Tutorial 3
Chapter 3: The fundamentals of economic growth
Chapter 4: Explaining economic growth in the long run
Multiple choice questions
Question 1
Which ONE of the following describes the ‘Solow Residual’?
*a. The share of GDP growth that is NOT explained by the growth in labour hours
and capital.
Feedback: Correct.
Page reference: 75
b. The share of GDP growth that is NOT explained by technological progress.
Feedback: Incorrect.
Page reference: 75
c. The share of GDP growth NEITHER explained by the growth of inputs, NOR
technological progress.
Feedback: Incorrect.
Page reference: 75
d. The share of GDP that remains after deducting consumption, government spending,
and net exports.
Feedback: Incorrect. Note that this misses the point that the chapter is devoted to
economic growth!
Page reference: 75
Question 2
Assume two economies with identical rates of growth of labour (n) and labouraugmenting technological progress (a), the same depreciation rate of capital (δ), and
the identical underlying production function relating capital per effective unit of
labour (K/(AL)) to output per effective unit of labour (Y/(AL)). Suppose that the saving
ratio (s) in Economy I is LARGER than that of Economy II. According to the Solow
model of growth, which ONE of the following will be true?
a. The Solow residual will be larger in Economy II than in Economy I.
Feedback: Incorrect. They have the same a.
Page reference: 66; 75
b. Economy I will grow faster than Economy II in the steady state.
Feedback: Incorrect.
Page reference: 66; 75
*c. Economy I will have a higher output per unit effective labour than Economy II.
Feedback: Correct.
Page reference: 66; 75
d. Economy I will be dynamically more efficient than Economy II.
Feedback: Incorrect.
Page reference: 66; 75
Question 3
Total hours worked and population have [(A)_____] at roughly similar rates over time
in a group of advanced countries discussed in the text, because the average hours
worked per employed person has [(B)______] at the same time that the proportion of
the population working has [(C)_______].
a. (A) declined; (B) gone down ; (C) declined
Feedback: Incorrect.
Page reference: 76, 77
b. (A) grown; (B) increased; (C) remained roughly constant
Feedback: Incorrect.
Page reference: 76, 77
c. (A) grown; (B) increased; (C) gone down
Feedback: Incorrect.
Page reference: 76, 77
*d. (A) grown; (B) gone down; (C) increased
Feedback: Correct.
Page reference: 76, 77
Question 4
Starting in the steady state, which (exogenous) shock would result initially in a
situation in which the capital stock would happen to be above its new steady state
value?
a. An economy experiences the reduction of much of its capital stock through a war
due to negative net investment during the war years.
Feedback: Incorrect. Part of the story of the recovery of post-war Europe was
rebuilding its capital stock.
Page reference: 75, 76
b. The population growth rate drops through a reduction in fertility (n decreases).
Feedback: Incorrect. See Figure 3.15.
Page reference: 73
*c. A sudden increase in labour-augmenting technological progress (a increases).
Feedback: Correct. See Figure 3.15.
Page reference: 73
d. The saving rate increases.
Feedback: Incorrect. See Figure 3.15.
Page reference: 73
Question 5
Endogenous growth theory differs in what essential aspect from the Solow theory of
economic growth?
a. Endogenous growth theory is a monetary theory, whereas the Solow theory is a real
theory.
Feedback: Incorrect. In both theories, money does not play any role whatsoever.
Page reference: 94
b. Endogenous growth theory assumes diminishing returns to capital and the Solow
theory assumes constant returns.
Feedback: Incorrect. Exactly the opposite is true.
Page reference: 94
*c. In endogenous growth theory, economies with the same technology and saving
rate need not converge to the same steady state as in the Solow model.
Feedback: Correct.
Page reference: 94
d. All of the other answers given are correct.
Feedback: Incorrect. The only answer that is true is that in endogenous growth
theory, economies with the same technology and saving rate need not converge to the
same steady state as in the Solow model.
Page reference: 94
Question 6
The fundamental disincentive for private producers to produce costly new knowledge
is the ___________ characteristic of knowledge.
*a. Non-excludability.
Feedback: Correct. Without intellectual property rights that can be enforced,
knowledge producers cannot reap much, if any, of what they sow.
Page reference: 97
b. Rivalrous.
Feedback: Incorrect. It is hard to imagine how your learning what I have learned
would make me ‘unlearn’ the new knowledge.
Page reference: 97
c. Learning by doing.
Feedback: Incorrect. This is treated in the textbook as an issue of the diffusion of
existing knowledge, although it was originally conceived in the literature as an
explanation for the falling costs in the production of airplanes.
Page reference: 97
d. All of the other answers given are accurate.
Feedback: Incorrect. Non-excludability is the only right answer.
Page reference: 97
Open question: Exercise 4 and 5 from the book (Chapter 4).
4. Conditional convergence means that countries will converge in levels and growth
rates of GDP per capita only if they share values of other attributes which are
essential or influential for economic growth. In addition to climate and geographical
factors, these include education, physical infrastructure, social infrastructure, political
stability, and health. Thus, it is not surprising that Ghana and South Korea have had
very different growth experiences in the period 1960-2005, even if they started this
period with similar values of per capita GDP.
5. First, it is important to note that the production function Y  K  H  L1  is a
Cobb-Douglas production function in three arguments with constant returns to scale.
Divide both sides by labour L to obtain the intensive form y  k  h  . Let population
growth be n (you could also set it equal to zero). It follows that physical capital and
~
~
human capital per capita evolve according to k  sy   k and h  sy   h
respectively. Define the steady state to hold when per capita values of physical capital
and human capital are constant. This implies
sy
~
k  0  sy   k  k  ~

