http://economicsentrance.weebly.com/uploads/1/1/0/5/1105777/24_june_2006_option_a.pdf The answer is that this allocation is not a competitive equilibrium but is pareto efficient. I get the pareto efficient part as now to make anyone better off we have to make the other agent worse off. But why is it not a competitive equilibrium? Does the competitive equilibrium in case of two min functions is only the locus joining the diagonals of the origins of both the agents? Someone please explain. I have a hard time in understanding the difference between the two.
An allocation is Pareto Efficient if you move away from it one individual gets worse off and other is equally/strictly better off ie. you cannot make someone better off without making someone else worse off.
An allocation is Competitive Equilibrium allocation if that is utility maximising bundle and market clears.
ie. for Competitive equilibirum, we need to check two conditions:
(i) Given prices, Agents maximize their utility i.e find demand.
(ii) Market clears for all goods.