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1
Q

What is a good example to understand the essence of technological progress?

A

Consider what happens when you add new software to your computer. The capital and labor involved in production have not changed at all. But suddenly, with the newly installed software, the output that you can produce with this capital and labor has increased.

2
Q

In terms of our modeling of the production function, how is technological progress of this sort is captured?

A

As a change in value of the parameter A in the Cobb-Douglas production function, y = A k^(α) h^(1-α).
In other words, an improvement in technology will mean that given quantities of physical and human capital can be combined to produce more output than was previously possible.

3
Q

Why can changes in technology affect the process of economic growth?

A

Because technology changes the way in which factors of production are combined to produce output.

4
Q

What is a crucial aspect of technological change in terms of growth?

A

It allows an economy to transcend the limitations imposed by diminishing returns. technology. As long as the parameter A can get bigger, income per capita can continue to grow.

5
Q

What is required to create new technologies?

A

Creating new technologies requires investment. As in the case of capital creation, someone must use resources that could have been devoted to something else to create, refine, and put into practice a productive idea.

6
Q

What is most R&D driven by?

A

Profit seeking.

7
Q

What is the most important way in which government aids R&D?

A

By providing inventors with legal protection against the copying of their work, in the form of a patent.

8
Q

What is the difference between technology and conventional factors of production (like physical and human capital)?

A

Although conventional factors of production are objects (even human capital exists as neural pathways inside a person’s brain), technologies are essentially ideas lacking a concrete physical existence.

9
Q

What is one result of technology’s nonphysical nature?

A

Although conventional factors of production are rival in their use, technology is nonrival. One person’s use of a piece of technology in no way prevents others from using it just as effectively.

10
Q

What does the nonrival nature of technology mean when studying it?

A

We will have to focus much more on transfers among firms or countries than we would with the more traditional factors of production.

11
Q

If a country is poor because it lacks capital, then it can raise its income only by undertaking the costly investment of building new capital. Taking capital from a rich country and moving it to a poor country would make the poor country better off but the rich country worse off. How does this differ for technology?

A

If a country is poor because it lacks technologies, then technologies can be transferred from elsewhere without making the country from which they were taken any worse off.

12
Q

What is the dark side to the non-rivalry of technology?

A

The nonrivalry of ideas is often bound up with a low level of excludability. Ideas are non-excludable.

13
Q

What is excludability?

A

The degree to which an owner of something can prevent others from using it without permission.

14
Q

Which fact diminishes the incentives for creating technology?

A

Because of nonexcludability, the person who has created a new technology will not reap most of the benefits from its creation.

15
Q

What is shop floor R&D?

A

The great deal of effort spent by firms in tinkering with production processes to raise quality or lower costs.

16
Q

A firm will engage in R&D in the hope of inventing something: a new product or a new, more efficient way of producing some existing product. What’s the outcome if the firm succeeds.

A

It will be able to raise its profits. In the best case, its invention will give it a monopoly on the sale of some product, allowing it to earn supernormal profits. Alternatively, a new invention may give the firm a means of producing a product being sold by other firms, but to produce it at a lower price.

17
Q

What determines how willing a firm is to engage in R&D?

A

The larger the profits associated with having invented something, the more the firm is willing to spend in the effort to invent it.

18
Q

What is the first of several of the considerations affecting the amount of R&D that firms conduct?

A

How much of an advantage a new invention will confer. If other firms can easily copy the new technology and use it in their own production, then the firm that did the R&D will not have benefited from its spending. For many inventions, the key to maintaining competitive advantage comes from having an invention that can be patented and thus protected from imitation.

19
Q

What is the second of several of the considerations affecting the amount of R&D that firms conduct?

A

The firm will be influenced by the size of the market in which it can sell its product. The larger the available market, the greater the profits that the new invention will earn. Thus, by allowing inventors to sell their products in more countries, international economic integration increases the incentive to conduct R&D.

