Consider the Solow growth model with no population growth and no technology growth, i.e., n =...

 

Transcribed Image Text:

Consider the Solow growth model with no population growth and no technology growth, i.e., n = x = 0. Output is created by a Cobb-Douglas production function combining Labor, Lt, and capital, Kt, such that output Yt is given by Y = A+ Ko La Recall that, without population growth, Lt = Lo and assume that Lo 1. Furthermore, recall that, without technology growth, At = A0 and assume that A0 = 1. The law of motion for capital is given by = (1) 1-a Kt+1 = (1-8) K + sA Ko La. Assume that the savings rate is s = 0.2, the depreciation rate is = 0.1, and that the capital share is a = 0.3. 1. Use equation (1) to solve for the steady state level of capital, Kss, and show that Kss = [3] . What is the steady state level of capital? (Replace the numbers in the expression) 2. Suppose that Ko = 1. Does capital grow or fall over time? What is the maximum level of capital this economy will ever have? 3. Suppose that Ko = 5. Does capital grow or fall over time? What is the maximum level of capital this economy will ever have? 4. Suppose that this economy was at its steady state level of capital Kss when it is hit by a natural disaster that destroys 10 percent of the capital stock. This catastrophe means that the economy must start anew with Ko= 0.9 Kss. Use equation (1) to compute Kt for the next 10 years. How long does it take to recover at least half of the lost capital stock, i.e., in which year is Kt 0.95 Kss. 5. Suppose that the government conducts a program of incentivizing investment and is able to take s = 0.21, i.e., the government increases the savings rate by 1 percentage point. Use the same Ko as in question 4, and compute the new path K for the next 10 years. Now, how long does it take to recover at least half of the lost capital stock, i.e., in which year is Kt 0.95 Kss. Is convergence faster or slower with this new savings rate? Explain why. Consider the Solow growth model with no population growth and no technology growth, i.e., n = x = 0. Output is created by a Cobb-Douglas production function combining Labor, Lt, and capital, Kt, such that output Yt is given by Y = A+ Ko La Recall that, without population growth, Lt = Lo and assume that Lo 1. Furthermore, recall that, without technology growth, At = A0 and assume that A0 = 1. The law of motion for capital is given by = (1) 1-a Kt+1 = (1-8) K + sA Ko La. Assume that the savings rate is s = 0.2, the depreciation rate is = 0.1, and that the capital share is a = 0.3. 1. Use equation (1) to solve for the steady state level of capital, Kss, and show that Kss = [3] . What is the steady state level of capital? (Replace the numbers in the expression) 2. Suppose that Ko = 1. Does capital grow or fall over time? What is the maximum level of capital this economy will ever have? 3. Suppose that Ko = 5. Does capital grow or fall over time? What is the maximum level of capital this economy will ever have? 4. Suppose that this economy was at its steady state level of capital Kss when it is hit by a natural disaster that destroys 10 percent of the capital stock. This catastrophe means that the economy must start anew with Ko= 0.9 Kss. Use equation (1) to compute Kt for the next 10 years. How long does it take to recover at least half of the lost capital stock, i.e., in which year is Kt 0.95 Kss. 5. Suppose that the government conducts a program of incentivizing investment and is able to take s = 0.21, i.e., the government increases the savings rate by 1 percentage point. Use the same Ko as in question 4, and compute the new path K for the next 10 years. Now, how long does it take to recover at least half of the lost capital stock, i.e., in which year is Kt 0.95 Kss. Is convergence faster or slower with this new savings rate? Explain why.