7. Two fishermen - Mckenna (M) and Natasha (N) - fish in Paradise Pond. They make their decisions simultaneously. The amount of fish, y, that each will catch (y and y ) depends on the amount of time (e) that each puts in each day (e and e ) and on the amount of time that the other spends fishing each day. Each player therefore has a production function for fish: Mckenna yM (em , eN ) 10 eM - 5 (em x ev ) (3) Natasha y" (e" , eN ) = 10 eN _ (el x eN ) (4) Each player derives utility from the amount of fish that they consume while disliking the effort that they need to exert : Mckenna - (M ) 2 (5) Natasha - (ew )2 (6) a. Given Mckenna's time fishing, what is Natasha's best response func- tion? Given Natasha's time fishing, what is Mckenna's best response? Explain what a best response function is. b. Define Nash equilibrium . Find the Nash equilibrium time spent fishing in this interaction. How many fish will each player catch and what level of utility will each of them have at the Nash equilibrium c. What is the value of Natasha and Mckenna's marginal rates of substitut tion at the Nash equilibrium ? Explain d. Graph Natasha and Mckenna's best response functions against each other with Mckenna's time spent fishing on the x-axis and Natasha's time spent fishing on the y-axis . Superimpose their indifference curves and show the Pareto-improving lens over the Nash equilibrium. e. What is the definition of a Pareto-efficient outcome? Find a Pareto- efficient level of fishing time for Natasha and Mckenna. How many fish do each of them catch and what would their utilities be at the Pareto efficient level of effort? (Hint: One way to find a Pareto efficient al- location of time spent fishing would be to assume a social planner maximizing social welfare)