^{2} + Y^{2} = 900

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Suppose the U.S. utility function for the Canadian lumber, X, and other exportable goods, Y, is:

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?????????????? U = X Y

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a.???????? Derive the conditions necessary to determine the ???Optimal Product Mix??? discussed in chapter 10.

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b.???????? Draw the PPF (partial just the first quadrant) with Y on the vertical axis. On the same graph, draw at least one indifference curve so as to show the ???optimal product mix???.?? Can this graph represent the ???pure exchange??? economy? Explain why or why not.

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c. ?????? Now draw in a price line that can make the ???optimal product mix??? a competitive exchange equilibrium. Can multiple prices satisfy the requirement? Explain why or why not possible to find one set of prices. In what sense is this price line similar to budget constraint (or budget line)?

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d. ???? On the basis of the work you have done so far, explain whether or not there is room for re-negotiation in terms of prices.??

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e. ?????? Can Canada accept any prices the U.S. can come up with? In other words, describe the limitations (production, resource etc.) that may hinder the negotiation from the production side.????

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f.?????????? In what sense does the graph you drew represent ???general equilibrium?????? Did you use an Edgeworth box? Explain why or why not.??