Neoclassical Growth

Neoclassical GrowthEcon 337

Vancouver School of Economics

Reading

• The papers I would like you to read for this section of the course are:Rogers, Mark. "A Survey of Economic Growth." Economic Record 79.244 (2003): 112-35

The Production Function

• The production function tells us how firms combine inputs, such as capital and labour, to produce output.

• We can define the production function as a function of• Technology (A) (which can include climate, culture,

arableland, institutions etc...)• Labour (L)• Capital (K)• Land (Z)

• One possible production function is the Cobb-Douglas function.

The Production Function

• The most important properties of the production function for our current model is that • Capital and labour are assumed to be

substitutable.• Constant returns to scale:

• Also requires that there is diminishing marginal product of capital.

Output Growth• Output growth is summarized by the following

term where where FK is the marginal product of capital, FL is the marginal product of labour.

• When we use the Cobb Douglas function this is

Solow Residual

• The final term in this equation is total factor productivity or the Solow Residual that measures all growth which is not created by increasing observable factors of production.

Output Growth• Given the production function, if an economy

is growing it has be to be true that one or more of these factors is increasing.

• However, finding that K, L, Z and A have increased does not explain why economies grow.

• In order to explain output growth, we need to explain the factors that might have caused K, L, Z and A to increase.

Capital Stock

• The supply of savings determines the level of investment:

St = sYt

• where St is the supply of savings in period t and s is the proportion of total income that is saved.

• The higher the savings rate (i.e. the lower the share of output that is consumed) the higher the level of investment in capital.

Capital Stock

• The change in the capital stock equals aggregate investment in period t, It, less depreciation (where δis the depreciation rate)

• Where in equilibrium It = St then

Note on Savings• In this model we have assumed that savings is a fixed

parameter – it is exogenous to the model.• This is directly in contradiction to what you might have

been taught in Econ 102 – that savings is a function of the interest rate.

• The interest rate is just equal to the marginal product of capital and so when capital increases the interest rate falls and savings falls with it.

• In reality there is little relationship between interest rates and savings, however savings is strongly influenced by factors like patience, religion, geography, climate, trade etc. – factors that are historically determined.

Labour

• The level of labour supply determines the level of employment / the size of the workforce.

• If the labour supply grows at a constant rate n, the aggregate labour force grows according to

• Equivalently Lt+1 = (1 + n) Lt

Note on Labour• Likewise, the growth rate of labour is assumed to be a fixed

parameter in this model – it is exogenous to the model.• In reality, particularly historically, the growth rate of the

population is a function of the model.• The wage paid to workers is the marginal product of labour

meaning that when capital increase, wages increase. • When wages increase immigration to the country increases –

the population growth rate increases.• When wages increase fertility rates might increase or

decrease along with the growth rate of the population.

Technology

• The growth rate of technology is constant at rate g:

• Equivalently At+1 = (1 + g) At

Note on Tecnology• Likewise, the growth rate of technology is

assumed to be a fixed parameter in this model – it is exogenous to the model.

• This is essentially true in that the nothing within this model determined the level of technology.

• However, this does not mean that technology growth rates do not vary from country to country and over time.

• Many factors, which we will discuss, determine how technologically advanced a nation becomes.

Human Capital and Land

• It makes the model much more complicated, but for completeness we should also be including land (Z) and human capital (H) in this model.

• Historically these factors are important, but incidentally not at the same time.• When agriculture was the primary output land was the

most important input.• As the US industrialized, human capital became much

more important.

• Later we will use these factors to explain the demographic transition – the fall in fertility rates.

Parameters

• The parameters in the model are exogenous, constants and are:• s - savings rate• n - growth rate of the labour force (or

population)• δ- the rate of depreciation• g - the growth rate of technology• α- the expenditure share on capital

The Intensive form production function

• The intensive form to presents a stationary representation in the long run and tells us how the economy evolves per unit of labour, or later per unit of effective labour.

• Writing the intensive form of the production function depends on the assumption of constant returns to scale.

• I will write these function on the board.

Inada Conditions

• You should already know the properties of the production function but the more important one for our purposes are the following:• When there is no capital there is no output.• When the level of capital is low small increases in

capital lead to large increases in output.• When the level of capital is high large increases

in capital lead to small increases in output.

• These conditions are needed to have a balanced growth path.

The Solow Model• Believe it or not, this is all we need to fully

describe the model (which I am going to do for you on the board).

• The important feature of this model is that countries grow whenever their aggregate savings is greater than the amount they need to save to keep capital per unit of labour constant.

• In the long-run, the only reason the US is richer than other countries is because of factors that have influence the parameters of the model.

Conditional Convergence

• The Solow model predicts that all countries with similar parameters and access to the same level of technology should converge to the same level of income per worker.

• This is important for us here, because it says that if we want to explain why it is that the US is so rich relative to other countries that are very similar, we have to explain the differences in these underlying fundamentals.

Conclusion

• We will return to this model again and again through out the term.

• It is the foundation on which we are building our understanding of US economic history.

• Every since topic we are studying this term essentially comes back to this model, even if sometimes that will not seem obvious.

Reading for Next Class• For the next section of the course on institutions,

please read:Sokoloff, Kenneth L., and Stanley L. Engerman. "Institutions, Factor Endowments, and Paths of Development in the New World." Journal of Economic Perspectives 14.3 (2000): 217-32Acemoglu, Daron, Simon Johnson, and James Robinson. Institutions as the Fundamental Cause of Long-Run Growth. National Bureau of Economic Research, Inc, NBER Working Papers: 10481, 2004.