Economic Growth

Models of economic growth

Extensive and intensive growth

Extensive economic growth is growth that happens when more L, K and N are employed in absolute terms. L is labour, K is capital and N is land/natural resources.

At some point in time any of these factors become scarce and a more important question comes to fore – how to use these production factors most effectively and productively when they become scarce.

This is the case of intensive economic growth that involves increases in Y/L, Y/K and Y/N, i.e. when productivity of labour, productivity of capital and productivity of land/natural resources are increased.

Two models that we consider – Malthus model and Solow model are considering productivity of labour, which is the key driver of economic growth. 

In modern economies productivity in general and labour productivity in particular are key factors of development.

“Productivity isn’t everything, but in the long run it is almost everything. A country’s ability to improve its standard of living over time depends almost entirely on its ability to raise its output per worker.” - Paul Krugman, The Age of Diminished Expectations (MIT Press, 1994).

The major difference between two models is that Malthus considers agriculture-based economy and labour productivity in agriculture and ignores accumulation of capital, while Solow consider labour productivity in modern mixed economy (with agriculture, manufacturing and services) and relates labour productivity to accumulation of capital.

Relationship between expensive and intensive growth

But does capital accumulation alone explain the phenomenal growth the world has observed in the past two hundred years?

And at very low levels of income, however, savings may be zero as all resources are needed for consumption.

So how did rich countries switch from being poor countries? What happened during the industrial revolution?

Britain’s industrial revolution involved a range of transitions: cottage-based industry -> factory-based production (economies of scale); investment into networks (rail, power, distribution); globalisation; colonisation (extraction of resources, wealth, new plants, people and ideas), etc. This supported rapid increases in GDP, permitting greater saving and a virtuous cycle of investment and capital accumulation.

Malthus model

Writing in 1798, around the time of the industrial revolution, Thomas Malthus predicted that if populations grew more quickly than agricultural productivity then a country would continuously slip into periods of starvation.

Malthus’ argument was that with limited land and low levels of capital, a growing population would suffer diminishing returns to labour: adding more workers drives productivity down.

Malthus figured that a larger labour force could produce more output.

There were limits: DMPL implied that eventually a larger labour force would fail to produce enough extra output to feed itself.

Malthus’ arguments helped dissuade the British prime minister of the day, William Pitt, from passing a “Poor Bill” which would give workers with families a benefit.

Promoting families would have increased the population without raising productivity, arguably distressing the poor even more.

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Output growing by less than the population would result in famine, starvation and death.

While technological improvements might improve productivity, this would allow the population to grow more quickly, driving the country back to starvation levels - a Malthusian trap.

How can we explain the persistent increase in output that most countries experience, and increases in per capita income? Why didn’t we fall into Malthus’ trap?

Output above subsistence level

One factor missing from Malthus’ model was capital, and in particular the accumulation of capital. When both labour and capital increase output can rise above the subsistence level.

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Another factor is technological progress and increases in labour productivity.

Specifically, in agriculture advances in production methods, new seeds, fertilisers enhanced agricultural productivity and prevented famines.

It should be noted though that still in many parts of Africa, Malthusian model may work. Specifically it works in arid countries around Sahara desert, where population growth is to large extend is not controlled, land available for production is limited, production technologies are not modern and droughts are frequent.

Solow model

Main assumptions

Model of Solow is non-Keynesian model, i.e. it assumes that:

• Economy is in full employment, Y = Yf
• Prices are flexible (not sticky)
• Production factors (labour and capital) are perfectly substitutable in production process
• It uses Cobb-Douglas production function Y = AKαL1-α
• Very importantly (but beyond the scope of this course), it assumes that shares of labour and capital in GDP are fixed, i.e. functional distribution of income does not matter.

Purpose of the model

The Solow growth model allows us a dynamic view of how savings and capital accumulation affects the economy over time.

Also Solow model shows the path of economic growth in particular country and convergence of GDP per capita across countries.

It also shows what can be the maximum possible economic growth rate in the country.

Assumption of diminishing returns to capital in Solow model

What happens to output when a single factor of production is increased (rather than all factors of production as with returns to scale)?

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Solow model in few words

Solow model instead of looking at aggregate Y, K, L, S and I looks as “per capita” variables – Y/L (labour productivity), K/L (capital per worker), S/L (savings per person) and I/L (investment per person). There variables are small letters – y, k, s and i.

Capital per person determines labour productivity and thereby output per capita. I.e. capital accumulation is centrepiece. Capital accumulation is driven by savings, i.e s → k → y.

Over time economy moves towards some unique level of k and y, and it can move away from them only temporarily. These are equilibrium k* and y*. And because they are stable, they are called “steady state equilibria”.

Equilibrium k and y are determined by both actual savings/investment and savings/investment required to maintain some fixed level of capital in economy.