3 Agent Problem


#1

I was wondering what would happen in an economy with more than 2 agents and i found the next problem.

Consider a Pure Exchange Economy between three agents (A, B and C).
The function of agent A is Ua = ln (Xa) + ln (Ya) and its endowment is (Xa, Ya)= (2,3)

The utility function of agent B is Ub = ln (Xa) + 2 ln (Ya) and its endowment is (Xb, Yb)= (3,2)

Finally, the agent C only consumes X in such a way that its utility function is Uc= Xc and its endowment is (Xc, Yc)= (0,10)

a) Under this context, what would be a competitive equilibrium?
b) Find the equilibrium normalizing Px=1


#2