. (i) Write each constraint in nominal terms then in real terms, in using the classic relationship between the price of bonds and the nominal interest rate, i.e. PB = 1/1+i i (ii) Write the intertemporal household budget constraint (iii) Precisely pose the household problem, then the first order conditions (iv) Write the consumption function of the first period.

There are N working age households in the economy and the population growth rate in the economy is assumed to be zero. Each household has a given and constant activity rate I, so that the number of households active in the economy is given by L = IN. Each household provides one hour of labor, so that the labor supply is given by Ls = 1 I IN. In return, households receive the nominal hourly wage Wt, t = 1, 2, for one hour of work offered, as well as the nominal net prots {dividends} as owners of the firms, Dth = l'lt -PtAutonancementt, t1, 2. Finally, they pay at taxes each period PtTt, t = 1, 2. Households save only by buying B bonds at the end of the first period, at the PB price. They start with an initial wealth of BB bonds which are reimbursed to them by the government at the price of $ 1 bond. Households also have an intertemporal utility function given by l \"Will-H} = 1110: + l + luC'g P where p:- 0 measures the rate of preference for the present