Week 2 Economic growth Flashcards
What are some basic facts about Economic growth?
Richer countries do not tend to grow faster than poorer countries
Before the industrutiral revolution, there were little differences between countries overtime.
After the Industrial revolution, per capita income growth has veen growing sustainially in the richest countries.
β’ There is a negative correlation between the population growth rate and output per worker across countries.
What thoery tries to explain economic growth?
The solow growth model
What is a key prediction of the solow growth model?
You can have sustained economic growth from technological improvements over time.
What assumption will we use for the solow growth model in terms of people, firms and government?
We will have an identical firm, consumer and there will be no government in this model
What assumption of the solow growth model will we have in terms of the goods produced and exchanged?
One homogenous good ie a cookie, can be transformed into investment goods (1:1) one cookie will transform to a engineering plant. Consumers dont care about lesiure.
What assumption of the solow growth model will we make about the peoples preferences of goods?
People donβt care about lesiure, people consume a constant fraction (1-s) of their income and sace the rest.
C = (1-S)Y s<1
S = sY
What assumption of the solow growth model will be assume in terms of the technology avaliable to firms?
Firms produce their output using a production function
Y = zF(K,N)
where Z = TFP, how effective is the production process, the higher the z the more efficient you are at combining capital and labour.
K = capital input
N = labour input ( each worker works 247
F = function
What assumptions of the solow growth model will we assume in terms of the resources avaliable in the economy. As consumers dont value lesiure whats their labour supply too.
We start with inital capital and labour inputs
K0 and No ( each worker has one unit of labour to offer to firms)
Overtime the number of people in the economy will change
(next period)Nβ = (1+n)N
N represents both the number of workers and the population at beginning of the year
n = the poplutation growth rate ( for the next year
Consumers do not value lesiure so labour supply = 1.
Kβ = (1-d)K+l
(1-d) is the number of capital depreciated to be left with what is left at the end of the year X K which is the the capital at the beginning of the year)
I = investment made for the next year will affect how much capital will grow next year
What are the end rules of the game?
Firms want to maximise profits
Consumers consume and save
Competitive equilbrium
Now looking at the production function, what are we going to assume about the production function, first of all lets make a zombie cafe example to prove the point?
Y = zF( K,N)
To produce cofee we need labour and capital inputs ( workers and cofee machine)
Lets say 1 worker and 1 coffee machine can produce output of 12
Lets say a second worker and 1 cofee machine produce an output of 20 cofees ( so 8 more coffees)
Lets say a 3rd worker and 1 cofee machine produces an output of 24 cofees in total ( 4 more coffess)
Same thing when I have 2 coffee machines and 1 worker i produce 18 coffees, when i increase the number of workers, output will increase but at a diminishing rate?
What does the cofee example tell us about the production function?
The increase that we have in the production from an additional unit of labour is called the Marginal product of labour, we assume it is positive everytime i hire another person, but at a diminishing rate.
Vice verse for the Marginal product of capital, it increases at a diminishing rate.
What is another property of the production function?
If i double the inputs i.e workers and cofee machines, my output will double e.g. from 12 to 24. This is called constant returns to scale.
What is the partial deratives of with respect to labour and capital of the production functions?
How do we illustrate the production function on a diagrams keeping capital fixed, to isolate, the labour input?
The slope of this is the production function is the marginal product of labour, we see the same thing on the diagram on the right, as the amount of labour increases, the MPn decreases.
How do we illustrate the production function on a diagrams keeping labour fixed, to isolate, the capital input?
What other assumption can we make about the Marginal product of captial and labour?
The marginal product of labour will be higher if we increase capital
The marginal product of capital will be higher if we incrrase labour.
This is the same vice versa
Showcase constant returns to scale assumption?
2Y = zF(2k, 2N)
If i double the amount of capital and workers i hire, i get double the output, if i half the capital and workers i hire, i get half the output.
Now would i demonstrate Output per worker using the production function and define some variables?
Y = Y/N = ( output per worker)
K = K/N ( capital per worker)
F(k) = F(K/N,1) capital per worker with labour inputs 1.
Thus, what can the production function be written as?
Y = zf(k)
this tells that the output per worker depends on the total factor productivity x the capital per worker.
How does Y = zf(k) look like?
So now we want to have all of the variables in per worker quanitities? but first now list all the equations we are going to need?
Kβ = (1-d)K + I
Y=zF(K,N)
Y = C + I +G+ Nx ( WE ASOME THERE IS NO GOVERMENT AND NO INTERNATIONAL TRADE SO
Y= C+I instead of add G+Nx
4) Consumers either consume or save Y = C+S
5) π = π π, πΆ = (1 β π )Y
So we want an equation that tells us how capital per worker next year is going to beb affected by capital per worker this year. Using this equation solve this Kβ = (1-d)K + I .
1) Kβ = (1-d)K + I
2) Y=zF(K,N)
Y = C + I +G+ Nx ( WE ASSUME THERE IS NO GOVERMENT AND NO INTERNATIONAL TRADE SO
3) Y= C+I instead of add G+Nx
4) Consumers either consume or save Y = C+S
5) π = π π, πΆ = (1 β π )Y
1)Y = C + I
Y = C+S
this implies I=S ( output saved by consumer will be transformed to investment goods, which adds to capital stock of the economy)
2) I can use equation 5,6 and 2 to get
I = szF( K,N)
3) Now you can plug what investment is into equation 1
Kβ = szF(K,N) + (1-d)k
4) Now i will divide by N
What is the next step, that tells me how capital per worker next year is affected by capital per worker this year?
