Consider the solow model and the production function as follows

Consider the Solow model studied in class where the investment rate 8 = 0.15, the depreciation rate is equal to d = 0.07 and the production function is equal to The total labor force does not change with time, _ = 100 and we assume it to be fully employed. TFP is A = 5. The capital accumulation equation is Kill = It + (1 -5)Kt where It = BYt. a) [4 points] Assume that time is t = 0 and the initial level of capital is Ko = 100. Compute the total level of physical capital at t = 1. Compute the growth rate of physical capital between period 0 and period 1. Show your work. b) [6 points] Define what steady state is in a dynamic model like the Solow model. Derive the expression for the steady state level of capital. Show your work. Given the numerical values above, what is the numerical value of physical capital in the steady state? Show your work. c) [8 points] Suppose the economy starts in the steady state that you derived. There is an unexpected permanent increase in TFP A by 50%. What is the immediate change in capital and total output at the time in which A increases? What about the next period after the shock? Show your work and provide economic intuition for your answer. d) [4 points] Graph the impulse response function for capital. Be as clear as possible in your graph, noting what happens when the shock hits and after it. Please explain as clearly as you can the economic mechanism behind the shape of the impulse response function that you have graphed