Only needs help on question number 3.What method should be adopted to explain the problem? How does it require us to understand this process? I was wondering where it was going to simplify the formula.

There are two types of agents, doctors (D) and athletes (A), and they live for two periods. For each type i E {D, A}, given an initial endowment (51 ,), we consider the following problem: _max logm'i + logrrg s.t. I; = 5'2 + (1 +r) (E: :r'1) zizoagzu where at? is the consumption of type i in period 1, 3:; is the consumption of type i in period 2, ,3 E (0, 1) is the discount factor, and r > 0 is the real interest rate. 1. Derive the demand function of each type. 2. Derive optimal individual savings of each type. 3. Suppose that (?,E)) = (0, 1) and (Ef,'24) = (1,0). Denote the num- bers of agents of type; D and A by N D and N A, respectively. Assuming the existence of equilibrium, derive the equilibrium value of 1', that is, the value of r such that the total optimal savings are zero