Solve for steady state capital stock per capita k*

1. This question has you investigate the speed of convergence in the Solow growth model. Specifi cally, assume that the functional form for the production function is given by: Yt = AK, LI-0 Assume the following values for all of the model's parameters: A = 1, 0=.3, s=.2, 8=.10, n =.02, 1 = 1300 (a) Solve analytically for the value of the steady state capital stock per capita, k*, for this econ- omy. (b) Assume that the economy starts quite far away from its steady state, in particular, assume that Ko = .20k*, i.e., the economy starts with only 20 percent of its steady state level of capital. One measure of speed of convergence that many people use is what is referred to as the half- life. Specifically, how long does it take for the economy to get halfway to the steady state relative to where it is today. So, for example, if the economy were to start with ko = .20k*, the half life would reflect how long it takes the economy to reach a level of capital equal to ko = .60k*. Compute this value. Then compute the half life starting from ko = .60k*, i.e., how long it takes to go from .60k* to .80k*. Do the same starting from .80k*, .90k*, .95k*, .975k*. Summarize your findings and explain why they suggest that the half life is a meaningful way to summarize the speed of convergence. (c) We can ask how various factors might influence the speed of convergence to the steady state. For example, consider another economy that is identical to the economy above except that in this economy individuals work much harder. Specifically, assume that I = 1500. Compute the value of k* and compute again how long it takes to go from .20k* to .60k*, from .60k* to 80k*, etc... How do the answers compare with what you found in (b)? Consider someone who makes the following claim: "If people work harder then the economy will get to the steady state faster." Respond to this statement in light of your findings. Specifically, is this consistent with your findings? If not, briefly explain why is this statement is not true