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the preferences of two individuals are represented by the following equations: U1 = X1Y1 and U2 =...

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Economics

the preferences of two individuals are represented by thefollowing equations:
U1 = X1Y1 and U2 = X2Y2; where U1 denotes the utility ofperson 1; X1 and Y1 denote this person's consumption of goods X andY, respectively; while U2, X2 and Y2 stand for the correspondingvariables of person 2. Person 1 is endowed with 2 units of X and 12units of Y, whereas person 2 is endowed with 4 units of X and 6units of Y.

A. Derive the first person's demand for X as a function of PXand PY; where PX and PY represent the prices per unit of X and Y,respectively.

B. Assuming that the two individuals exchange as perfectcompetitors, find the equilibrium value of the price ratioPX/PY.

C. Calculate the first person's gain from exchange.

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