In a twoperiod model, suppose the Alfred's lifetime utility[ function is U{c1, cg} = Mel} + ,Bu(c2], 1where ILL] is a concave function. The market interest rate in constant, 1". Alfred's income are yl and y: in Period 1 and 2, respectively. The initial wealth endowment is tun. {a} Derive the Euler equation in this case. {h} Further assume that ,8 = l and r = I], solve for the optimal consumption {cL c5} i.n Period 1 and 2. {c} Further assume that income in Period 2 is a random variable, g, 1which takes two values, y" and y', with equal probability, i.e., Ely2] = 1 2" = yz. What is the agent's optimal consumption in Period 1, if the utility function takes the quadratic form, i.e. u(c) = n.c-;c-? Is there any precautionary saving? Why or why not