Kβ/N is not capital per worker next year, it would have to be Kβ/Nβ so we times this by population next year (Nβ/Nβ) to get (1+n)kβ=
szF(K.N) = szF(K/N, N/N) = szf( K/N , 1) + (1-d)K/N
then follow the steps and get the answer.
How does capital per worker next year in terms this year look on a diagram?
It looks very similar to the production function.
How can we use this diagram to show how captial per worker evolves in this theory?
This function with the 45* line tells us what capital per worker will be next year, you start with an inital level of capital , then to find out capital per worker in year 2, you draw a line horizontal up to the 45 degree line, then you keep plugging in the functions to find it the next coming years.
What can we say about captial per worker over time?
Capital per worker is growing over time, meaning output per worker is growing over time, thus living standards is growing over time. Notice they are growing at a diminishing rate though ( e.g. Ko to K1 > K1 to K2.
Do we grow forever by making capital per worker increase and increase?
No, at some poiny the growth rate becomes smaller and smaller and growth stopes, this is where we reach K*, the next year the growth rate is 0, this is called the steady state.
How will the steady state equation look like?
When i do some rearrangments on this equation what would i get? and what does this mean
The value of capital per worker at the steady state will be determined by this equation
This equation tells me : on the left hand side i have investment per worker ( so the new amount of capital the economy is making for each worker) the right hand side tells me that i have capital per worker K* and every year i have to cover for 2 things, when deciding how much investment to do, each year you will have more workers and some machines will break down
How can i plot the steady state equation on a diagram?
We plot both sides of the equation
If we are on the left of the steady state it means investment is greater than depreciation meaning capital stock is growing, If we are on the right of the steady state it means investment is lower depreciation, meaning capital stock is strinking
What does thee steady state equation tell you?
Tells you the capita per worker in the steady state is determined by the savings rate S, the z total factor productivity, the growth rate of the population n and the depreciation rate d.
If i want to find the value of the capital per worker in the steady state i need to know these numbers.
What happens if S goes up ( savings/ investment ) and what about TFP?
The slope of szf(k*) depends on s and marginal product of capital, if i increase s, the slope at every level of capital per worker will be a bit higher.
If there is higher savings, we will stop growing a later on meaning a higher capital per worker and living standards
The same shift will happen for Z.
What happens when n goes down?
The slope will be lower still through the orgin, but with higher level of capital per worker at the steady state.
Capital per worker What happens when we are not in the steady state ?
A. If capital per worker is lower than π β , then living standards growth rate is positive
B. If capital per worker is lower than π β , then aggregate capital growth rate is negative
C. If capital per worker is higher than π β , then living standards growth rate is positive
D. If capital per worker is lower than π β , then living standards growth rate increases over time
E. If capital per worker is lower than π β , then aggregate capital growth rate decreases over time until it reaches zero
F. If capital per worker is lower than π β , then aggregate capital growth rate decreases over time until it reaches n
A and F and maybe D
Lets look at A - C
The diagram on the left shows that we start from an inital level of capital k0, then draw horizontal lines to find k1 k2 and k3 to get the curve, getting closer and closer to the steady state ( as you can see capital per worker will grow faster at the beginning the increasing slowly ( MPk is diminishing) So A is right,
we can also see this in the capital per worker growth rate diagram where we do for the each year, percentage increase e.g. for yr 1 k1 - k0/k1 and second year k22-k1/k1.
Aggregrate variables What happens when we are not in the steady state ? E-F
A. If capital per worker is lower than π β , then living standards growth rate is positive
B. If capital per worker is lower than π β , then aggregate capital growth rate is negative
C. If capital per worker is higher than π β , then living standards growth rate is positive
D. If capital per worker is lower than π β , then living standards growth rate increases over time
E. If capital per worker is lower than π β , then aggregate capital growth rate decreases over time until it reaches zero
F. If capital per worker is lower than π β , then aggregate capital growth rate decreases over time until it reaches n
We start with a growth rate of aggregrate capital higher than n at the inital period then will slowly go down untill it reaches n or the steady. ( aggregrate capital grows faster than population then slowly aggregrate capital goes down then the ratio balances ( so growth rate is n) )
Growth rate of Aggregrate variables below the steady state decreases untill it reaches n.
What happens to capital per worker, growth rate of captial per worker, GDP per worker, consumption per worker, Aggregrate capital natural log, GDP natural log, when we start from an initial level of capitial at the steady state.
When we are in the steady state, we stay there
What happen scapital per worker, growth rate of captial per worker, GDP per worker, consumption per worker, Aggregrate capital natural log, GDP natural log, if we are the steady state for 20 years and savings go up?
The steady states jumps up after 20 years, so MPk is higher after new steady state then grows slowly to the new steady state.
With consumption ( if you save more, this means c = (1-s)Y goes down.
What happen scapital per worker, growth rate of captial per worker, GDP per worker, consumption per worker, Aggregrate capital natural log, GDP natural log, if we are the steady state for 20 years and TFP increases?
For 20 years, nothing happens, then, At every level of capital each worker is more productive, the steady state is higher with higher capital per worker but growth rate decreases slowly after time. GDP per worker increases as i am able to produce more, meaning i can consume more ( remember consumers owns firms)
What happens capital per worker, growth rate of captial per worker, GDP per worker, consumption per worker, Aggregrate capital natural log, GDP natural log, if we are the steady state for 20 years and there is an increase in population growth rate?
The capital per worker in the steady state will be lower, os llibing sttandards, will go down and consumption wiill go down
Growth rate is negative.
Notice with aggregrate variables, they will go to a new steady state path, having a new growth rate, we are growing at a higher growth rate as the population growth rate is higher. (slope changes)
Lets say TFP grows constantly each year what is the equation of tfp for next year?
