1. Consider the following dynamic optimization problem for an individual: e-ptIn(c(t))dt w(t) = rw(t)- c(t) w(0) = wo, w(T) = WT max s.t. where c(t) denotes consumption, w(t) denotes total wealth, p is the discount rate, r is the interest rate, r > p > 0, and wo > WT > 0. (1) Present the current-value Hamiltonian function and the necessary conditions using the current-value Hamiltonian function. (2) Use the conditions in (2) to derive a system of first-order differential equations in the state and co- state variables. Indicate a possible solution trajectory in the phase diagram drawn based on this system.