DSE2009 (Ques#29, Option A)

[vikram]

Consider an exchange economy with two consumers (A&B) and two goods (x&y).  Assume that total amount of x available is 4 and total amount of y available is 2 which is to be optimally distributed between A & B. A’s utility function is UA = xA^2 + 4*xA*yA + 4*yA^2  and B’s utility function is UB = xB + yB. The contract curve for this exchange economy will be what?

How can the answer for this be "allocations satisfying (xA=0, 0≤yA≤2) and (0≤xB≤4, yB=0)"? My estimate was the entire Edgeworth box.

Please tell me where I am going wrong.

[Rain Man]

the first agent's utility fn is  ( x + 2y ) ^2 . so it is a case of perfect substitutes // indifference curves will be straight lines
the second agent's utility fn is x + y , so this too is a case of perfect substitutes // indifference curves will be straight lines

but the magnitude of the slope for agent 2 > the magnitued of the slope for agent 1 .

so when we draw the indifference curves we find that the utility of agent 2 can be increased w/o affecting the utility of agent 1. and the optimum (efficient) point is reached along the Y axis where x = 0 and y varies .

[vikram]

Thanks!