OGM (the basic): Consider the following OGM where the representative agent lives two periods as an adult and a retire. The utility function of an individual born at the beginning of period t is given by: U = ln ct + ln c o t+1 (15) where ct and c o t+1 represent current and old age consumptions, respectively. The adult supplies a unit of labor when young to earn income that she allocates between consumption and savings, where the latter plus return are used for old age consumption. The budget constraint is given by: ct + st = !t (16) c o t+1 = (1 + rt+1) st (17) where st is saving; !t and rt are the wage rate and the interest rate respectively. Assume also a complete depreciation of capital and zero population growth rate. The representative rm uses the following production function: yt = Ak1 t L = Ak1 t (18) where the total labor force in the economy is standardized as one, L = 1. (a) Form the household problem and derive the household optimal saving rate. (b) Dene the rms optimization problem, solve for optimal wage rate and the rental rate of capital, and dene market equilibrium conditions. (c) Derive the growth rates or the steady-state values (whichever is appropriate) of consumption, output and capital. (d) Discuss the main features of overlapping generation model, and compare and contrast it with the Ramsey mode