The preferences of two individuals are represented by the following equations: U1 1 1 2 2 2 1 1 1 = X Y and U = X Y ; where U denotes the utility of person 1; X and Y denote this person' 2 2 2 s consumption of goods X and Y, respectively; while U , X and Y stand for the corresponding variables of person 2. Person 1 is endowed with 2 units of X and 12 units of Y, whereas person 2 is endowed with 4 units of X and 6 units of Y. A. Derive the first person's demand for X as a function of PX and PY; where PX and PY represent the prices per unit of X and Y, respectively. B. Assuming that the two individuals exchange as perfect competitors, find the equilibrium value of the pr X Y ice ratio P /P . C. Calculate the first person's gain from exchange.