Question 2: Economic growth (25 points)

Consider a version of the Solow model where the population, ?", grows at rate ?, but labour efficiency is constant and normalized to one. A fraction ? of income is invested in capital, ?" , every period. Capital depreciates at rate ?. The production technology is Cobb-Douglas and given by:

? = ?1/2? 1/2 """

1. Derive an expression for the accumulation of capital per worker in this economy, i.e. ??"@1, where ?" ? ?"/?". (5 points)
2. What is the steady state condition in this economy? Illustrate the equilibrium in a diagram. (4 points)
3. Suppose that ? = 1/10, ? = 1/10 and ? = 2/5. Compute the steady-state level of capital per worker, i.e. ??. (4 points)
4. Analyse the effects of a higher depreciation rate using a diagram. Explain the intuition. (5 points)
5. What is the main criticism of the Solow model? (2 points)
6. Suppose instead that the production technology is given by:
7. ?=1? "2"
8. A constant fraction, ? = 2/5, of income is still invested in capital each period and capital still depreciates at rate ? = 1/10. The population is constant and normalized to 1. Is there GDP growth in this model? Why/Why not? Motivate your answer. (5 points)

Question 2: Economic growth (25 points) Consider a version of the Solow model where the population, Le, grows at rate n, but labour efficiency is constant and normalized to one. A fraction s of income is invested in capital, Kt, every period. Capital depreciates at rate 6. The production technology is Cobb-Douglas and given by: Yt = K./2L, 1/2 a. Derive an expression for the accumulation of capital per worker in this economy, i.e. Akt+1, where ke = Kt/Lt. (5 points) b. What is the steady state condition in this economy? Illustrate the equilibrium in a diagram. (4 points) c. Suppose that n = 1/10, 8 = 1/10 and s = 2/5. Compute the steady-state level of capital per worker, i.e. k*. (4 points) d. Analyse the effects of a higher depreciation rate using a diagram. Explain the intuition. (5 points) e. What is the main criticism of the Solow model? (2 points) f. Suppose instead that the production technology is given by: A constant fraction, s = 2/5, of income is still invested in capital each period and capital still depreciates at rate o = 1/10. The population is constant and normalized to 1. Is there GDP growth in this model? Why/Why not? Motivate your answer. (5 points)