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Question: an economy has a production possibility frontier given by x2...

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An economy has a production possibility frontier given by X2 + 4Y2 = 100.
(i) Graph this ppf.
(ii) Calculate the opportunity cost of an extra unit of good X when
a. X = 2 b. X = 8.
[Hint: you need ΔY/ΔX; either use calculus; or calculate Y when X=2 and X=3 to get an approximation. Excel might be helpful for this.]
(iii) If consumers want to consume equal amounts of X and Y, how much of each should be produced?
(iv) Now the country can trade. It produces only X, and for every unit of X that it ships abroad it gets one unit of Y in return. Graph this consumption possibility curve.
(v) Given that the country can trade on these terms, and that consumers still want to consume equal quantities of X and Y, how much X and Y will they consume?
(vi) How much does this country benefit by being able to trade?

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