L14 - The Neo-Classical Model of Economic Growth Flashcards
Why did economic growth dramatic change after the war?
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
What are some Key National Accounts details?
- 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
What is the Production Function?
- 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)
What is the Marginal Product of Capital?
- 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
What does the Basic Neo-Classical Model of Economic Growth look like?
- 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
How is Savings defined in the Neo-classical Growth model?
- 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
How is Investment defined in the Neo-classical Growth model?
- 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
What is Equilibrium Savings and Investment?
- 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
What does the Neo-Classical Growth model look like Including Saving and Investment?
- 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
How can the Neo-Classical Growth model including Saving and Investment be interpreted on a graph?
- 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.
How can you calculate rates of change of y?
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
How can calculate the rate of change on k?
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
What happens when there is a rise in the saving rate?
- 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
What happens to the Growth Rate of Labour during a increase in the Savings Rate?
- 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}
What is the summary of the Neo-Classical Growth model including Saving and Investment?
- 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)