# ISI 2017 Entrance Exam PEB Question

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## ISI 2017 Entrance Exam PEB Question

 Hi, Please Help me to solve this problem. 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 ??
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## Re: ISI 2017 Entrance Exam PEB Question

 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.