4. Consider a consumer that maximises the following intertemporal utility function, In Ct max _ ( 14 0 ) " Ct subject to At+1 = (1 + r)(At + Yt - Ct), where C is consumption, Y is labour income, A is private wealth, r is the interest rate, and p is the discount rate. Assume that the transversality condition holds: lim - At = 0. t-woo (1+r)t (a) Show that the state difference equations At+1 = (1 + r)(At + Yt - Ct), can be transformed into a life-long budget constraint. (b) Obtain the Euler's equation by the Lagrangian method with the above life-long budget constraint. Continue with question 4. Use a Bellman's equation to obtain the Euler equation between Co and C1