For the following intertemporal utility maximisation problem, V = max c(t) In(c(t) 07) e-ptdt , o subject to dk(t) dt = (k(t) ) - Sk(t) - c(t), where c(t) denotes consumption at t, k (t) denotes capitals at t, p is time preference rate, S is the depreciation rate. Assume that transversality condition is satisfied. Show the optimal path for consumption (Euler equation for consumption). Note that if the Hamiltonian method is used, you can use the following Hamiltonian, H = In(c(t)0.7) empt + a(t) (k(t)) 0.5 - Sk(t) - c(t) ), with OH da OH ac = 0 and = dt ak