A researcher has 100 hours of work which have to be allocated between two research assistants, Aditya and Gaurav. If Aditya is allocated x hours of work, his utility is −(x − 20)2. If Gaurav is allocated x hours of work, his utility is −(x−30)2. The researcher is considering two proposals: [I] Aditya works for 60 hours and Gaurav works for 40 hours. [II] Aditya works for 90 hours and Gaurav works for 10 hours.
Which of the following statements is correct.
(a) Proposal I is Pareto efficient but Proposal II is not.
(b) Proposal II is Pareto efficient but Proposal I is not.
(c) Both proposals are Pareto efficient.
(d) Neither proposal is Pareto efficient.
How do you getting this Aditya 60 hours and Gaurav 40 hours ??
I took this exam and I remember doing this. Graph out the utility of both as a function of no of hours worked for say Gaurav. Bothwill be concave downwards. Then look for a mutually beneficial deviation graphically. Should be easy.
You need to graph the utilities as a function of x (two downward shaped parabolas, so -(20-x)^2 and (70-x)^2), not in the edgeworth box. Then you should check, for any x, whether you can find an x' such that graphs of both guys at x' are above their respective graphs at x.