Consider a Solow Growth Model with Cobb-Douglas production, saving rate s, depreciation rate δ, population growth rate n, and the rate of technological progress equal to g. You can use algebraic solutions from previous problem sets or class notes while answering the following questions.
a. Consider the following empirical observations for the U.S.:
Capital stock is 2.5 times GDP
Population growth is around 2%
Depreciation accounts for 10% of GDP
GDP grows at a rate of 3%
Capital owners' share of output (α) is roughly 30%
Based on these data, is the U.S. currently at the golden-rule level of capital?
b. Based on these data, what is the golden-rule level of capital?
c. Suppose the U.S. government implements a policy that achieves the savings rate needed to achieve the golden-rule level of capital. Using impulse response graphs, show how the following variables would change as the U.S. transitions to its new balanced growth path: capital, output and consumption.