Consider an economy with two goods (1,2) and three consumers (A,B,C). The consumers have identical preference relations given by the following utility function:

uA(x1,x2)=uB(x1,x2)=uC(x1,x2)=x1x2

The initial endowments of the consumers are:

eA=(1,1)

eB=(1,5)

eC=(4,0)

(a) Is the allocation e = (e^A , e^B , e^C) Pareto-optimal? Justify your answer.

(b) Let x be the allocation given by:

xA=(2,2)

xB=(3,3)

xC=(1,1)

Is x Pareto-optimal? Does it lie in the core? Justify your answers.