Reference no: EM133202785
Assignment:
1. Assume that the time evolution of a fish stock, when it is not harvested, is described by the equation
X = 0.7 (1- X(t)/50) X2 (t)
The fish is harvested by using the harvest function H = 0.5EX and it is sold in the market at the constant price p = 5. The cost of effort E is described by the function C(E) = 10E.
a) Describe the main properties of the given growth function.
b) Define, compute and graphically sketch the yield-effort relationship.
c) Define, calculate and graphically represent the static open access equilibrium.
d) Define the common property equilibrium effort and prove that, for this specific case, its value is equal to 15.211. Graphically sketch this solution and compare it to what found in (c).
2. You are the owner of a mine that initially contains a stock of a mineral equal to Ro and you know that the mine will be exhausted at time T (T known). The profit you will derive from selling the mineral is given by Π(t) = aq(t) - (b/2)q(t)2 - C. Your discount factor takes the standard exponential form of e-δt. Verify that the optimal extraction rate over time as a function of T is given by q(t) =a/2bT- a-√4bc/2bδ (1-e-δT). Base your answer on the relevant theory.