Inputs, Outputs and Growth

Question 1

What is the growth/log relationship?

Answer 1

• When x(t) grows at a proportional rate, log x(t) grows linearly
• If x1(t) and x2(t) both grow by 10%, x1(t) - x2(t) will also grow, while log x1(t) - logx2(t) will remain constant

Question 2

What does diminishing returns to capital explain?

Answer 2

• Catch up effect or convergence

- Poorer economies per capita incomes will tend to grow at faster rates

Question 3

∆K =

Answer 3

∆K = I - D

Question 4

What is net investment?

Answer 4

I - D = I - dI = (1-d)I

Question 5

How is labour measured?

Answer 5

• Measure labour input by the number of hours worked
• Hours worked = population x (employment/population) x hours worked by the employed
• Measurement of labour is not generally subject to change in quality (captured in TFP)

Question 6

How do we do grown accounting?

Answer 6

• (∆Y/Y) = (∆A/A) + β(∆K/K) + (1 - β)(∆L/L)

- Multiplicative to additive when considering growth

Question 7

How do we measure labour productivity generally and in CD?

Answer 7

• Measured by the amount of output per unit labour Y/L

- For a CD production function: Y/L = A(K/L)^β

Question 8

CD y =

Answer 8

y = Ak^β

Question 9

What determines labour productivity?

Answer 9

• So labour productivity depends on A and k

Question 10

What is capital deepening?

Answer 10

growth in the amount of capital per worker (rise in K/L ratio)

Question 11

How do we determine the contribution to output growth by each input?

Answer 11

A contribution = (∆A/A)/(∆Y/Y)
K contribution = β(∆K/K)/(∆Y/Y)
L contribution = (1-β)(∆L/L)/(∆Y/Y)