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 Derive an expression for the accumulation of capital per worker in this economy, i e 1, where (5 points) What is the steady state condition in this economy Illustrate the equilibrium in a diagram (4 points) Suppose that 1 10, 1 10 and 2 5 Compute the steady state level of capital per worker, i e (4 points) Analyse the effects of a higher depreciation rate using a diagram Explain the intuition (5 points) What is the main criticism of the Solow model (2 points) Suppose instead that the production technology is given by 1 2 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)

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Question 2: Economic growth (25 points) Consider a version of the Solow model where the population, ?, grows at rate ?, but labour efficiency is

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 """

Derive an expression for the accumulation of capital per worker in this economy, i.e. ??"@1, where ?" ? ?"/?". (5 points)
What is the steady state condition in this economy? Illustrate the equilibrium in a diagram. (4 points)
Suppose that ? = 1/10, ? = 1/10 and ? = 2/5. Compute the steady-state level of capital per worker, i.e. ??. (4 points)
Analyse the effects of a higher depreciation rate using a diagram. Explain the intuition. (5 points)
What is the main criticism of the Solow model? (2 points)
Suppose instead that the production technology is given by:
?=1? "2"
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)