20
Q

What is the third of several of the considerations affecting the amount of R&D that firms conduct?

A

The firm will take into account how long the advantage conferred by a new invention will last. The longer the firm will have a competitive advantage as a result of its invention, the more money it will be willing to spend on R&D to achieve such an advantage.

21
Q

What is the fourth of several of the considerations affecting the amount of R&D that firms conduct?

A

The uncertainty surrounding the research process. Firms that are better able to share the risks of R&D investments, or economies where such risks are better shared, will be more likely to undertake such risky investments.

22
Q

What is the larger, more general cost of R&D?

A

Much of the time, the profits a firm earns as a result of creating a new technology come at the expense of other firms.

23
Q

What is creative destruction?

A

The process by which new inventions create profits for firms, these profits serve as the incentive to engage in research in the first place, and the new technologies so created (often, along with the firms that created them) are eventually supplanted by yet newer technologies.

24
Q

How does Schumpeter’s phrase about creative destruction nicely capture the double-edged nature of the process of technological advance?

A

Although we often celebrate the triumphs of new technologies, our enthusiasm ignores the dislocations suffered by firms and workers that the new technologies displace.

25
Q

What increases the rate of invention of new technologies.

A

Allowing an inventor to enjoy more of the benefits that result from his or her labor.

26
Q

What is a patent?

A

A grant made by a government that confers on the creator of an invention the sole right to make, use, and sell that invention for a set period of time, generally 20 years.

27
Q

Which types of items are patentable?

A

Patentable items include new products and processes, chemical compounds, ornamental designs, and even new breeds of plants. (Copyright, a related form of intellectual property protection, applies to writing, music, images, and software, among other things).

28
Q

To receive a patent, What must an inventor produce?

A

Something that is both novel and nonobvious. Further, one cannot patent laws of nature, physical phenomena, or abstract ideas. Inventors generally must file for a patent separately in every country where they want to protect their invention.

29
Q

What are 2 types of patent standards used worldwide?

A
  • First-to-file

- First-to-invent

30
Q

Describe the first-to-file patent system.

A

In a “first to file” system, the party that brings its application to the patent office first receives the patent.

31
Q

Describe the first-to-invent patent system.

A

In a “first to invent” system, the patent is granted to whoever can prove that they were the first to come up with the idea.

32
Q

What are the drawbacks of the first-to-invent system? (2)

A

It can involve complex investigation and litigation to establish who actually came up with an idea first. Further, a patent in the first to invent system is never fully secure because it is always possible that a previous inventor will show up and take it away. This makes it difficult for inventors to sell their patents and makes firms less confident in investing in patented technologies.

33
Q

What are the drawbacks of the first-to-file system?

A

Established firms with large legal departments have a significant advantage in filing patents relative to small startups. Further, under a first-to-file system, firms may be forced to file patents before their inventions are fully developed, running the risk that they will give away the thrust of their research without receiving a patent.

34
Q

What is the first problem associated with any patent system?

A

The first is simply the inefficiency associated with any monopoly. Once a firm has developed a particular technology, the firm will act as a monopolist, maximizing its revenue by charging a high price and, in doing so, limiting the benefits of the technology.

35
Q

What is the second problem associated with any patent system?

A

In some cases, the balance between encouraging new R&D, on the one hand, and holding back progress of other firms doing similar work, on the other, can go awry.

36
Q

What are patent trolls?

A

Companies that collect patents that they have no intention of using themselves, often buying them in bulk from firms that are going bankrupt. Patent trolls also often take out numerous patents related to technologies that have not yet been developed.

37
Q

What’s the difference between the motives of regular R&D companies and patent trolls?

A

Unlike firms that invent portfolios of useful technology that they can then license to others who want to use them, and thus publicize their patents and actively look for users, the goal of a patent troll is to wait until another firm independently develops and incorporates into its own products technology similar to a patented technology already in the troll’s portfolio. Once the target company has become locked in to using the new technology, the patent troll sues for infringement and threatens to shut down the operations of the target company, allowing the patent troll to extort a hefty payment.

