Lectures 7-10: The era of sustained economic growth Flashcards
What is the simplest model of modern economy?
Y = AL
What is the Solow model of a modern economy also known as?
- 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
State the GDP equation for a modern economy given by the Solow model
Y = K^βL^1-β
where K is the stock of capital in the economy
State the GDP per capita equation for a modern economy given by the Solow model
y = Y/L = K^βL^1-β/L = K^βL^-β
What are the two main differences between the GDP equations for both a traditional and a modern economy?
- In a modern economy, A is kept in the background
- X is fixed whereas K can change over time
Rewrite the GDP per capita equation for a modern economy
- y = K^BL^-β = K^β*1/L^β = (K/L)^β = k^β
where k = K/L = capital per worker
What does the rewritten GDP per capita equation for a modern economy tell us?
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
How do we calculate how k changes from one year to the next?
- We differentiate k with respect to time using the quotient rule:
˙k = dk/dt = dK/L/dt
Find the expression which tells us how k changes from one year to the next by using the quotient rule
See slide 19 in lecture 7-10
What is the expression for ˙k?
˙k = 1/L˙K - nk
What does the expression for ˙k tell us about what ˙k depends on?
˙k depends on K˙
Why do we need to extend the model of ˙k?
- 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
What can we divide GDP (Y) into?
We can divide GDP (Y) into Capital goods and Consumption goods
What is the relationship between K and Y given by a supply side view?
Every year, a share of Y is new K
What is the relationship between K and Y given by a demand side view?
Every year a share of GDP goes into new K
What is the relationship between capital and depreciation?
Capital depreciates, a portion of it disappears every year
State the verbal model of K˙
- Every year a portion of Y represents new K
- However, every year a portion of K is destroyed by depreciation
State the mathematical model of K˙
K˙ = sY - δK
where s and δ are between 0 and 1 and they are the economy’s savings rate and depreciation rate
State and derive the equation for ˙k which tells us how capital accumulates over time in a modern economy
˙k = sk^β - (δ+n)k
What point does k grow till and explain how we know this
- We have found that GDP per capita is increasing in k as given by y = k^β
- We also found that k increases over time until it reaches k*
- Therefore there must be growth in GDP per capita until k reaches k*
In a modern economy, how long is there growth in GDP per capita?
There is growth in GDP per capita until k reaches k*
Derive and state the equation for the growth of GDP per capita in a modern economy
g = β˙k/k
See slide 44 of lecture 7-10
What are the two conclusions we can draw from the GDP per capita growth equation in a modern economy (g = β˙k/k)
1- Capital accumulation is an additional engine of growth in a modern economy
2- The kind of growth that is driven by capital accumulation is decreasing over time and eventually reaches zero
State the Solow model equation with and without technological progress (A)
- Y = K^βL^1-β
- Y = K^β(AL)^1-β
What is AL in the adjusted Solow model equation known as?
AL is known as the number of efficiency units of labour or labour augmenting technological progress
What does labour augmenting technological progress actually mean (AL)?
Labour augmenting technological progress essentially means that for example one worker today does the same job as ten workers in the 1960s
What does the symbol y squiggly bar mean?
y squiggly bar represents GDP per efficiency units of labour
State and derive the equation for GDP per efficiency units of labour
y squiggly bar = k squiggly bar^β where k squiggly bar = K/AL which is the capital per efficiency unit of labour
What does a squiggly line above a variable mean?
A squiggly line above a variable means that is divided by efficiency units of labour
