The firms. Firms are competitive but only make static choices in this matter. Thus, they choose the working hours at each period Ldt, t = 1; 2, which they pay at nominal hourly wage rate Wt, t = 1; 2, generate nominal profits t, t = 1; 2, that they partly use to maintain the existing capital stock through self-financing, such so that on each date the investment is given by PtIt = PtKt, and that it is financed by retaining part of the profits: PtIt = PtAutofinancementt and the rest of the profits are redistributed to households owners

Part 1: There are N working age households in the economy and the population growth rate in the economy is assumed to be zero. Each household at a rate of given and constant activity ', so that the number of households active in the economy is given by L = N. Each household provides one hour of work, so that the supply of work is given by Ls = 1 * N. In return, households receive the nominal hourly wage Wt, t = 1; 2, for one hour of work offered, as well as the nominal net profits (dividends) in as owners of firms, DIVt = t - PtAutofinancementt, t1; 2. Finally, they pay flat-rate taxes at each period PtTt, t = 1; 2.

Households save only by buying B bonds at the end of the first period, at the price PB. They start with an initial wealth of B0 bonds paid back to them by the government at a price of $ 1 bond.

Households also have an intertemporal utility function given by

U (C1, C2) = lnC1 +(1 /1 + )lnC2

Where > 0 measures the rate of preference for the present tense

1) 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 )

 2) Write the intertemporal household budget constraint

 3) Precisely pose the household problem, then the first order conditions

4) Write the consumption function of the first period