38
Q

What is another strategy used by patent trolls?

A

To patent technologies that are already in wide use, having been viewed by other firms as being too obvious to patent.

39
Q

How does the existence of patent trolls holds back technological progress?

A

Potential inventors now fear that much of the value of their new idea could be siphoned off by patent trolls. New products might contain thousands of conceivably patentable components, making it impossible for innovators to be certain that a new product is immune to an infringement suit.

40
Q

Why are patents somtimes not the best way for firms to protect their innovations?

A

Because patenting an invention requires a detailed public description. Such a description may make it easy for competitors to come up with a close substitute—and once the patent has expired, others will be able to copy it exactly. Patents are also only useful if the legal sanctions against copying an invention can be enforced.

41
Q

What are 2 barriers to international technology transfer?

A
  • Appropriateness

- Tacit knowledge

42
Q

Technology is summarized by the parameter A, and if two countries had different technologies (i.e., different values of A), then clearly the country with a higher value of A had the better technology. Further, because a follower country would be better off using the leading country’s technology, what does the fact that the follower country does not immediately switch to the leading country’s value of A imply?

A

That there is some barrier, such as patent protection or secrecy, hindering the transfer of technology. It is also possible that technologies developed in the richest countries will not be “appropriate” to poorer countries. If a particular new technology is available to but not appropriate for a poor country, it is unlikely to be used there.

43
Q

As long as technologically advanced countries continue to do R&D, cutting-edge technology will advance. How will this technological advance will eventually bring productivity improvements even to a country far from the cutting edge?

A

Even if a technologically backward country does almost no R&D, it someday will be able to copy, and thus benefit from, the inventions of the most advanced countries.

44
Q

Consider the situation in which technological change is “neutral” in the sense that it does not apply differently to different mixes of factors of production. This would be the case if, for example, the production function was of the Cobb-Douglas form, y = Ak^α, and technological change took the form of an increase in the parameter A. How would this technological advance be represented graphically?

A

By a proportional shift upward in the production function. This shift would be just as significant—that is, just as large a percentage of the country’s income—for a poor country as for a rich country. Thus, if technological change took this neutral form, a poor country would benefit just as much as a rich country from a technological advance, even if the invention itself took place in the rich country.

Graphically, output per worker is raised at all levels of capital per worker

45
Q

Consider the alternative case is a “capital-biased” technological change—that is, a technological change that is useful only to capital-rich countries. How would this technological advance be represented graphically?

A

For a country with high capital per worker, capital-biased technological change will lead to an increase in output per worker. But a country with low capital per worker will experience little or no increase in output.

Graphically, output per worker is raised only at high levels of capital per worker, leaving the lower levels as they were.

46
Q

Why don’t R&D labs in developed countries create technologies that developing countries can use?

A

Developing countries typically enforce property rights to new technologies laxly. The inventor of a new technology that benefits producers in poor countries will find it almost impossible to get those producers to pay to use his or her invention and thus to earn a return on his or her investment. Such slack enforcement weakens the incentive to create technologies that are useful in poor countries.

47
Q

Describe how tacit knowledge can prevvent the adoption of technological advances in poor counrties.

A

An alternative explanation for why technology is not transferred from rich to poor countries is that poor countries are unable to use technology developed in rich countries. In other words, there are barriers to the transfer of technologies among countries.

48
Q

Why has experience with the transfer of technologies from rich to poor countries shown that there is much more to such transfer than simply carrying the blueprints for new production processes across national borders?

A

In addition to the codified knowledge represented by a set of blueprints, there also exists tacit knowledge in the minds of engineers—thousands of small details about the workings of a technology, learned over years of experience and transferred from person to person, not in written form but through informal training. Often the users of a technology are unaware themselves of the extent of this tacit knowledge, so the transfer of blueprints alone, without tacit knowledge, can (and frequently does) lead to expensive failures.

