Spreadsheet Project 4: Solow Growth Model
Assume that the economy is described by the following production function: Y = K.3L.7
where the initial values of the inputs are K = 25 and L = 5.
Furthermore, assume that the savings rate for this economy is s = 0.20, the depreciation rate is δ = 0.05, the growth rate in the population (and labor force) is n = 0.01, and the growth rate in technology is g = 0.02.
Q1: What is the per capita production function?
Q2: What is the steady-state value of k* and y*? Derive an equation that calculates each of these so that we can easily recalculate the steady state values whenever any of the above parameter values change.
Q3: What happens to the steady state values of k* and y* under the following circumstances :
Q4: Create a table showing y, i, and (δ+n+g)k for various levels of k. Under the k column, put data running from 0 to 10, in 1-unit increments. Based on this table, create an X-Y chart showing the i and (δ+n+g)k curves, and thereby showing the steady-state value of k. (Make sure the table calculations are anchored to the initial values of the parameters. Also, please make sure that the scaling on your axes are fixed.)
Q5: Create another table showing the steady state values of k*, y*, c*, i* for various levels of the saving rate, s. Under the s column, put data running from 0 to 1, in .05 increments. Based on this table, what is the approximate Golden Rule level of savings? What is the level of consumption per worker, c, at this level?
Q6: Given the current capital/labor ratio of k = 5, what must society do (in terms of the saving rate) in order to get to the Golden Rule? Suggest two policies that might accomplish this.
You must submit your work to me as an Excel spreadsheet via email.
Due Date: April 22, 2011