In: Economics
1. The following table shows the data for Canada’s aggregate production function with constant return to scale and the output elasticity with respect to capital equal to 0.3.
Year |
GDP (billions of 2002 dollars) |
Capital Stock (billions of 2002 dollars) |
Employment (millions) |
1961 |
264.5 |
525.6 |
6.06 |
1971 |
437.7 |
824.7 |
8.08 |
1981 |
647.3 |
1277.4 |
11.31 |
1991 |
808.1 |
1715.1 |
12.86 |
2001 |
1120.1 |
2071.1 |
14.94 |
2010 |
1325 |
2668.7 |
17.04 |
a). Find the values of total factor productivity for the given years above.
I only used the Capital output elasticity(0.3) mentioned in the question here even though in my notes it mentions it being 0.7 in Canada
Y= (A)(K^αK*)(N^αN)
A= TFP, Y= GDP, K= Capital, N=Labor αK=Capital output elasticity, αN=Labor output elasticity
A= Y/(K^αK)(N^αN) THEREFORE
TFP(1961)= (264.5)/((525.6)^0.3(6.06)) = 6.65
TFP(1971)= (437.7)/((824.7)^0.3(8.08)) = 7.23
TFP(1981)= (647.3)/((1277.4)^0.3(11.31)) = 6.69
TFP(1991)= (808.1)/((1715.1)^0.3(12.86)) = 6.73
TFP(2001)= (1120.1)/((2071.1)^0.3(14.94)) = 7.59
TFP(2010)= (1325)/((2668.7)^0.3(17.04)) = 7.29
Just want to verify my numbers are correct here before moving forward?
b). Complete the following table by calculating the average annual growth rates (%) for GDP, capital stock, employment, and total factor productivity. While it is not necessary to show all your calculations, show the formulae you use, and also explain and illustrate how you obtain your answers.
Year |
GDP |
Capital Stock |
Employment |
TFP |
1961-1971 |
||||
1971-1981 |
||||
1981-1991 |
||||
1991-2001 |
||||
2001-2010 |
a)The TFP values are incorrect. They should be calculated using the labour elasticity as well which is taken to be .7
So the values are -
Year | TFP |
1961 | 11.44 |
1971 | 13.52 |
1981 | 13.86 |
1991 | 14.48 |
2001 | 17.074 |
2010 | 17.072 |
b) Annual growth rate is calculated using the formula
[(EV/BV)-1]*100 where ev is ending value of the time period which in this case will be the upper limit in the following case and BV is beginning value which will be the lower limit in this case.
For ex for GDP 1961-71 the form will be
{(437.7/264.5) - 1}*100 which comes out to be 65.48
The other fields have been filled similarly.
All the figures are in %
Year | GDP | Capital Stock | Employment | TFP |
1961-71 | 65.48 | 56.91 | 33.33 | 18.19 |
1971-81 | 47.88 | 54.89 | 39.97 | 2.49 |
1981-91 | 24.84 | 34.26 | 13.70 | 4.47 |
1991-01 | 38.61 | 20.75 | 16.17 | 17.91 |
2001-10 | 18.29 | 28.85 | 14.05 | -.011 |
Average AGR | 39.02 | 39.132 | 23.44 | 8.61 |
CAGR | 29.41 | 29.68 | 17.98 | 6.61 |
Average Annual growth rate is calculated as sum of the individual growth rates over different periods/no of periods
CAGR = (end value/beginning value)*1/n -1