49
Q

In the cases in which tacit knowledge a barrier to international technology transfer, what underlies this difficulty?

A

In these cases, the crucial difference lay neither in the quality of physical capital nor in the formal education of workers in different countries, but in the practical experience of key engineers and managers.

50
Q

Why do nations rarely attempt to restrict the transfer of technology outside their borders for economic reasons these days (as opposed to national security reasons)?

A

To a large extent because firms that do R&D view their domestic competitors as just as much of a threat as their foreign rivals. Large multinational firms further reduce the relevance of national borders.

51
Q

Why aren’t all examples of technological progress are as simple as software?

A

New technology is often built into capital goods.

52
Q

What is embodied technological progress?

A

The linking of technology to specific pieces of capita (by contrast, software is an example of disembodied technological progress).

53
Q

What’s a main difference between embodied and disembodied technological progress?

A

If a technological change is embodied in capital, the technology is not upgraded until the capital good is replaced.

54
Q

How can we think of technological progress as being embodied in the human capital that students acquire during their schooling?

A

Education has both a general component (skills that are always applicable) and a specific component (e.g., skills for using current technology). As in the case of software, it is possible to upgrade the “wetware” inside a worker’s head to deal with a new technology, but such skill upgrades require new investment in human capital. And as workers get older, improving the technology that they can work with gets more difficult and less worthwhile because the working life over which older workers can use their new skills is shorter. Thus, these workers are less likely to be able to use the most advanced technologies.

55
Q

What does the fact that technology is embodied in physical and human capital broadly imply?

A

That we cannot so easily separate factor accumulation from technological progress. A country with a high investment rate will have, on average, capital goods that are younger (more recently produced). As a result, these capital goods will embody more recently developed technologies, and the country with high investment will be technologically more advanced than one with low investment. Similarly, a country with an older population will have a harder time staying on the technological cutting edge, for a large fraction of its workers will have been educated farther in the past.

56
Q

What does the embodiment of technology in capital goods also gives rise to?

A

The possibility of technological leapfrogging.

57
Q

What is technological leapfrogging?

A

The process by which technologically backward countries or firms jump ahead of the leaders.

58
Q

How can leapfrogging can also occur at the level of countries?

A

In countries where recently developed technology is incorporated into capital goods, firms may not find it worthwhile to scrap their existing capital to adopt the newest innovations. Countries that are farther behind, by contrast, will do so.

59
Q

The existence of tacit knowledge complicates technology transfer. Recognizing the importance of tacit knowledge also helps explain other phenomena. What’s the first such phenomena?

A

Tacit knowledge makes it much more difficult for technology to pass from developed to developing countries than within developed countries because much of the tacit knowledge is not specific to a given technology so much as to a given type of technology.

60
Q

The existence of tacit knowledge complicates technology transfer. Recognizing the importance of tacit knowledge also helps explain other phenomena. What’s the second such phenomena?

A

If tacit knowledge is important, the successful transfer of a single technology to a developing country may have a large externality effect because in the process, the stock of tacit knowledge will build up, allowing the easy transfer of further technologies.

61
Q

Upgrading our Solow model, it is convenient to define a new measure of productivity, which will simply be a transformation of our old measure, A. How is this new varible defined?

A

e = A^(1/1-α)
or alternatively
ê(1-α) = A

62
Q

Using our newly defined variable e, what is the new production function?

A

Y = ê(1-α) k^(α) L^(1-α)
More simply
Y = K^(α) (eL)^(1-α)

63
Q

How should we come to think about our new variable e in the upgraded production function?

A

With the equation in this form, we can think of the technology variable, e, as measuring the number of effective workers per actual worker. That is, increasing e and increasing L have the same effect on the total amount of output. The product of these two variables, eL, is the total number of effective workers in the economy.

64
Q

In Chapter 3 we transformed the production function by dividing both sides by L to put output and capital in per-worker terms. What should we do to parallel this with the introduction of our new variable e?

