Hi I am trying to answer the following questions:
#1) Consider the following production
1. Y = AK1/2L1/2
2. Y =AK+BL
3. Y = (AK)2/3L2/3
4. Y = AH1/3L
For each of the production functions listed above:
- Determine whether the function exhibits CRS, diminishing returns to physical capital (or human capital, when applicable), and diminishing returns to labor
- Check whether it satisfies the Inada conditions.
- Compute the per capita production function.
#2) Consider the Solow-Swan model of growth. Imagine that the production function is Y = AKαL1−α
1. Use the production function to compute output per capita, y = Y /L, as a function of capital per person, k = K/L.
2. Derive the fundamental equation of the Solow-Swan model. Please show all the steps.
Furthermore, imagine that the savings, depreciation, and population growth rates take the values s = 0.2, δ = 0.1 and n = 0.01. You do not know the value of A.
3. Use the fundamental equation of the Solow-Swan model to compute the growth rate of capital per person as a function of k.
4. In the steady-state, the growth rate of capital is zero. Using the parameters assumed above, find the steady-state level of the capital stock, k∗.
5.Imagine that this country is in its steady state so its capital stock is k∗. Imagine that the country receives a gift of one unit of capital from the world bank (so, suddenly, the capital stock is k∗+1). Can you say what is going to happen to the growth rate immediately after the donation? Why? What will the capital stock be in the long run? Explain.