Chapter 9 - Economic growth II: Technology, empirics and policy

Question 1

How does the production function with technological progress look?

Answer 1

Exogenous technological progress

Production function is now: Y=F(K,L·E)

E = efficiency of labour, reflect society’s knowledge about production methods. Increases from technological progress, improvements in health, education or skill

L*E = the effective number of workers

Question 2

What is labour augmenting?

Answer 2

Technological progress is labour-augmenting: it increases labour efficiency at the exogenous rate g

g = labour-augmenting technological progress

g = ΔE/E

Question 3

Which rate does the effective number of workers grow at?

Answer 3

Remember, labour force growing at rate n

L*E is growing at rate n+g

Question 4

What is the expression for break-even investment (including E) ?

Answer 4

(δ+n+g)k

Now, however, because k = K /(L × E), break-even investment includes three terms:

to keep k constant, δk is needed to replace depreciating capital

nk is needed to provide capital for new workers

gk is needed to provide capital for the new ‘effective workers’ created by technological progress

Question 5

What is the change in capital stock equal to (including technological progress)?

Answer 5

k=sf(k)-(δ+n+g)k

Change in capital stock Δk equals investment sf(k) minus break-even investment (δ+n+g)k

At k*, the level of k at which capital and output per effective worker are constant - long-run equilibrium of the economy - steady state

Question 6

What are the effects of technological progress (in the steady state)?

Answer 6

Output per actual worker (Y/L=y*E) - as y is constant in the steady state and E is growing at rate g, output per worker is growing at rate g

Total output (Y=y·(E·L))- as y is constant, E is growing at rate g and L is growing at rate n, total output grows at rate n+g in steady state

Thus, according to the Solow model, only technological progress can explain sustained economic growth

Question 7

What is the Golden rule now (that technological progress is included)?

Answer 7

Golden Rule level of capital - the steady state that maximizes consumption per effective worker

c* = f(k) - (δ + n + g)k

Steady state consumption maximized if MPK = δ + n +g OR MPK - δ = n + g

At GR level, net marginal product of capital, MPK - δ, equals rate of growth of total output

Question 8

What leads to growth in the Solow model?

Answer 8

In the Solow model, saving leads to growth temporarily, but diminishing returns to capital eventually force the economy to approach a steady state in which growth depends only on exogenous technological progress.

Question 9

What is meant by balanced growth in the Solow model?

Answer 9

Balanced growth - according to Solow model, technological progress causes the values of many variables to rise together in steady state

Solow model predicts Y/Land K/L grow at the same rate (g), so K/Yshould be constant - This is true in the real world.

Solow model predicts real wage grows at same rate as Y/L, while real rental price is constant - Also true in the real world.

Question 10

What is convergence?

Answer 10

Convergence - the world’s poor economies will subsequently start to grow faster than economies that start of rich, they will catch up

Question 11

In the real world, many poor countries do NOT grow faster than rich ones. Does this mean that the Solow model fails?

Answer 11

Solow model predicts that, other things equal, poor countries (with lower Y/Land K/L) should grow faster than rich ones.

The answer is: No, the Solow model does not fail. The reason is that “other things” aren’t equal:

According to Solow model, whether two economies will converge depends on why they differ

Suppose two economies start off with different capital stocks, but have the same steady state, as determined by their saving rates, population growth rates and the efficiency of labour. In this case, we should expect the two economies to converge; the poorer economy with the smaller capital stock will naturally grow more quickly to reach the steady state.

If two economies have different steady states, perhaps because the economies have different rates of saving, then we should not expect convergence.

In real world: the economies of the world exhibit conditional convergence: they appear to be converging to their own steady states, which in turn are determined by such variables as saving, population growth and human capital

Question 12

Why might income per person differ between countries?

Answer 12

International differences in income per person is due to either (1) differences in factors of production, (2) differences in efficiency

In terms of the Solow model, the question is whether the large gap between rich and poor is explained by differences in capital accumulation (including human capital) or differences in the production function.

Question 13

Is capital accumulation and production efficiency correlated ? Why?

Answer 13

Common finding - they are positively correlated: nations with high levels of physical and human capital also tend to use those factors efficiently

Hypotheses:

An efficient economy may encourage capital accumulation

Capital accumulation may induce greater efficiency (positive externalities to physical and human capital)

Both factor accumulation and production efficiency are driven by a common third variable - e.g. the nation’s institutions

Question 14

Many empirical studies have examined to what extent the Solow model can help explain long-run economic growth. What are the results?

Answer 14

The model can explain much of what we see in the data, such as balanced growth and conditional convergence. Recent studies have also found that international variation in standards of living is attributable to a combination of capital accumulation and the efficiency with which capital is used.

Question 15

What is endogenous growth theory?

Answer 15

Endogenous growth theory reject the Solow model’s assumption of exogenous technological change

Question 16

What is the basic endogenous growth model? And what is the key difference to the Solow growth model?

Answer 16

Simple production function Y=AK

Y - output, K - capital stock, A - constant measuring the amount of output produced for each unit of capital

The absence of diminishing returns to capital is the key difference between endogenous growth model and the Solow model, hence, MPK is constant and equal to A (in Solow, diminishing MPK)

Question 17

What determines growth according to the basic endogenous growth model?

Answer 17

∆Y/Y=ΔK/K=sA-δ

This equation shows what determines the growth rate of output ΔΥ/Υ.

As long as sA > δ, the economy’s income grows forever, even without the assumption of exogenous technological progress i.e. in this model saving and investment can lead to persistent growth

Question 18

Is it reasonable to abandon assumption of diminishing marginal returns?

Answer 18

Depends on how we interpret K

If K is e.g. computers - not reasonable

If K includes knowledge - less natural to assume knowledge has diminishing returns

Question 19

What is the two-sector model?

Answer 19

Two sectors in the economy - manufacturing firms and research universities

Firms produce goods and services, which are used for consumption and investment in physical capital.

Universities produce a factor of production called ‘knowledge’, which is then freely used in both sectors.

u - fraction of the labour force (L) in universities, (1 - u is fraction in manufacturing)

E - stock of knowledge (determines efficiency of labour)

g is a function that shows how the growth in knowledge depends on the fraction of the labour force in universities

Constant returns to capital as long as capital is broadly defined to include knowledge

Persistent growth arises endogenously because the creation of knowledge in universities never slows down

Question 20

How does the two-sector model relate to the Solow model?

Answer 20

At the same time, however, this model is also a cousin of the Solow growth model. If u is held constant, then the efficiency of labour E grows at
the constant rate g(u). This result of constant growth in the efficiency of labour at rate g is precisely the assumption made in the Solow model with technological progress

Also manufacturing production function and the capital-accumulation equation resemble the Solow model

Question 21

What is break-even investment in the two-sector endogeneous growth model?

Answer 21

(δ+n+g(u))k = sf(k)

The same as the Solow model, despite from g being a function of u