Stages of growth and capital accumulation models

Week 3: Stages of growth, capital accumulation models, neo-classical growth theory.

Course objective

Don’t use plagiarized sources. Get Your Custom Essay on
Stages of growth and capital accumulation models
Just from $10/Page

Order Essay

Provide you with a set of historical facts to provide context to debates about growth and globalisation.

Learn some of the core and contemporary theories and learn the “language of economics”. This will help you when conducting your own research.

Foster a) a critical mindset for interrogating theories and the evidence for/against them, and b) an appreciation of details.

Simulate an interest in economics! This course is what you make of it – so what do you want to learn about? Ask questions! No tutorials to this is your chance.

The big idea

“Under what impulses did traditional, agricultural societies begin the process of their modernization?

When and how did regular growth become a built-in feature of each society?

What forces drove the process of sustained growth along and determined its contours?

What common social and political features of the growth process may be discerned at each stage?

What forces have determined relations between the more developed and less developed areas; and what relation if any did the relative sequence of growth bear to outbreak of war?”

Stages of growth

A broad descriptive classification of the common features of economies at different stages.

Traditional society

Preconditions for take-off


Drive to maturity

Age of high mass consumption


Some causal claims and identification of mechanisms – how and why do societies move from one stage to the next? Political will a binding constraint, technology, war and invasion also potential causal factors.

Limited insight into how to peacefully promote growth and development in 2018!

Harrod and Domar

This is really the first “economic-sy” model of growth.

Identifies capital accumulation as the mechanism for growth and for unemployment — tries to understand what causes the business cycle, and to deflect from Marxist writings at the time.

Developed independently by Roy Harrod (1939) and Evsey Domar (1946).

There is no natural reason to have balanced growth (Harrod’s “knife edge”), but output is essentially determined by the size of the capital stock.

Labor productivity is not a function of technological progress in the abstract, but technological progress embodied in capital goods, and the amount of capital goods. Even without technological progress, capital accumulation increases labor productivity, at least to a certain point, both because more capital is used per workman in each industry and because there is a shift of labor to industries that use more capital and can afford to pay a higher wage. So if labor productivity is affected by capital accumulation, the formula that the latter should proceed at the same rate as the former (and as the increase in labor force) is not as helpful as it appears.

We shall assume instead that employment is a function of the ratio of national income to productive capacity.


Harrod and Domar

y = f(K)

= K/Y

f(0) = 0

sY = S = I ⇒ C = (1-s)Y

∆K = I – σK

Output = some function of capital stock

The marginal product of capital is constant; production has constant returns to scale.

Capital is required for any output

Savings is a constant share of output and equals investment

Change in capital stock equals investment less the depreciation of existing capital.

The basic Harrod-Domar model

Harrod and Domar

What determines the growth rate in this simple common-sense model? Our assumptions already imply something about this, so we just use them to look for which combination of parameters equals ∆Y/Y (where ∆Y = Yt+1 – Yt) which is the growth rate, g, of output, Y.

∆Y/Y = g = s/ — σ


First, rearrange the

capital-output ratio equation: Yt = Kt

Now substitute this into: Kt+1 = Kt + ∆K = sYt + (1-σ)Kt

Implying that: Yt+1 = sYt + (1-σ) Yt

This can be expanded to: Yt+1 = sYt + Yt -σ Yt

So: Yt+1 – Yt = sYt -σ Yt

Divide through by Yt Yt+1 – Yt /(Yt) = ∆Y/Y = g = s/ – σ


Harrod and Domar

∆Y/Y = g = s/ — σ

In words that means “The growth rate of output equals the savings rate divided by the ratio of capital to output, minus the depreciation rate.

Or “The growth rate in output equals the net rate of growth of capital”


First, rearrange the

capital-output ratio equation: Yt = Kt

Now substitute this into: Kt+1 = Kt + ∆K = sYt + (1-σ)Kt

Implying that: Yt+1 = sYt + (1-σ) Yt

This can be expanded to: Yt+1 = sYt + Yt -σ Yt

So: Yt+1 – Yt = sYt -σ Yt

Divide through by Yt Yt+1 – Yt /(Yt) = ∆Y/Y = g = s/ – σ


Harrod and Domar

Interpretation: Savings rate and Capital-Output ratio positively affect growth; depreciation negatively affects growth.

However: Be very cautious here about what “savings” means. Remember, by assumption, the savings rate was the rate of investment. It means spending on non-consumption new goods.

A very common confusion in economics (including the textbooks!)


First, rearrange the

capital-output ratio equation: Yt = Kt

Now substitute this into: Kt+1 = Kt + ∆K = sYt + (1-σ)Kt

Implying that: Yt+1 = sYt + (1-σ) Yt

This can be expanded to: Yt+1 = sYt + Yt -σ Yt

So: Yt+1 – Yt = sYt -σ Yt

Divide through by Yt Yt+1 – Yt /(Yt) = ∆Y/Y = g = s/ – σ


Growth in H-D

Warranted rate “The warranted rate of growth is taken to be that rate of growth which, if it occurs, will leave all parties satisfied that they have produced neither more nor less than the right amount.” (a moving equilibrium)

Natural rate “the maximum rate of growth allowed by the increase of population, accumulation of capital, technological improvement and the work/ leisure preference schedule, supposing that there is always full employment in some sense.”

