## Question

###### Consider a two-person (1 and 2) two good (X and Y) one-input (L)production economy. The utility function of person 1 is given byU1 = 208 x1 - 2x12 + y1 - (x2 / 7 + x22)and the utility function of person 2 is given byU2 = 208 x2 - 2x22 + y2 where xi and yi denoterespectively person i's consumption amount of good X and of goodY, i=1, 2. Each person has Li = 208 units of labour, i =1,2.The production function of good X and that of good Y aregiven respectively by X = 2 Lx and Y =Ly, wh

Consider a two-person (1 and 2) two good (X and Y) one-input (L) production economy. The utility function of person 1 is given by U1 = 208 x1 - 2 x12 + y1 - ( x2 / 7 + x22) and the utility function of person 2 is given by U2 = 208 x2 - 2 x22 + y2 where xi and yi denote respectively person i's consumption amount of good X and of good Y, i=1, 2. Each person has Li = 208 units of labour, i = 1,2. The production function of good X and that of good Y are given respectively by X = 2 Lx and Y = Ly, where LJ denotes the amount of labour used in the production of good J, J=X, Y. Derive the efficient amount of good X for person 1, x1*. Then enter the value of x1* below.

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