Write fundamental equation of solow-swan model » Full Grade

Assignment ID: FG133082338

Consider the Solow-Swan growth model, with a savings rate, s, a depreciation rate, δ, and a population growth rate, n. The production function is given by Y = AK + BKαL1-α, with α ∈(0,1), where A and B are positive constants.

1. Does this production function exhibit constant returns to scale? Explain why.

2. Does it exhibit diminishing returns to capital? Explain why.

3. Express output per person, y = Y/L, as a function of capital per person, k = K/L

4. Write down an expression for y/k as a function of k and graph. (Hint: as k goes to infinity, does the ratio y/k approach zero?)

5. Use the production function in per capita terms to write the fundamental equation of the Solow-Swan model.

6. Suppose first that sA < δ+n Draw the savings curve and the depreciation curve. What number does the savings curve approach as k goes to zero? As k goes to infinity, the savings curve approaches a number: what number is that? Is it zero?

7. Under these parameters, will there be positive growth in the long run? (Remember that A and B are constants). Why?

8. Imagine that we have two countries with the same parameters (same A, B,s,δ, and n). One of them is rich and the other is poor. Which one of the two will grow faster? Why? Does this model predict convergence?

9. Suppose now that sA > δ+n. Draw the savings and depreciation curves. Under these circumstances, will there be positive growth in the long run? Why?

10. If s = 0.3, A = 2, B = 2,δ = .3 and n = 0.03, the growth rate converges to some value as time goes to infinity. What is this value?