Question

5. Calibrated Cobb-Douglas Growth Model Assume an economy has the following production function: Y = F(K, AL) = K 0.4 (AL)0.6. (a) Write down the production function per effective worker. (20 marks) (b) For this economy, the savings rate is 20%, the depreciation rate is 10% per year, the population growth rate is 2% per year, and the technology growth rate is 3% per year. Calculate the steady-state capital stock per effective worker, output per effective worker, and consumption per effective worker. (40 marks) (c) If the technology growth rate accelerates, becoming twice higher, what would happen to the capital stock per effective worker and output per effective worker? Will this change cause total output to increase or decrease? (20 marks) (d) According to the Solow growth model, why will an economy move towards its steady state if the current capital stock per worker is above the steady state value? Use a diagram to explain your answer. (20 marks)

Answer 1

A) production function per effective worker is :

Y/AL= K​​​​​​0.4(AL)0.6 /(AL)

y = K​​​​​​0.4/ (AL)0.4 = k​​​​​​0.4

==> y = k​​​​​​0.4

Above is the production function per effective worker where y is the output per effective worker and k is the capital per effective worker.

B) s= 0.2 , d= 0.1