Flashcards in L14 - The Neo-Classical Model of Economic Growth Deck (25):

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## Why did economic growth dramatic change after the war?

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In 1952 Moses Abramowitz surveying the theory of economic growth concluded that little progress had been made since the Classical period

This changed dramatically in the in post-war years, partly due to:

- the theoretical stimulus of Keynesian economics

- the western world embarked on a period of sustained growth

- economists increased knowledge of mathematics

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## What are some Key National Accounts details?

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- Total Output (Q) consists of consumption goods (C) and capital goods (I) so: Q = C + I

- National Income (Y) earned from productive activity is either spent on consumption goods (C) or saved (S) so: Y = C + I

- In equilibrium Y= Q and thus S = I

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## What is the Production Function?

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- A production function can be written as: Y=F(K, N) where Y is output, K is the stock of capital (machines) and N is the supply of labour. The production function defines the technology that translates inputs into output

- Constant returns to scale is when if all inputs are doubled output doubles.

- Generally: zY=F(zK, zN), where z can be any positive number. If K and N are both increased by 5% z =1.05 and Y also rises by 5%.

- If z =1/N then the production function becomes: Y/N=F(K/N, 1) This says that output per worker increases as capital per worker increases, which can be written more easily as y=f(k)

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## What is the Marginal Product of Capital?

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- The Neo-Classical model, like the Classical model before it, focuses on the role of capital – specifically a diminishing marginal product of capital.

- This says that as more and more capital is employed for a given labour force, the marginal product of the capital (MPK) will eventually decline

- In other words the production function is non-linear and becomes flatter as more of the variable input in added – as shown by the following diagram

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## What does the Basic Neo-Classical Model of Economic Growth look like?

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- With Output per head y=Y/N on the y-axis and Capital per head k=K/N on the x-axis.

- With a positive gradient curve of y=f(k)

- the MPK given by slope of production function. Tangents get flatter as k rises showing declining MPK

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## How is Savings defined in the Neo-classical Growth model?

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- It is assumed that savings depends positively on income (Y) then S= sY where s is the average (and marginal) propensity to save and 0 < s < 1

Dividing through by N gives the expression in per capita terms and replacing y with its equal f(k) gives:

- S/N = s(Y/N) = sy = sf(k)

- which says that savings per worker will be fixed proportion of output per worker

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## How is Investment defined in the Neo-classical Growth model?

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- Investment is defined as I = ∆K+dK – new investment (∆K) plus depreciation (dK).

- To determine the equilibrium value of K/N, the question is how much investment is needed to keep K/N constant? There are 2 factors: the rate of depreciation, d; and the rate of growth of the labour, n

- If capital depreciates at rate d per period then investment per head must be d x k to stop the K/N from falling

- If labour grows at rate n per period, then an additional investment of n x k will be needed to keep K/N constant

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## What is Equilibrium Savings and Investment?

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- Hence (d+n)k is called the required investment to keep K/N constant

The long-run equilibrium condition is:

- Δk= i – (d+n)k = 0

- In equilibrium S = I (and so s = i) which means for a constant K/N we have:

- sf(k)= (d+n)k

- This is the equilibrium growth relation where savings and investment are equal. It says that output, capital and labour all grow at rate n as illustrated below

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## What does the Neo-Classical Growth model look like Including Saving and Investment?

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- With Output per head y=Y/N on the y-axis and Capital per head k=K/N on the x-axis.

- With a positive gradient curve of y=f(k)

- Another positive gradient curve of savings y=sf(k) but it is smaller than the curve y=f(k)

- a straight diagonal line of Investment that maintains the capital labour ratio, (d+n)k

- Equilibrium it at the point where y=sf(k) and (d+n)k intercept and the corresponding value for y for the function y=f(k) given the value of k of the equilibrium point

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## How can the Neo-Classical Growth model including Saving and Investment be interpreted on a graph?

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- The point E is the steady-state level of output and capital per head. At levels of k to the left of k{1} k is rising; at points to the right of k{1}, k is falling.

Although output per head is constant the economy’s total output,Y, will be growing at the same rate as the total population, n. This is an important conclusion for the Neo-classical model.

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## How can you calculate rates of change of y?

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equilibrium in the Neo-classical model is a dynamic meaning it is a growth rate not a stationary point:

Y = Y/N --> Output per head

y(hat) = Y(hat)-N(hat)

- where (hat) is percentage rate of change

- in the diagram at point y, y(hat) is 0 therefore Y(hat)=N(hat)=n

- where the rate of growth of output is the same as the rate of growth of the labour force

- so at equilibrium y is growth at rate n

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## How can calculate the rate of change on k?

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k=K/N --> capital stock per head

k(hat)=K(hat)-N(hat)

- where (hat) is percentage rate of change

- in the diagram k(hat)=0 therefore K(hat)=N(hat)=n

- where the rate of growth of capital stock is the same as the rate of growth of the labour force

- so at equilibrium k is growth at rate n

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## What happens when there is a rise in the saving rate?