A

We divide both sides by eL to put output and capital in per-effective-worker terms. We define:
output per effective worker = y = Y/eL,
capital per effective worker = k = K/eL.

65
Q

What is the production function for output per worker given our new variable e if we define k = K/eL and y = Y/eL?

A

y = k^(α)

66
Q

To derive the equation for the change in the capital stock over time, we start with the definition of capital per effective worker and differentiate with respect to time. (Recall that we use a dot over a variable to indicate a derivative with respect to time). Derive this.

A

kdot = (Kdot/eL) - (L^ + ê)k
= γk^(α) - (ê + δ)k

The intuition for this equation is that ê, the growth in the number of effective workers per actual worker, is playing the same role that population growth played in the version of the Solow model studied in Chapter 4. Specifically, when ê is large, it dilutes the amount of capital per effective worker.

67
Q

What is the steady state capital per worker given our new variable e?

A

kss = (γ/(ê + δ))^(1/(1-α))

68
Q

What is the steady state output per worker given our new variable e?

A

yss = kss^(α) = (γ/(ê + δ))^(α/(1-α))

69
Q

What is consant in the steady state given technological progress?

A

Output per effectvie worker.

70
Q

What’s the equation defining Y^ in the steady state?

A
y^ = Y^ - ê - L^
= Y^ - ê 
since L^ = 0
y^ = 0 in the steady state therfore:
Y^ = ê
In other words, total output grows at the growth rate of e.
71
Q

To focus on the issue that are introduced once we start thinking about technology creation, we use a simplified version of the production function that we examined in previous chapters. Specifically, we ignore the roles of both physical and human capital, so the only input to production is labor. Ley LY be the number of workers who are involved in producing output. Similarly, let LA be the number of worker who are involved in creating new technologies. The total size of the labor force is L and because producing output and creating new technologies are the only activities that can occupy workers, which equation do we have?

A

L = LY + LA

subscript A)(subscript Y

72
Q

From L = LY + LA
(subscript A)(subscript Y)
how do we define the fraction of the labor force engaging in R&D mathematically?

A

γA = LA/L

Here “γA”(subscript A) means fraction of the labor force engaging in R&D not saving rate

73
Q

Given γA = LA/L, how can we express the number of worker involved in producing output?

A

LY = (1 - γA)L
Because we assume that workers are the only input into producing output - that is, we ignore the role of physical and human capital - the production function is simple. Total output is equal to the number of workers involved in producing output multiplied by the level of productivity:
Y = ALY
Combining the previous two equations, we can rewrite the production function as:
Y = A(1 - γA)L
or in per worker terms
y = A(1 - γA)

74
Q

What does the equation

y = A(1 - γA) say?

A

This equation says that the level of output per worker is higher when the level of productivity A is higher and, for a given value of A, when a smaller fraction of the labor force is involves in doing R&D.

75
Q

At first, it may seem paradoxical that having fewer people doing R&D would raise the amount of output produced. To resolve this apparent paradox, what should we note?

A

That if fewer people are doing R&D today, more people are producing output today - but if fewer people are doing R&D today, the level of productivity, and this output, will indeed be lower in the future.

76
Q

We now turn to the process of productivity growth, that is, the creation of new technologies. We assume that the rate of technological progress is a function of the number of workers who are devoting their time to R&D. Specifically, we model technological progress as being determined by which equation?

A

A^ = LA/μ
where A^ is the growth rate of productivity. On the right side of the equation, LA is the number of workers engaged in R&D, and μ is the “price of a new invention, measured in units of labor.

77
Q

In other words, what does “μ “ in A^ = LA/μ tell us?

A

How much labor is required to achieve a given rate of productivity growth. The larger μ is, the more labor must be devoted to R&D to achieve a given rate of technological progress.

78
Q

How can we rewrite the equation for technological progress A^ = LA/μ as?

