2. (Discrete Time] The International Whaling Commission wishes to maximize the use plus non-use benets of the whale stock: Maximize i[ph+U{x) ch}e'"df where p=$19 is the per unit price of whales for consumption, It is harvest, c = $25M is per unit cost of harvest, U(x) is the utility people get from l-mowing there are x whales in the ocean, and r = 0.05 is the social discount rate. The constraints are the population dynamics and non-negativity conditions: i=g(x)h and 13.633, where g{x}=.1.x{lxf 100,000} is the net growth of 1whales. Assume that the annual marginal preservation value (utility) of whales is UTx} = IMO0.0 11'. Find the optimal amount that should be harvested every year and the optimal level of the stock of whales. {Continuous Time). Maximize Euthht 'l' \"('55) Chg] where p=$19,50{] is the per unit price of whales for consumption, in is harvest at time t, c=$2,5[l is per unit cost of harvest, (Kn) is the utility people get at time I from knowing there are x: 1Whales in the ocean, and = l! 1.05 is the social discount factor {r = {105 is the discount rate). The constraints are the population dynamics and non-negativity conditions: x~1x:=g(.r.u) h: and 1:, h: 2 U, V: where gL'o) = {11 so {1 gramme) is the whale {logistics} growth function. Assume that the annual marginal preservation value (utility) of whales is U'(xr) = 11100 {)1}le (a) Write out the current value Hamiltonian