4.3. Numerical Example of Endogenous Growth (20 Points) Problem 3. In this question you will calculate the aggregate consumption and quantity of human capital of a discrete human capital model under different scenarios and then compare them. To begin with lets first define a basic discrete version of the model. Aggregate consumption will be defined as (1) C = wuH where . w = is the wage rate. H = Units of Human Capital today HE (0,1] = Fraction of time spend working The technology for accumulating human capital is (2) H' = B(1 - u - 8)H where H' = Units of Human Capital tomorrow 8 = Fraction of time sleeping (or unemployed) H' (a) Calculate the growth rate of human capital, i.e 1. (Hint: Use Equation (2)) H C' (b) Show that the growth rate of consumption, i.e 1, is the same as the growth rate of C human capital from part (a). (Hint: Use Equation (1 and (2)) Now assuming that w = 1, B = 4.2 and the economy begins with 100 units of human capital H = 100. For the following question calculate aggregate consumption and quantity of human capital for each of the periods. You should use excel and draw the graphs each of the question. (C) Suppose that for period 1,2,..., 20, u = .7 and 8 = 0.05. (d) Suppose that periods 1 - 10 are the same as in part (c), then in period 11, y = 0.6 and s = 0.15. Finally, in period 12,..., 20, u = .7 and s = 0.05. (e) Suppose that periods 1 - 10 are the same as in part (c), then in period 11, = 0.6 and s = 0.05. Finally, in period 12,..., 20, x= .7 and 8 = -0.05. (f) Suppose that periods 1 - 10 are the same as in part (c), then in period 11, y = 0.7 and s=0.10. Finally, in period 12,..., 20, u = .7 and s = = 0.05. (g) What do you conclude from your results in parts (c) - (f)? 4.3. Numerical Example of Endogenous Growth (20 Points) Problem 3. In this question you will calculate the aggregate consumption and quantity of human capital of a discrete human capital model under different scenarios and then compare them. To begin with lets first define a basic discrete version of the model. Aggregate consumption will be defined as (1) C = wuH where . w = is the wage rate. H = Units of Human Capital today HE (0,1] = Fraction of time spend working The technology for accumulating human capital is (2) H' = B(1 - u - 8)H where H' = Units of Human Capital tomorrow 8 = Fraction of time sleeping (or unemployed) H' (a) Calculate the growth rate of human capital, i.e 1. (Hint: Use Equation (2)) H C' (b) Show that the growth rate of consumption, i.e 1, is the same as the growth rate of C human capital from part (a). (Hint: Use Equation (1 and (2)) Now assuming that w = 1, B = 4.2 and the economy begins with 100 units of human capital H = 100. For the following question calculate aggregate consumption and quantity of human capital for each of the periods. You should use excel and draw the graphs each of the question. (C) Suppose that for period 1,2,..., 20, u = .7 and 8 = 0.05. (d) Suppose that periods 1 - 10 are the same as in part (c), then in period 11, y = 0.6 and s = 0.15. Finally, in period 12,..., 20, u = .7 and s = 0.05. (e) Suppose that periods 1 - 10 are the same as in part (c), then in period 11, = 0.6 and s = 0.05. Finally, in period 12,..., 20, x= .7 and 8 = -0.05. (f) Suppose that periods 1 - 10 are the same as in part (c), then in period 11, y = 0.7 and s=0.10. Finally, in period 12,..., 20, u = .7 and s = = 0.05. (g) What do you conclude from your results in parts (c) - (f)? 4.3. Numerical Example of Endogenous Growth (20 Points) Problem 3. In this question you will calculate the aggregate consumption and quantity of human capital of a discrete human capital model under different scenarios and then compare them. To begin with lets first define a basic discrete version of the model. Aggregate consumption will be defined as (1) C = wuH where . w = is the wage rate. H = Units of Human Capital today HE (0,1] = Fraction of time spend working The technology for accumulating human capital is (2) H' = B(1 - u - 8)H where H' = Units of Human Capital tomorrow 8 = Fraction of time sleeping (or unemployed) H' (a) Calculate the growth rate of human capital, i.e 1. (Hint: Use Equation (2)) H C' (b) Show that the growth rate of consumption, i.e 1, is the same as the growth rate of C human capital from part (a). (Hint: Use Equation (1 and (2)) Now assuming that w = 1, B = 4.2 and the economy begins with 100 units of human capital H = 100. For the following question calculate aggregate consumption and quantity of human capital for each of the periods. You should use excel and draw the graphs each of the question. (C) Suppose that for period 1,2,..., 20, u = .7 and 8 = 0.05. (d) Suppose that periods 1 - 10 are the same as in part (c), then in period 11, y = 0.6 and s = 0.15. Finally, in period 12,..., 20, u = .7 and s = 0.05. (e) Suppose that periods 1 - 10 are the same as in part (c), then in period 11, = 0.6 and s = 0.05. Finally, in period 12,..., 20, x= .7 and 8 = -0.05. (f) Suppose that periods 1 - 10 are the same as in part (c), then in period 11, y = 0.7 and s=0.10. Finally, in period 12,..., 20, u = .7 and s = = 0.05. (g) What do you conclude from your results in parts (c) - (f)? 4.3. Numerical Example of Endogenous Growth (20 Points) Problem 3. In this question you will calculate the aggregate consumption and quantity of human capital of a discrete human capital model under different scenarios and then compare them. To begin with lets first define a basic discrete version of the model. Aggregate consumption will be defined as (1) C = wuH where . w = is the wage rate. H = Units of Human Capital today HE (0,1] = Fraction of time spend working The technology for accumulating human capital is (2) H' = B(1 - u - 8)H where H' = Units of Human Capital tomorrow 8 = Fraction of time sleeping (or unemployed) H' (a) Calculate the growth rate of human capital, i.e 1. (Hint: Use Equation (2)) H C' (b) Show that the growth rate of consumption, i.e 1, is the same as the growth rate of C human capital from part (a). (Hint: Use Equation (1 and (2)) Now assuming that w = 1, B = 4.2 and the economy begins with 100 units of human capital H = 100. For the following question calculate aggregate consumption and quantity of human capital for each of the periods. You should use excel and draw the graphs each of the question. (C) Suppose that for period 1,2,..., 20, u = .7 and 8 = 0.05. (d) Suppose that periods 1 - 10 are the same as in part (c), then in period 11, y = 0.6 and s = 0.15. Finally, in period 12,..., 20, u = .7 and s = 0.05. (e) Suppose that periods 1 - 10 are the same as in part (c), then in period 11, = 0.6 and s = 0.05. Finally, in period 12,..., 20, x= .7 and 8 = -0.05. (f) Suppose that periods 1 - 10 are the same as in part (c), then in period 11, y = 0.7 and s=0.10. Finally, in period 12,..., 20, u = .7 and s = = 0.05. (g) What do you conclude from your results in parts (c) - (f)