3. Suppose the consumer has preferences over consumption today and tomorrow repre sented by la C, la C +5E } UECECil=1a la where a = '2 and b E [[}f 1]. The consumer has nonlabor income 3,: and 3f today and tomorrow. Assume there are no taxes {t = t' = D) and take the interest rate 'r as given. (a) 1Write down and solve the consumer's lifetime optimization problem. In particu lar, nd expressions for current and future consumption and savings in terms of y, y'. a, b, and 'r. Denote by 315,1\") the savings decision of the consumer given the parameter b and the interest rate r. (b) Consider the special case of ti = 1 and r = D. How do your answers from part {a} change? Describe the consumer's savings decision. [c]: Consider the special case of b = D for any i". How do your answers from part (a) change? Describe the consumer's savings decision. Ed} Provide an economic interpretation of the parameter b