Assume an economy has the following aggregate production function: Y = K;"(AL)-- where K is the country's capital stock,

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Assume An Economy Has The Following Aggregate Production Function Y K Al Where K Is The Country S Capital Stock 1 (53.57 KiB) Viewed 99 times

Assume an economy has the following aggregate production function: Y = K;"(AL)-- where K is the country's capital stock, Lis the number of employed workers and A is labour-augmenting technological stock at time t. There is no population growth, the technological stock grows at rate g = 2% and a = 1/3. Furthermore, the capital stock evolves according to the following capital accumulation equation: Ke = sy, - de where s is the investment/saving rate and d is the depreciation rate of the capital stock. We assume this economy begins at its steady state. At time t = 0, the rate of technological progress g falls permanently from 2% to 1%. All the other parameters of the model remain the same. a) What happens to the steady state capital output ratio? What happens to the growth rate of the capital output ratio? Justify your answer showing the appropriate derivations. Briefly explain the intuition. (15 marks] b) What is the steady state growth rate of output per worker before and after the change in the rate of technological progress? (5 marks] c) Derive the growth accounting equation for this country. Calculate the contributions to the growth rate of output per worker of the growth in capital per worker and of TFP growth both before the change in the rate of technological progress and after the economy has reached its new steady state. [10 marks] d) In what sense does the growth accounting exercise in c) provide a misleading picture of the cause of the change in the growth rate of output per worker? [5 marks]