Lectures 7-10: The era of sustained economic growth

Question 1

What is the simplest model of modern economy?

Answer 1

Y = AL

Question 2

What is the Solow model of a modern economy also known as?

Answer 2

• The Solow model is also known as the neoclassical model of growth
• It was published in the 1957 Quarterly Journal of Economics and is now cited in 28684 other articles
• It is one of the most famous and useful models ever written in economics
• It was awarded the 1987 Nobel prize

Question 3

State the GDP equation for a modern economy given by the Solow model

Answer 3

Y = K^βL^1-β
where K is the stock of capital in the economy

Question 4

State the GDP per capita equation for a modern economy given by the Solow model

Answer 4

y = Y/L = K^βL^1-β/L = K^βL^-β

Question 5

What are the two main differences between the GDP equations for both a traditional and a modern economy?

Answer 5

• In a modern economy, A is kept in the background
• X is fixed whereas K can change over time

Question 6

Rewrite the GDP per capita equation for a modern economy

Answer 6

• y = K^BL^-β = K^β*1/L^β = (K/L)^β = k^β
  where k = K/L = capital per worker

Question 7

What does the rewritten GDP per capita equation for a modern economy tell us?

Answer 7

y = k^β
- The higher the stock of capital per worker, the higher GDP per capita is
- The effect of additional increases is smaller and smaller as GDP per capita is concave in k

Question 8

How do we calculate how k changes from one year to the next?

Answer 8

• We differentiate k with respect to time using the quotient rule:
  ˙k = dk/dt = dK/L/dt

Question 9

Find the expression which tells us how k changes from one year to the next by using the quotient rule

Answer 9

See slide 19 in lecture 7-10

Question 10

What is the expression for ˙k?

Answer 10

˙k = 1/L˙K - nk

Question 11

What does the expression for ˙k tell us about what ˙k depends on?

Answer 11

˙k depends on K˙

Question 12

Why do we need to extend the model of ˙k?

Answer 12

• We need to extend the model to find out about the determinants of K˙
• If K˙ is exogenous there is no need to extend the model but K˙ is likely to be endogenous as it will depend on other variables in the model, most notably it will depend on GDP

Question 13

What can we divide GDP (Y) into?

Answer 13

We can divide GDP (Y) into Capital goods and Consumption goods

Question 14

What is the relationship between K and Y given by a supply side view?

Answer 14

Every year, a share of Y is new K

Question 15

What is the relationship between K and Y given by a demand side view?

Answer 15

Every year a share of GDP goes into new K

Question 16

What is the relationship between capital and depreciation?

Answer 16

Capital depreciates, a portion of it disappears every year

Question 17

State the verbal model of K˙

Answer 17

• Every year a portion of Y represents new K
• However, every year a portion of K is destroyed by depreciation

Question 18

State the mathematical model of K˙

Answer 18

K˙ = sY - δK
where s and δ are between 0 and 1 and they are the economy’s savings rate and depreciation rate

Question 19

State and derive the equation for ˙k which tells us how capital accumulates over time in a modern economy

Answer 19

˙k = sk^β - (δ+n)k