[4ii] Introducing technological progress and human capital to Long Run Growth

Question 1

4 Real Life Examples of Tech Progress?

Answer 1

U.S. farm sector productivity nearly tripled from 1950 to 2009.

The real price of computer power has fallen an average of 30% per year over the past three decades.

2000: 361 million Internet users, 740 million cell phone users -> 2011: 2.4 billion Internet users, 5.9 billion cell phone users

2001: iPod capacity = 5gb, 1000 songs. Not capable of playing episodes of popular TV shows. ->
2012: iPod touch capacity = 64gb, 16,000 songs. Can play episodes of popular TV shows.

Question 2

What new variable do we add to the Solow model?

Answer 2

A new variable: E = labour efficiency

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

g = change in E / E

Question 3

How is the production function written with new Variable ?

Answer 3

Y = F (K, L x E)

L x E = the number of effective workers

Hence, increases in labour efficiency have the same effect on output as increases in the labour force.

Question 4

Notation:
y = Y/LE =
k = K/LE =

Production function per effective worker:

Saving and investment per effective worker:

Answer 4

Notation:
y = Y/LE = output per effective worker
k = K/LE = capital per effective worker

Production function per effective worker: y = f(k)
Saving and investment per effective worker: s y = s f(k)

Note: no longer in merely “per worker” terms.

Question 5

How do you write break investment 4 variables?

How can we define break-even investment

Explain what each variable represents?

Answer 5

( d + n + g)k = break-even investment: the amount of investment necessary to keep k constant.
[note: δ = d]

Consists of: d k  to replace depreciating capital n k  to provide capital for new workers g k  to provide capital for the new “effective” workers created by technological progress

Question 6

3 Main Differences Between Solow Growth model with and without Tech progress

Answer 6

Main difference is that in the steady state, income per worker/capita is growing at rate g instead of being constant.

With tech, k and y are in “per effective worker” units rather than “per worker” units.

The break-even investment line is a little bit steeper: at any given value of k, more investment is needed to keep k from falling - in particular, gk is needed. Otherwise, technological progress will cause k = K/LE to fall at rate g (because E in the denominator is growing at rate g).

Question 7

Steady-state growth rates in the Solow Model with tech. progress:

Capital per effective worker?
Output per worker?
Output per Effective worker?
Total Output?

Answer 7

k is constant (has zero growth rate) by definition of the steady state

Output per worker (Y/L) grows at rate g

y is constant because y = f(k) and k is constant

Y grows at rate g + n.

Question 8

Why does Output per worker (Y/L) grow at rate g?

Answer 8

To see why Y/L grows at rate g, note that the definition of y implies (Y/L) = yE. The growth rate of (Y/L) equals the growth rate of y plus that of E. In the steady state, y is constant while E grows at rate g.

Question 9

Why does Y grow at rate g + n.?

Answer 9

Note that Y = yEL = (yE) x L.

The growth rate of Y equals the growth rate of (yE) plus that of L. We just saw that, in the steady state, the growth rate of (yE) equals g. And we assume that L grows at rate n (no. of new workers)

Question 10

What is the golden rule capital stock with tech prog?

what does MPK equal when c* is maximised?

Answer 10

c* = y* - i*
= f (k* ) - ( d + n + g) k*
[investment in steady state, i* =break-even investment]

c* is maximized when MPK = d + n + g
or MPK - d = n + g

In the Golden Rule Steady State, the marginal product of capital net of depreciation equals the pop. growth rate plus the rate of tech progress.

Question 11

Growth empirics: Balanced growth

What does K/L grow at the same rate as?
and therefore what does this mean should be constant?
Is this true irl?

What does Y/L grow at same rate as?
and therefore what does this mean should be constant?
Is this true irl?

Answer 11

Solow model predicts Y/L and K/L grow at the same rate (g), so K/Y should 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 12

What does Solow model predict for poor countries?

why does this not mean the solow model fails?

Answer 12

Solow model predicts that, ceteris paribus, poor countries (with lower Y/L and K/L) should grow faster than rich ones.

If true, then the income gap between rich & poor countries would shrink over time, causing living standards to converge. In real world, many poor countries do NOT grow faster than rich ones.

No, because “other things” aren’t equal:
In samples of countries with similar savings & pop. growth rates, income gaps shrink about 2% per year.

In larger samples, after controlling for differences in saving, pop. growth, and human capital, incomes converge by about 2% per year.

Question 13

What the Solow model really predicts is ____ convergence — countries converge to their own steady states, which are determined by ___, ___ growth, and e____

Answer 13

What the Solow model really predicts is conditional convergence—countries converge to their own steady states, which are determined by saving, population growth, and education

Question 14

Two reasons why income per capita are lower in some countries than others:

does one reason influence the other explain?

Answer 14

Differences in capital (physical or human) per worker

Differences in the efficiency of production (the height of the production function)

[note: countries with higher capital (physical or human) per worker also tend to have higher production efficiency]

Question 15

Explain why Countries with higher production efficiency also tend to have higher physical or human capital per worker ? 3 stage analysis

Answer 15

Production efficiency encourages capital accumulation

Capital accumulation has externalities that raise efficiency

A third, unknown variable causes cap accumulation and efficiency to be higher in some countries than

Question 16

If (MPK - d ) > (n + g ), then we are ____ the Golden Rule steady state and should ____ _.

