Question

Anna and Bess are assigned to write a joint paper within a 24-hour period about the Pareto optimal provision of public goods. Let tA denote the number of hours that Anna contributes to the project and tg the number of hours that Bess contributes. The numeric grade that Anna and Bess earn is a function, 22In(tA+). of the total number of hours that they contribute to the project. If Anna contributes tA, then she has (24-tA) hours in the day for leisure. Anna's utility function is UA -221n(tA +tB)+In(24 -tA), and Bess's utility function is If they choose the hours to contribute simultaneously and independently, what is the Nash equilibrium number of hours that each will provide?

Answer 1

t A 2 ta+ts 22(2h-tu).-ㄧ-ild쇼.tte).. -으 5.2.8 .. 22 52 3 zs Not 2-2 22 (21-t 2. 528 23 2 s t A 528 2-3 Max

7 t: es 2-tA) Lu 2 pm ts tatts--...._.-2노.ts lo 56一ー노'1..tß rlono Lo tA 22-95 s 二23-25