Consider two fishers John (J) and Amanda (A) are both fishing at a public lake. Let us use the following notation:

3/, = number of fish caught by i = J, A over some given period. ei = amount of time that i = J, A spend fishing, measured in fraction ofthe time period (effort level). 1r,- = the net payoff of fisher i= J, A. 2 Let's assume that Tti = yi %, where yA = 2(1 0.Se])eA and y] = 2(1 0.53A)e].Note that 2. the term 9?\" denote the cost of effort. Assume the reservation payoff for fishers are 11?, nf. IV. VI. Find the Nash equilibrium effort level. What is the efficient effort level? Now suppose Amanda owns the lake, so she can set the effort levels. She sells a permit for a fixed fee F to John. What is the maximum F, she can charge? Now suppose again that the lake is public. The local government would like to set a tax on effort level in order to make sure that each fisher only fishes at the efficient level. How much should be the tax per unit of effort level? Suppose that the lake is public, but now each fishers care about the other fisher's 2 a? payoff, i.e.1tA = yA 9f + any and Hi = yj % + am, where O S at S 1 . What is the Nash equilibrium effort level now? What will be the Nash equilibrium effort level if a = 1? What will it be if a = 0? Now suppose the power relation is such that Amanda has the right to fish rst and then John is allowed to fish. What will be the effort level in this case? Will the effort levels be efficient