Consider an economy whose production function is Y=Kθ(AN)1-θ, with A=4(K/N). Suppose that it has a saving rate of .1, a population growth rate of .02, and an average depreciation rate of .03 and that θ=.5.
a. Reduce the production function to the form y = ak. What is a?
b. What are the growth rates of output and capital in this model?
c. Interpret a. What are we really saying when we assume that the labor-augmenting technology, A, is proportional to the level of capital per worker?
d. What makes this an endogenous growth model?