Question

1. Suppose I give you the following data on Canada: Year Output Capital Population 1960 100 100 1000 2000 300 200 1500 a) What are the growth rates of output, capital and population between 1960 and 2000? b) Suppose that the aggregate production function is: Y = AK^(1/2)N^(1/2) What is the growth rate of productivity between 1960 and 2000? c) Do the growth accounting excercise. What share of output growth can be attributed to productivity, capital and population? Hint: The shares should sum up to 1. d) What is the average annual growth rate of output, productivity, capital and population over these 40 years? Hint: Just divide the total growth rates by 40.

Answer 1

a) Calculation of growth rate of output = [(Output in 2000 - Output in 1960) / Output in 1960]  

(300 - 100) / 100 = 200%

Growth rate of capital = [( capital in 2000 - capital in 1960) / Capital in 1960]

(200 - 100) / 100 = 100%

Growth rate of population = [( Population in 2000 - Population in 1960) / Population in 1960]

(1500 - 1000) / 1000 = 50%

b) Production function =  Y = AK^(1/2)N^(1/2)

Where Y = Real production

A = Level of technology (Assumed 1)

K = Capital

N = Population

Production in 1960 = 1 * 100^(1/2) * 1000^(1/2)

= 316.22

Production in 2000 = 1 * 200^(1/2) * 1500^(1/2)

= 547.72

Growth rate of productivity = ( Production in 2000 - Production in 1960) / Production in 1960

= ( 547.72 - 316.22 ) / 316.22  

= 73.21 %

c) Share of growth attributable to the Productivity, capital and population

Total of productivity, capital and population growth = ( 223.21)

Productivity share = (73.21/223.21) * 200% = 65.60%

Capital share = ( 100/ 223.21) * 200% = 89.60%

Population share = ( 50 / 223.21) * 200% = 44.80%

In total ( 65.60 + 89.60 + 44.80) = 200%

Hence share sum up to 1 (200/200)

d) Average annual growth rate of

Output = (200/ 40) = 5%

Productivity = ( 73.21/ 40) = 1.83 %

Capital = ( 100 / 40 ) = 2.5%

Population = (50 / 40) = 1.25%