sy
~
h  0  sy   h  h  ~



 sy   sy 
So y   ~   ~  which can be solved as
   
 
 s  1  
y  ~
 
It is easy to see that per capita GDP is higher, the higher the saving rate and the lower
the depreciation rate (assumed equal for human and physical capital).
Yet there is no economic growth per capita in the steady state, and economic growth
occurs at rate n. To change this, it would be necessary to introduce total factor
productivity growth in the usual way.
Extra questions: Exercises 1, 6, 9, and 10 from the book (Chapter 4).
1. The Solow model assumes a common production technology and an exogenous and
common rate of technical progress, a. Under these conditions, the level of capita per
effective unit of labour is the only distinguishing feature between two economies –
capital accumulation is the sole means of achieving higher productivity relative to
other nations. In the diagram below, two nations 0 and 1 share the same constant
returns production function. When divided by AL, this yields the same intensive-form
production function: y = f(K/AL). The only factor distinguishing them is their levels
of capital per unit of effective labour. The Solow model predicts that both economies
will converge in level to GDP per capita y* with capital per capita k* and per capita
output growth in both will converge to a.
6. A Marshallian externality is a positive externality in which each individual agent
causing the externality is not aware of the effects of his or her actions, or the effect is
simply so small to be of any aggregate consequence. At the same time, if many or all
individuals perform the same action, there will be perceptible aggregate effects. For
example, individuals may reap private rewards from their education but may also
bestow advantages on others, even if these others are not educated themselves,
especially if a great deal of people are well-trained. (It is always good to have a welleducated workforce). Similarly, research and development may yield private benefits
for firms in the form of patentable inventions, yet there may be advantages to the
community at large in the form of research spillovers and networks. Network
externalities is another example of a Marshallian externality. If I buy a mobile
telephone, I improve not only my own communication capabilities, but I also improve
others’ ability to communicate with me.
Please note that we use the general definition of an externality, given in the chapter
and glossary. The definition of a Marshallian externality given in the glossary is
never discussed in the main text.
9. The distinction refers to public goods. Some public goods are non-excludable; by
legal construction, design or nature, it is impossible to restrict access to them. Public
resources such as parks, athletic facilities, public roads and beaches are examples, as
are national defense and radio transmissions. The fact that their access cannot be
restricted may or may not mean that they are rivalrous. Rival goods imply that there
may be congestion or dilution. Thus, some nonexcludable goods can well be rivalrous
– parks and highways, clean air, or public parking spaces. Some, however, are both
nonexcludable and non-rivalrous - national defense or knowledge are standard
examples. Some non-rivalrous goods are excludable, usually meaning that while the
marginal cost of extending the service is low or nonexistent, there exist legal means to
prevent “free-riding.”
10. Since the production of knowledge is a public good that is both non-rival and
nonexcludable, it may not be very attractive for private firms and individuals to
produce very much of it. To see why, consider James Watt, the inventor of the steam
engine, who truly revolutionized the progress of mankind with his invention but
received in his lifetime precious little for his trouble. Often inventive activity
produces spin-offs which are hardly related to the invention or discovery which is
actually sought.
Because knowledge is so essential to human progress, the state often encourages
inventive activity and basic research. Governments (and international agreements
among governments) offer patent protection for a limited time which grants exclusive
rights to some discoveries and inventions. Similarly, copyrights and trademarks offer
limited monopoly power to exploit so-called intellectual property commercially for
some period of time. Second, governments frequently subsidize basic research and
scientific development activities, either by providing competitive grant funds or by
financing research institutions such as laboratories and universities. Third,
governments can also offer financial incentives in the form of tax breaks for firms to
engage in research and development. They may also subsidize the education of
specialists in areas which are normally not particularly lucrative in the private sector.
Patents shield firms which innovate from competition by granting them monopoly
rights over the innovation for some period of time. In general, it is not a good idea to
restrict competition, so patent protection is granted only for a limited time. In the long
run these ideas become part of the public domain and can be produced by anyone
willing to pay the costs of production.