If (MPK -d ) < (n + g ), then we are ____ the Golden Rule steady state and should ____ _

Answer 16

If (MPK - d ) > (n + g ), then we are below the Golden Rule steady state and should increase s.

If (MPK -d ) < (n + g ), then we are above the Golden Rule steady state and should reduce s.

Question 17

To estimate (MPK - d ), we use three facts about the economy of the U.K.: [write expressions for each]

The capital stock is about ___ times one year’s GDP

About __of GDP is used to replace depreciating capital.

Capital income is about ___ of GDP

Answer 17

1. k = 2.5 y
   The capital stock is about 2.5 times one year’s GDP.
2. d k = 0.1 y
   About 10% of GDP is used to replace depreciating capital.
3. MPK x k = 0.3 y
   Capital income is about 30% of GDP

Question 18

How do we estimate the depreciation rate using the 3 facts about the UK economy?

Answer 18

dk/k = depreciating capital / capital stock = 0.1 y / 2.5 y

therefore, depreciation (d) = 0.04

Question 19

How can we estimate MPK using the 3 facts about the UK economy?

Hence what doe MPK - d equal?

Answer 19

(MPK x K) / K = Capital Income / Capital Stock = 0.3 y / 2.5 y

so, MPK = 0.12

Hence MPK - d = 0.12 - 0.04 = 0.08

Question 20

U.K. real GDP grows an average of 2.5%/year,

so n + g = 0.025
Thus, in the U.S., MPK - d = 0.08 > 0.025 = n + g

The U.K. is ____ the Golden Rule steady state:

Answer 20

2.5%

The U.K. is below the Golden Rule steady state:

Question 21

x4 Policies to increase the saving rate

Answer 21

Reduce the government budget deficit(or increase the budget surplus)

Increase incentives for private saving:
reduce capital gains tax, corporate income tax, inheritance tax as they discourage saving

replace income tax with consumption tax

expand tax incentives for savings through retirement pension funds and other retirement savings accounts (such as ISAs)

Question 22

How many types of capital in Solow Model?

In the real world there are many types that are divided into what 3 categories?

Answer 22

In the Solow model, there’s one type of capital.

In the real world, there are many types,which we can divide into three categories:
private capital stock
public infrastructure
human capital: the knowledge and skills that workers acquire through education

Question 23

What is the industrial policy for Allocating Investment?

Answer 23

Govt should actively encourage investment in capital of certain types or in certain industries, because they may have positive externalities (by-products) that private investors don’t consider.

Question 24

2 Possible problems with industrial policy for Allocating Investment?

Answer 24

Does the gov’t have the ability to “pick winners” (choose industries with the highest return to capital or biggest externalities)?
Would politics (e.g. campaign contributions) rather than economics influence which industries get preferential treatment?

Question 25

4 ways of encouraging technological progress?

Answer 25

Patent laws: encourage innovation by granting temporary monopolies to inventors of new products

Tax incentives for R&D

Grants to fund research at universities

Industrial policy: encourage specific industries that are key for rapid tech. progress (subject to the preceding concerns)

Question 26

x4 explanations for the worldwide slowdown in growth in output per person after 1972

Answer 26

Measurement problems -Increases in productivity not fully measured.
But: Why would measurement problems be worse after 1972 than before?

Oil prices- Oil shocks occurred about when productivity slowdown began.
But: Then why didn’t productivity speed up when oil prices fell in the mid-1980s?

Worker quality: 1970s - large influx of new entrants into labour force (baby boomers, women). New workers are less productive than experienced workers.

The depletion of ideas-Perhaps the slow growth of 1972-1995 is normal and the true anomaly was the rapid growth from 1948-1972.

Question 27

What is made Endogenous in Endogenous Growth Theory? (prev exogenous in Solow model)

In the Solow model, the long-run economic growth rate equals the rate of ___ ___, which is ___ in the model. Hence, the Solow model is basically saying “all I can tell you is that growth in living standards depends on ___ ____. I have no idea what drives/causes changes to it.”

Answer 27

a set of models in which the growth rate of productivity and living standards is endogenous

In the Solow model, the long-run economic growth rate equals the rate of technological progress, which is exogenous in the model. Hence, the Solow model is basically saying “all I can tell you is that growth in living standards depends on technological progress. I have no idea what drives technological progress.”

Endogenous growth theory tries to explain the behavior of the rates of technological progress and/or productivity growth, rather than merely taking these rates as given.

Question 28

Key difference between Endogenous growth theory model & Solow?

Investment:
Depreciation:
Law of motion for total capital:
ΔK =

Answer 28

MPK is constant here, diminishes in Solow

Investment: s Y
Depreciation: d K
Law of motion for total capital:
ΔK = s Y - d K

Question 29

Y = AK, so the growth rate of Y equals the sum of the growth rates of _ and _. A is ___, so its growth rate is ___. Hence, ___ and ___ grow at the same rate.

