2. Consider the two main equations for the Neoclassical Growth Model with exogenous labor: du/act of -+ (1-5) Bou/Oct+1 0ki+1 f ( ke, Zin) = c+ (ki+1 - (1 - 8)kt) where Z, is labor-augmenting technological progress. In the steady state, Z and n grow at rates of y and 7% such that (dZ/di) /Z = y: and (dn/dn) = 9%. Assume that both production and utility take the Cobb-Douglas form: f(ke, Zin) = ki"(Zin)1- (a) Solve for the steady state expressions for capital and output. (b) Solve for the steady state expressions for the real interest rate and the real wage rate, given that capital and labor are paid their respective marginal products. (c) Kaldor (1957) asserted growing economies exhibit the following 'stylized facts' in the long run: i. Output per unit of labor grows at a rate equal to growth in technical progress. ii. Capital per unit of labor grows at a rate equal to growth in technical progress. iii. The capital-output ratio is constant. iv. The real interest rate is constant. v. The wage rate grows at a rate equal to growth in technical progress. Use your solutions from parts (a)-(b) to mathematically show that each of these stylized facts hold in the steady state of the neoclassical growth model