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- This is captured on the chart by s rise in the sf(k) line, as s rises from s{1} to s{2}.

- Gross investment will now exceed required investment and the capital stock will increase until k reaches k{2}. - While k is between k{1} and k{2} average labour productivity will be increasing, so the growth of Y will be exceeding that of N. Once equilibrium is reached Y/N is again constant

- Thus savings alone cannot permanently raise the growth rate, because of the diminishing marginal product of capital

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## What happens to the Growth Rate of Labour during a increase in the Savings Rate?

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- growth rate has not permanently increased only temporarily

- during the time between the original capital stock per head k{1} to the new capital stock per head k{2} there will be a jump in the growth rate because savings is higher than investment so as investment rises to meet it, but it will come back down once we reach k{2}

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## What is the summary of the Neo-Classical Growth model including Saving and Investment?

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- The Neo-classical growth model says that economic growth is dependent on technical progress – which raises the productivity

- A rise in the savings rate will only lead to a temporary rise in the growth rate as the K/N ratio rises to the new equilibrium – where production is more capital intensive. Once this level is reached the economy grows at rate n, as before

- The model suggests convergence in Y/N over time with poor countries (or regions) growing faster than rich countries (or regions)

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## What are two shocks that could affect the Neo-Classical growth Model?

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- savings shock

- technical process shock

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## What is a Technical Progress Shock?

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- Technical progress is an improvement in knowledge that enables a higher output to be produced from existing resources

- A technical improvement shifts up the whole production function (and hence also the savings function) to give a higher level of average labour productivity (Y/N)

- If technology continues to improve the production function will continue to shift out and aggregate output will continue to grow over time

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## What does a Technical Progress Shock look like on the Neo-Classical Growth model?

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- This has caused a change in the production function

- A technical Progress Shock move y=f{1}(k) up to y=f{2}(k) which also increased the saving function from i=sf{1}(k) to i=sf{2}(k)

- both having at equilibrium was at k{2} and to y{2}

- the increase in Output head is much more than with a shock to savings

- technical shock is said to be continuous so y with be rising continuously as well as k

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## What is a Summary of the shocks that can occur in the Neo-Classical growth model?

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- The Neo-classical growth model says that economic growth is dependent on technical progress – which raises the productivity --> but become more capital intensive

- A rise in the savings rate will only lead to a temporary rise in the growth rate as the K/N ratio rises to the new equilibrium – where production is more capital intensive. Once this level is reached the economy grows at rate n, as before

- The model suggests convergence in Y/N over time with poor countries (or regions) growing faster than rich countries (or regions)

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## What is the Framework for the Sources of Growth?

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-The production function: Y=AF(K, N), where Y is output, A is technical progress, K is the capital stock and N the level of labour inputs.

- In terms of changes this can be written as:

ΔY = F(K, N)ΔA+F{K}ΔK+F{N}ΔN

-where F{K} and F{N} are the marginal product of capital (MPK) and the marginal product of labour (MPN) respectively

Divide through by Y: ΔY/Y = F(K, N)ΔA/Y+F{K}ΔK/Y+F{N}ΔN/Y

Multiply the first RHS term top and bottom by K and the second RHS term top and bottom by N, which gives:

ΔY/Y = ΔA/A+((F{K}xK)/Y)ΔK/K+(F{N}xN/Y)ΔN/N

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## What do the terms in the framework for the sources of growth mean?

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The term (F{K} x K) equals total capital income (income per unit times the number of units) and the term(F{K}xK)/Y equals capital share of total output

Similarly for labour. If labour is paid a real wage equal to its marginal product then total labour income is (F{N} x N) and (F{N} x N) /Y equals labour share of total income

-As there are only two terms in the production function then the shares of capital and labour income must sum to one. Let capital share be α and labour’s share be (1-α)

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## What can the framework for the sources of growth be simplified to?

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ΔY/Y = ΔA/A+αΔK/K+(1-α)ΔN/N

This says that the growth of the economy depends upon

- the rate of technical progress

- the rate of growth of the capital stock weighted by the share of capital in income and

- the rate of growth of the labour force weighted by the share of labour in total income

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## What is Total Factor Productivity?

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- Rewriting the equation in terms of ΔA/A we can redefine ΔA/A as total factor productivity (TFP). That is, all growth not accounted for by labour and capital, such as entrepreneurship, or the legal environment

- ΔA/A = ΔY/Y-αΔK/K-(1-α)ΔN/N

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## What is some Empirical Analysis of Factor Shares?

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- Factors shares have remained largely constant over a long period of time in both the UK and the US (and indeed in other developed countries) so from the data α = 0.3 and hence (1 - α ) = 0.7.

A table can be drawn up showing the contributions to UK economic growth from Angus Maddison (1991)

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