Two roommates, Eric and Noah, decide independently of each other how much time to spend cleaning...

 

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Two roommates, Eric and Noah, decide independently of each other how much time to spend cleaning the common area of the aparment they share. Specifically, Eric chooses hE 20 (hours per week), while Noah chooses hy 0. They both enjoy living in a clean space, and both pay a cost for cleaning (as it leaves them less time to do other things). Their utility when the apartment has been cleaned for h hours (where h = hE+ hy is the total number of hours the two roommates spend cleaning) is 8h, while their hourly cost is a variable c > 1. To summarize, their payoff functions are: UE(hE, hN) = 8hE+ hN - chE UN(hE, hN)=8hE+hN-chN. (a) (2 points) Compute the (pure-strategy) symmetric Nash equilibrium (how many hours will each roommate spend cleaning?). (b) (1 point) Is the Nash equilibrium computed in (a) Pareto efficient? Explain. (c) (1 point) Suppose Eric and Noah are getting busy with exams coming up. This increases their cost of cleaning, from c to c'> c. What impact does this have on the equilibrium number of hours they spend cleaning? Two roommates, Eric and Noah, decide independently of each other how much time to spend cleaning the common area of the aparment they share. Specifically, Eric chooses hE 20 (hours per week), while Noah chooses hy 0. They both enjoy living in a clean space, and both pay a cost for cleaning (as it leaves them less time to do other things). Their utility when the apartment has been cleaned for h hours (where h = hE+ hy is the total number of hours the two roommates spend cleaning) is 8h, while their hourly cost is a variable c > 1. To summarize, their payoff functions are: UE(hE, hN) = 8hE+ hN - chE UN(hE, hN)=8hE+hN-chN. (a) (2 points) Compute the (pure-strategy) symmetric Nash equilibrium (how many hours will each roommate spend cleaning?). (b) (1 point) Is the Nash equilibrium computed in (a) Pareto efficient? Explain. (c) (1 point) Suppose Eric and Noah are getting busy with exams coming up. This increases their cost of cleaning, from c to c'> c. What impact does this have on the equilibrium number of hours they spend cleaning?

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a To find the symmetric Nash equilibrium we need to find the optimal hours each roommate should spen... View the full answer