A

A^ = (γA/μ)L

79
Q

To analyze the behavior of this model (A^ = (γA/μ)L), we begin with the case in which the fraction of the population engaged in R&D, γA, is constant.

A

Looking at the production function in per-worker terms, y = A(1 - γA), we see that as long as γA is constant, the level of output per worker, y, is just proportional to the level of technology, A. Therefore, the two variables must grow at the same rate, that is:
y^ = A^

80
Q

Combining y^ = A^ with the equation for the growth rate of technology, A^ = (γA/μ)L, what do we get?

A

y^ = A^ = A^ = (γA/μ)L

81
Q

What is the equation

y^ = A^ = (γA/μ)L saying?

A

This equation says that increases in the fraction of the population involved in R&D, γA, will increase the growth rate of output. It also says that growth will be higher if the cost of new inventions is lower, that is, if μ is smaller.

82
Q

Given
y^ = A^ = A^ = (γA/μ)L,
let’s now consider what will happen if γA suddenly increases.

A

From A^ = A^ = (γA/μ)L, we know that this increase in γA will increase the growth rates of both output, y, and productivity, A. But there is a second effect of increasing γA: Moving workers into the R&D sector will mean involving fewer workers in producing output. From the production function y = A(1 - γA), it is clear that output will thus fall.

83
Q

(Example of broken straight lines on the ratio scale with different slopes)
When γA rises, the growth rate of technology rises as well. This increasing steepness in the line representing A illustrates this rise. What happens to output?

A

The line representing y also becomes steeper, indicating that the growth rate of output per worker has increased. But at the moment γA increases, there is a jump downward in y, representing the loss of output from workers shifting away from production and into R&D. Eventually, output will regain and then pass the level it would have reached had there been no change in γA.
Thus, a country that devotes more of its resources to R&D will suffer a reduction in output in the short run but be better off in the long run.

84
Q

What is the conclusion from the example of broken straight lines on the ratio scale with different slopes?

A

That spending more on R&D lowers output in the short run but raises it in the long run, similar to our findings in chapter 3 about investment and physical capital.

85
Q

According to the Solow model, raising investment will lower the level of consumption in the short run because output that was previously consumed is devoted to building new capital. But in the long run, higher investment will lead to higher output and thus an increase in consumption. There is a crucial difference, however, between the Solow model’s findings with respect to physical capital investment and this chapter’s findings with respect to R&D spending. What is it?

A

In the model we consider in this chapter, an increase in R&D leads to a permanent increase in the growth rate of output. In the Solow model, an increase in investment leads to a higher steady-state level of output, so the investment increase’s effect on output growth is only transitory.

86
Q

Finally, this one-country model allows us to examine how population size relates to technology growth. An important implication of y^ = A^ = A^ = (γA/μ)Lis that the bigger the labor force, L, the larger the growth rate of technology, A^ (holding μ and γA constant). What is the logic for this result?

A

If two countries devote the same fraction of their labor force to inventing new technologies, then the country with more people will have more workers doing R&D. It stands to reason that more people doing R&D should be able to come up with more inventions, so the more populous country should have faster technological progress.

87
Q

What does the finding that more people doing R&D should be able to come up with more inventions, so the more populous country should have faster technological progress suggest?

A

Over time, countries with more people should have higher levels of technology, and thus should be richer, than countries with fewer people.

88
Q

Over time, countries with more people should have higher levels of technology, and thus should be richer, than countries with fewer people. Yet this prediction does not hold true in the data: There s no evidence that countries with more people either grow faster economically or are systematically richer than countries with few people. What is the explanation for this “failure” of the model?

A

That a country’s level of technology depends on R&D done not only within that country’s borders but also abroad. Technologies cross borders.

89
Q

Two-Country Model.
Our analysis of technology transfer stresses the interplay of which two different means by which a country can acquire new technology?

A
  • Innovation: the invention of a technology.

- Imitation, or copying a technology from elsewhere.

