Assignment
The Cobb-Douglas production function was developed by Charles Cobb and Paul Douglas in 1927. Subsequent work by Cobb and Douglas, and others, has shown thatthe output elasticities of capital and effective labour were approximately 1/3 and 2/3 respectively for a range of countries.
Suppose that aggregate production in a Caribbean country can be described by a similar function. In this country, the average annual growth rate of per capita real GDP since 1980 is 4.0%, the capital stock depreciates at an average rate of 8.4%, the population growth rate is 1.2%, and the country adopts technology at a rate of 3.5% each year.
(a) Using the above information, state the aggregate production function for the Caribbean economy.
(c) Assuming that the Solow model of growth is an appropriate model of growth for the Caribbean economy, determine each of the following at the Golden Rule level: (i) capital stock per effective worker (ii) output per effective worker (iii) saving rate (iv) investment and (v) consumption. Round your answers off to three decimal places.
(d) Next, suppose that the initial capital stock per effective worker for this economy in 1980 was 0.09 units. Using Excel, determine in what year the Caribbean economy would reach its Golden Rule steady state. Format your values to three decimal places.