Week 1 - Growth accounting

Question 1

Why focus on economic growth?

Answer 1

• Growth is necessary for development and poverty alleviation.
• Small but sustained growth rates can cumulate into very large differences in living standards

Question 2

What is the equation for a Cobb-douglas production function with constant returns to scale.

Answer 2

Yt = F(Kt,Lt)
Yt = AtKtLt

K is to the power of alpha, Labour is to the power of 1-alpha

Question 3

What is A in the cobb-douglas production function?

Answer 3

At = TFP. Includes technology, but possibly also human capital, quality of institutions, government policies.

Question 4

How do you prove that the production function has constant returns to scale?

Answer 4

If there are constant returns to scale:
zYt = F(zKt,zLt)

Therefore:
(At)(zKt)^a(zLt)^(1-a)

Which simplifies to zYt (look at slides for maths)

Question 5

What is marginal productivity?

Answer 5

The increase in output caused by a 1 unit increase in a factor of production

Question 6

What is the marginal productivity of labour and capital?

Answer 6

You take the partial derivative wrt both factors of production:

MPL = (1-a)At(Kt/Lt)^a

MPK = aAt(Kt/Lt)^-(1-a)

Question 7

Does marginal productivity increase or decrease with an increase in capital/labour

Answer 7

decreases - the law of diminishing marginal productivity of capital/labour

Question 8

What are factor shares?

Answer 8

The share of national income that is paid out (used as payment) for capital/labour in production

Question 9

In a competitive market, what is each factor paid?

Answer 9

Each factor is paid its marginal product.
MPL = wage
MPK = interest rate

Question 10

How do you work out the factor share? (in words and as an expression)

Answer 10

labour/capital income as a share of total income:

(MPLLt)/Yt
(MPKKt)/Yt

Question 11

What do we normally see when working out the factor shares of a cobb-douglas production function?

Answer 11

Factor share = exponent of the factor:

labour = 1-a
capital = a

Question 12

True or false: Factor shares of economies stay relatively stable over time?

Answer 12

True - wages, interest rates and amount of capital and labour in an economy may fluctuate over time, but factor shares are stable parameters

Question 13

What is a general rule we can use to get the growth rate of a variable?

Answer 13

Take the natural log and derive it wrt time

Question 14

What is the growth rate of output in a CD production function

Answer 14

gY= gA + aK + (1-a)gL

Question 15

what is growth rate of TFP (gA) known as

Answer 15

The Solow residual

Question 16

What are some disadvantages of this simple way of growth accounting?

Answer 16

1. Omitted things from the production function such as human capital and external shocks (e.g. weather)
2. There could be a misallocation of factors across sectors and firms
3. Hard to measure variables on an aggregate level e.g. capital stock, factor shares. Introduces measurement error into our results
4. Assumptions e.g. factors are paid their marginal product, might not hold