Consider an economy whose production function is Y = Kθ(AL)1-θ with A = 4K/L. Suppose that it has a saving rate of 0.1, a population growth rate of 0.02 and an average depreciation rate of 0.03 and that θ = 0.5.
1. Reduce the production function to the form y = ak. What is a?
2. What are the growth rates of output and capital in this model?
3. 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?
4. What makes this an endogenous growth model?