SOLOW GROWTH MODEL

1. Consider a modified version of the Solow Growth Model in which there is a represen- tative laborer (L), a representative financier (F), and a representative firm. The total population of the economy evolves according to Ni+1 = (1 + xt) N where it is the population growth rate. The laborer represents an exogenously given fraction Of E (0, 1) of the total population Nt at date t. She supplies her labor inelastically to the representative firm each period, but is not allowed to invest in capital. Her budget constraint is CL = w.ON. where we is the real wage and Of is her consumption at date t. The financier represents the remaining fraction (1 - 0:) of the total population Me at date t. She owns the capital stock and invest a fraction st E [0, 1] of her income each period in new productive capital, but is not allowed to work. Her budget constraint is OF + h = niki and her capital accumulation equation is Kit1 = It + K.(1 -8,). where rt is the rental rate, of E (0, 1) is the depreciation rate, K, is the capital stock, and C, is her consumption at date t. The representative firm is competitive and has access to the production technology Yl = = ( Kd ) a ( N ) 1 -a where Ka and Ne are capital and labor employed in the production process, respec- tively, z > 0 is total factor productivity, and a E (0, 1). (a) What is the policy rule of the laborer? (b) What are the policy rules of the financier? (c) Use the problem of the representative firm to derive expressions for the rental rate, T't, and the wage rate, wt. (d) What are the market clearing conditions