Answer 29

Y = AK, so the growth rate of Y equals the sum of the growth rates of A and K. A is constant, so its growth rate is zero. Hence, output and capital grow at the same rate.

Question 30

If capital is narrowly defined (only plant & equipment), Does capital have diminishing returns or not?

Answer 30

Yes, Does capital have diminishing returns

Advocates of endogenous growth theory argue that knowledge is a type of capital.
If so, then constant returns to capital is more plausible, and this model may be a good description of economic growth

Question 31

A two-sector model: Two sectors:

• ____ firms produce goods
• research universities produce knowledge that increases labour ____ in manufacturing

There are two differences:
First, a fraction of the labour force does not produce ___ & ___, but rather produces “____” by doing research in universities.

Second, the rate of tech progress is not ____, but rather depends on how fast the stock of ___grows, which in turn depends on how much labour the economy has allocated to ____.

Answer 31

• manufacturing firms produce goods
• research universities produce knowledge that increases labour efficiency in manufacturing

There are two differences:
First, a fraction of the labour force does not produce goods & services, but rather produces “knowledge” by doing research in universities.

Second, the rate of tech progress is not exogenous, but rather depends on how fast the stock of knowledge grows, which in turn depends on how much labour the economy has allocated to research.

Question 32

In Two sector model, the steady state growth rate of the standard of living equals the growth rate of ___ ___, just like in the ___ model with tech progress, covered at the beginning of this chapter. The difference here is that the rate of tech progress, g, is not ___, but rather it depends on how much labor the economy has allocated to ____.

Answer 32

In Two sector model, the steady state growth rate of the standard of living equals the growth rate of labor efficiency, just like in the Solow model with tech progress, covered at the beginning of this chapter. The difference here is that the rate of tech progress, g, is not exogenous, but rather it depends on how much labor the economy has allocated to research.

Question 33

Would an increase in u (fraction of labour in research) be unambiguously good for the economy?

Answer 33

No. On one hand, higher u means faster growth. On the other hand, higher u means less labor is devoted to the production of goods & services.

If we increase u, output of goods & services per capita will fall in the near term. But, with faster growth, output per capita will eventually be higher than it would have.

Of course, if we increase u to its maximum possible value, 1, then no goods and services would be produced, and you’d have a bunch of starving geniuses.

Question 34

Three facts about R&D in the real world:

Who is most of research done by?

Why do they do most of the research? x2

What further influences does innovation have?

Answer 34

1. Much research is done by firms seeking profits.
2. Firms profit from research because:
   - new inventions can be patented, creating a stream of monopoly profits until the patent expires
   - there is an advantage to being the first firm on the market with a new product
3. Innovation produces externalities that reduce the cost of subsequent innovation.
   Much of the new endogenous growth theory attempts to incorporate these facts into models to better understand tech progress.

Question 35

What phrase did Schumpeter coin?

and explanation?

Answer 35

Schumpeter (1942) coined term “creative destruction” to describe displacements resulting from technological progress:

the introduction of a new product is good for consumers but often bad for incumbent producers, who may be forced out of the market.

Question 36

SUMMARY:

1. Key results from Solow model with tech progress:
   - steady state growth rate of income per person depends solely on the___ rate of __ ___
   - most economies have ___ __ capital than the Golden Rule steady state
2. Ways to increase the saving rate:
   - increase __ ___ (reduce budget deficit)
   - tax incentives for __ __

Answer 36

SUMMARY:

1. Key results from Solow model with tech progress

• steady state growth rate of income per person depends solely on the exogenous rate of tech progress
• most economies have much less capital than the Golden Rule steady state

2. Ways to increase the saving rate
   - increase public saving (reduce budget deficit)
   tax incentives for private saving

Question 37

SUMMARY:

Productivity slowdown & “new economy”:

Early 1970s: fall in ____ growth in the U.K. and other countries.
Mid 1990s: productivity growth ____, probably because of advances in _ _
Late 2000s: growth ___ because of global ___ ___ and recession.

Answer 37

Productivity slowdown & “new economy”:

Early 1970s: fall in productivity growth in the U.K. and other countries.

Mid 1990s: productivity growth increased, probably because of advances in I.T.

Late 2000s: growth fell again because of global financial crisis and recession.

Question 38

SUMMARY:

4. Empirical studies
   Solow model explains ____ growth, ___ convergence

Cross-country variation in living standards due to differences in capital ____ and in __ ___

5. Endogenous growth theory:
   - models that examine the ____ of the rate of tech progress, which ___ takes as given
   - explain decisions that determine the creation of ‘_____’ through R&D

Answer 38

4. Empirical studies
   Solow model explains balanced growth, conditional convergence
   Cross-country variation in living standards due to differences in cap. accumulation and in production efficiency
5. Endogenous growth theory: models that
   examine the determinants of the rate of tech progress, which Solow takes as given
   explain decisions that determine the creation of knowledge through R&D