Actual rate

Domar’s conclusion

“the maintenance of full employment requires investment to grow at a constant compound-interest rate”

Which was if investment growth, r, was equal to the marginal propensity to save (the capital share of GDP, α) times “the the increase in productive capacity of the whole society”,σ.

r = ασ

Harrod’s conclusion












GN = GW = G




GW = G












So what?

HD model (now often referred to as the AK model) doesn’t really tell us about any mechanism for getting higher capital investment.

It tries to capture the idea that any equilibrium growth rate is unstable, making room for policy responses to push back towards equilibrium OR to full employment.

Identifies capital investment as the key mechanism at play.

Solow and Swan

What is often known as “neo-classical growth theory”

Arose in reaction to Harrod-Domar because of the fixed capital to output ratio.

Independently derived by Robert Solow and Trevor Swan in 1956.

Mostly a theory of “equilibrium in an economy over time”

Tries to describe the mix of real production factors and limits of capital deepening within capital widening.

Solow and Swan

Single good produced with a constant technology.

No government or international trade.

All factors of production are fully employed.

Labor force grows at constant rate, n. Though I think it’s better to think about it as a “per capita” model.

Decreasing marginal product of capital (the addition of the same amount of new capital in a poor country generates higher additional output)

Why is this important?

The ‘factors of production’ approach is the theoretical basis of the whole national accounting system — the measurement of GDP, productivity, etc.

Diminishing returns to capital assumption has lead to a focus on multi-factor productivity as the only source of long run growth for developed economies.

Y(t) = A(t) K(t)α L(t)(1-α)

Per capita is: y(t) = A(t) k(t)α

Putting that into math

Output at a given point in times is a function of technology at that time (A) times the capital stock raised to α<1, times the labour force.

Per capita output at a given point in times is a function of technology at that time (A) times the capital stock per capita raised to α<1.

When α=1 it is the AK model.


α is the elasticity of output with respect to capital.

Depreciation on capital stock is is a constant share of the stock, δK.

Investment is sY(t), where s is the “savings share”

Rate of change of capital stock is: sY(t) — δK

Steady state

Economy can grow (per capita) until: k(t+1) = k(t) = k* i.e. the capital stock is constant.

This means that the capital stock is not growing over time. This happens when depreciation of the stock equals the new investment (so that net new investment is zero) i.e. δK = sY(t)


Draw lines here and show solution with maths too!

A =“Technology”

What is it? Does it just grow automatically over time?

“Since we know little about the causes of productivity increase, the indicated importance of this element may be taken to be some sort of measure of our ignorance about the causes of economic growth in the United States and some sort of indication of where we need to concentrate our attention.” Abramovitz (1956)

Recall growth accounting

Growth Factor Share Growth from factor Share of growth explained
Land 1% 20% 0.2% 6.7%
Labour 2% 60% 1.2% 40.0%
Capital 2% 20% 0.4% 13.3%
Output (GDP) 3% 100% 1.8% 40.0%



Permanent growth through capital investment is not possible. Increasing the amount of capital for each worker leads to falling marginal product.

In the long run there is no growth without “technology change”, and the long run growth rate equals the rate of technology change (recall Domar said technology was ‘in’ capital)

Increasing savings and investment rate generates temporary growth.

Predicts convergence – low income countries should grow faster than high income countries.


How do the 5 key parts of globalisation fit with these models?


A major prediction of the model is that poor countries should find growth easier to achieve because of higher returns to capital.

But the data doesn’t really support this.

Conditional convergence

Sort of an escape route for the model. Perhaps countries differ in terms of how their capital depreciates or their access to technology, or some characteristic not captured in the model.

Countries with more common political factors and economic structures are more likely to see convergence.

“Clubs” of countries with similar factors with converge within the club, but there can remain divergence between clubs.


Just the OECD – so convergence here.


Harrod and Domar wanted to explain cycles, growth and unemployment, and thought that capital investment was the major factor. They say a ‘knife-edge’ equilibrium where the “warranted” (equilibrium of markets) growth rate could be pushed off the equilibrium by shocks with no mechanism to pull it back.

Fundamental insight of capital being the main cause of growth persists, and was justified based on the evidence that high investment countries grow faster.


Solow-Swan model still focusses on capital, but assuming diminishing returns shifts the focus onto “technology” in order to understand long run growth.

Unlike HD, imposes stability of investment paths and growth over time (in the absence of ‘shocks’).

Evidence shows that predicted convergence the exception rather than the rule, and therefore some of the main ‘causes of growth’ are outside the model (or are they in the ‘technology’ part?)

Growth policy

As a policy-maker seeking higher growth or better development, how can these theories help you?

Not rhetorical!


Focus on capital investment.

Cycle driven by capital investment, so smoothing the cycle means intervening in capital investment

Technology change seems important, but not sure how – seems to be embedded in capital – perhaps we can import capital good that we can’t yet make?

Leave a Comment