Problem 1: Fisheries Population Dynamics [3.5 points] Consider a tuna stock at the beginning of time t, denoted by the variable XE, measured in metric tons. Suppose that in each period, the stock of tuna grows according to the difference equation X H1 = X; + F{Xt} Ht, where 15(th is a function representing the net growth of tuna and HE is the harvest of tuna at time t. Suppose that net growth of tuna depends on the size of the fish stock and is given by the function FIX!) = Xe\" Xi}- 1.3. [0.5 points] Is there some level of X at which the net growth of tuna is maximized? If so, what is it? LC. [0.5 points] Now suppose that we have the following simple rule for determining the harvest of tuna: Ht 2 0X}. Determine the steady state stock and harvest levels of tuna. {Note Actually, there are two steady states, one when X = ll I'm onlyr interested in the second one.) 1D. [1}.5 points] Suppose your goal is to maximize sustainable harvests of tuna. 'Wl'lat level of (I would you choose