4. Consider a consumer that maximises the following intertemporal utility function, 111 Ct 0(1 + 9)" subject to At+1=t=(1 + r)(At + Y: 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: A; = il{g (1+?)t 0' (a) Show that the state difference equations At+1 = (1 + 1') (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 C0 and Cl