7. A and B are assigned to write a joint paper within a 24-hour period about the Topic - “Pareto optimal provision of pu

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7 A And B Are Assigned To Write A Joint Paper Within A 24 Hour Period About The Topic Pareto Optimal Provision Of Pu 1 (70.77 KiB) Viewed 27 times

7. A and B are assigned to write a joint paper within a 24-hour period about the Topic - “Pareto optimal provision of public goods”. Let ta denote the number of hours that A con- tributes to the project and to the number of hours that B contributes. The numeric grade that A and B earn is a function, 23 Inſta + to), of the total number of hours that they contribute to the project. If agent i, i = a, b, contributes ti, then she has (24 – tị) hours in the day for leisure. A's utility function is Ug = 23 In(ta +ty) + ln(24 – ta) and B's utility function is Ug = 23 In(ta + to) + ln(24 – to). i) If they decide to choose hours to contribute simultaneously and independently, what is the Nash equilibrium number of hours that each will provide? ii) What is the number of hours each should contribute to the project that maximizes the sum of utilities? (5+3)