Consider the following simple dynamic macroeconomics model: Households maximize utility: Ei=0Bu(Ct+i, nt+i), Where Ct+i, and nt+l are consumption and work effort at time period t+i, respectively. The household's time period t+i budget constraint is given by : f(ne+ike+i) + (1 + rt+i-1)be+i+(18)kt+iCt+i - Ke+i+1-bt+i+1 = 0 Where f(nt+i, kt+i) is output of the household and depends on labor input and capital in put at t+i and bt+i is the mount of real bonds held by household. Assume that both labor and capital are characterized by diminishing marginal product. Households choose Ce+in+ke+i+1, be+i+1 for i = 0,1,..... a) Set up household's intertemporal maximization problem and write out first order conditions. b) Rewrite the first order conditions in terms of marginal rated of substitution between leisure (work) and consumption, consumption over time, leisure over time, and their relative prices as well as the relationship of the return to physical capital and bonds. c) Consider the steady state in which Ct = Ct+1 = Ct+2 =.= C n = nt+1 == n, etc. d) Let = 1/(1+ p)