2 Deterministic optimal growth model. Let f ( k ) = ka u(c) = 1 - a A representative individual solves max e-ptu( ct) dt C subject to kt = f ( kit ) - ct ko = k* 2.1 Write the appropriate Hamiltonian [10 points] 2.2 State the solution for consumption as a function of the costate vari- able. [10 points] 2.3 State the equation for the costate variable. [10 points] 2.4 State the steady-state capital. [15 points] 2.5 State the steady-state interest rate. [15 points] 2.6 State the flow of profit in the steady state. [15 points] 2.7 State the price of an equity share in the representative firm in the steady state. [15 points] 2.8 State the equation for the interest rate along the growth path (not just at the steady state), assuming that the initial capital is ko. [10 points]