Question

# Hi I am trying to answer the following questions:

#1) Consider the following production

functions:

1. Y = AK^{1/2}L^{1/2}

2. Y =AK+BL

3. Y = (AK)^{2/3}L^{2/3}

4. Y = AH^{1/3}L

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.

and

#2) Consider the Solow-Swan model of growth. Imagine that the production function is Y = AK^{α}L^{1−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.