Output in an economy is given by the production function Y = AK0.3N0.7, where Y is output, A measures productivity, the capital stock AT is fixed at 30, and employment N is fixed at 100. Output equals 100 in the year 2011 and equals 105 in 2012.
a. Find the Solow residual in the years 2011 and 2012, and its growth rate between those two years.
b. What is the relationship between the growth in the Solow residual between 2011 and 2012 and the growth in productivity (as measured by the parameter A) in the same years? Assume that the rates of utilization of capital and labour remain unchanged.
c. Repeat part (b) under the assumption that utilization of labour increases by 3% between 2011 and 2012. You will have to modify the production function along the lines of Eq. (11.2).
d. Repeat part (b) under the assumption that the utilization rates of both labour and capital increase by 3% between 2011 and 2012.