Dependence of the saving rate, population growth rate, and depreciation rate on the capital intensity. Assume that the production function satisfies the neoclassical properties.
a. Why would the saving rate, s, generally depend on k?
b. How does the speed of convergence change if s (k) is an increasing function of k? What if s (k) is a decreasing function of k? Consider now an AK technology.
c. Why would the saving rate, s, depend on k in this context?
d. How does the growth rate of k change over time depending on whether s (k) is an increasing or decreasing function of k?
e. Suppose that the rate of population growth, n, depends on k. For an AK technology, what would the relation between n and k have to be in order for the model to predict convergence? Can you think of reasons why n would relate to k in this manner?
f. Repeat part e in terms of the depreciation rate, δ. Why might δ depend on k?