## Monday, 13 May 2013

### Solow Model

What is it?

It is a neo-classical model developed in the 1950s by Nobel Laurette Robert Solow. The model is used to show that although capital and labour have diminishing returns induvidually, together they have constant returns to to scale with GDP. Thus, in the long run growth can only be achieved through exogenous technological progress i.e. the Solow Residual.

Assumptions

1. Labour grows constantly and exogenously at rate n.
2. Capital and llabour have diminshing returns to scale
3. S=I= sY
4. The economy only produces one good, although this can be extended

Model

The Cobb-Douglas model

Y = A Kl ¹⁻ᵅ

A is the total factor productivity, it is exogenous and is determined by the S=I rate.
Labout is also exogenous but it is assumed to be constant too.

If we take b to be any positive real number then:

bY = F(Kb, Lb)

To write in labour form divide by 1/L:

Y/L = F (K/L , L/L)

Y/L = F (K/L)

Y = f(k)  (lower case k as when you divde labout you are looking at capital per worker now)

y = Ak , output per worker

The Solow equation gives the growth of the capital-labour ratio, k, and shows that growth of the ratio is dependant on savings , after allowing for the amount of capital required to service depriciation  and providing it can provide capital for any new growth in labour.

The further away an economy from its solow equilibrium, the faster it should be growing, this is because these economies tend to have higher capital labour ratios.

The Model depicts the economy tending to long-run equilibrium with capital, labour and output growing at same natural rate.

The (n +d)k rate is the demand for capital adjusted by labour growth and depriciation.

Three main sources of growth.:

1. Disequibrium between sy and (n+d)k
2. Changes in the savings rate, causing shifts in the sy curve, this does not however affect long-run growth rate as does not affect the y=f(k) curve
3. Technical progress, this will affect the longrun steady state equilirbiurm as it will shift the y=f(k) curve

The Solow model shows that both output per worker and capital per worker in an economy will converge to a particular steady state value in the long run and once this steady state value has been achieved, technological process alone can further increase any output.

Policy Implications

According to neoclassical growth theory, output growth results from investment:

1. Increases in the quality and quantity of labour
2. Increase in capital (savings and investment)
3. Technology

Open economies experience income convergence at higher levels as capital flows from rich countries to  poor countries

Criticisms

1. Technical progress is exogenous and what developing countries should be looking too, this is problematic when trying to apply the Solow model.
2. Failure to take into account entreprenuership, strength of institutions etc
3. Does not explain why technological progress occurs
4. All inputs are assumed to be independant of one another in the Solow model, this is a limitation because it mean investment and technological progress cannot be linked hence it is difficult to practically test this model.
5. The model says technological progress is the only way for the economy to grow, whereas actually the government is too, as R&D is crucial for technological progress and this requires a government and a patent regulation system,
6. Ignores the demand side of the economy
7. Why care about the long run? We are all dead anyway - Keynes
8. Ronar like many economist argues that growth is actually to be found endogenously, he says long run growth comes through positive externalities from education etc