Question 7. Malthusian Growth Model (Continuous Time): Brander and Taylor (1998) described a Ricardo-Malthus model of a resource dependent population on Easter Island. They posit the following relationships between human population (L) and resource stock (S): S = rS(1 S/K) LS L = L(b d + S) where rS(1 S/K) is natural stock growth, LS is harvesting from the stock, (bd) are baseline human birth and death rates and S represents how a more bountiful harvest increases human population growth. Expressing S and L in (000's), the parameters take the values r = 0.05, K = 12, = 0.01, = 0.4, (b d) = 0.1, = 4.

(a.) Identify all the steady states of the system.

(b.) Provide an analysis of the dynamic properties of the interior steady state i.e. with S > 0 and L > 0 (Use the equations of isoclines and derive directions of S and L).

(c) Draw the phase diagram of the system for S > 0 and L > 0 in the (L, S) space.

(d) Discuss the stability property of the interior steady state.