(c) * Prove that the household lifetime budget constraint can be written as: ao R+ - C, + mt W+(1 tt)Lt Tt 1+ Rt La T] (Q11.6) t=1 where ao = (1+ro)bo + mo/(1+ 10). Provide an intuitive interpretation for (Q11.6). (d) Set up the Lagrangian expression for the household's optimization problem, using 1 as the Lagrange multiplier. Derive and interpret the first-order neces- sary conditions characterizing the household's optimal plans regarding con- sumption, labour supply, and money holdings