90
Q

Countries acquire new technologies either by creating them from scratch or by copying from abroad. Of course, technologies can be copied from abroad only if they have already been invented - a country cannot copy something that doesn’t exist. What does that say about the option of imitation?

A

Thus, the option of imitation is only open to the country that is the “technology follower”. The “technology leader” will have to acquire new technologies through invention. We assume that if a given technology already exists in the leading country, it will be less expensive for the follower country to imitate the technology than to reinvent the technology on its own.

91
Q

How does the value of A relate to technology in a two-country model?

A

In our model, the variable A represents the level of technology. Thus, the technological leader will have a higher value of A than the technology follower.

92
Q

In the case of the technology leader, the process of creating new technologies is the same one that we examined previously:
A1^ = (γA1/μi)L1.
What’s the only difference?

A

That we have now designated the cost of invention - which in the last section was simply called μ - as μi where i stands for invention.

93
Q

We now turn to Country 2. Call μc the cost of acquiring a new technology via imitation (the x is for copying). Our key assumption is that the cost of copying goes down as the technology gas between the follower and the leading country widens. There are several ways to justify this assumption. What’s the first?

A

Not all technologies are equally easy to imitate, and that the farther behind the leader a follower is, the more easy-to-imitate technologies there are available to copy.

94
Q

We now turn to Country 2. Call μc the cost of acquiring a new technology via imitation (the x is for copying). Our key assumption is that the cost of copying goes down as the technology gas between the follower and the leading country widens. There are several ways to justify this assumption. What’s the second?

A

What affects the cost of imitation is the time since a new technology was invented - thus, the farther the follower lags behind the leader, the older (and thus easier to copy) are the technologies that the follower wants to imitate.

95
Q

How do we mathematically formulate the assumption that what affects the cost of imitation is the time since a new technology was invented - thus, the farther the follower lags behind the leader, the older (and thus easier to copy) are the technologies that the follower wants to imitate.

A

We say that μc is a function of the ratio of technology in Country 1 to technology in Country 2, where the function that describes the relationship is denoted as c():
μc = c(A1/A2)

96
Q

We make three assumptions about this “cost of copying” function. What’s the first?

A

We assume that it is downward sloping - that the cost of copying falls as the technology gap between the two countries increases (i.e., as the ratio of technology in Country 1 to technology in Country 2 increases).

97
Q

We make three assumptions about this “cost of copying” function. What’s the second?

A

We assume that as the ratio A1/A2 goes to infinity, the cost of copying falls to 0. In other words, if the gap in technology were infinitely large, then imitation would be costless.

98
Q

We make three assumptions about this “cost of copying” function. What’s the third?

A

We assume that as the ratio of A1/A2 approaches 1, the cost of copying approaches the cost of invention.

99
Q

What does it mean for the cost of copying to approach the cost of invention as the ratio of A1/A2 approaches 1?

A

This means that if the follower country is very near the technology leader, it gets little benefit from copying technology rather than inventing its own. (The cost-of-copying function is not defined if A1/A2 is less than 1 because int his case, there would be nothing for Country 2 to copy.)

100
Q

Given a value of μc, the rate of technology growth in Country 2 is given by an equation in the same form as the growth rate f technology in Country 1:
A2^ = (γA2/μc)L2
We are now in a position to look at the steady state of the model. What is the key insight?

A

In the steady state, the two countries will grow at the same rate A^.

101
Q

In the steady state, the two countries will grow at the same rate A^. How does figure 8.3 show why this is this the case?

A

It graphs the growth rate in each country as a function of A1/A2, the ratio of technology in the leader country to technology in the follower country.

102
Q

In the steady state, the two countries will grow at the same rate A^. Figure 8.3 graphs the growth rate in each country as a function of A1/A2, the ratio of technology in the leader country to technology in the follower country. If this ratio were 1 - that is, if Country 2 had the same level of technology as Country 1 - then we would know that technology would be growing more quickly in Country 1 than in Country 2. Why?

A

In this case, the two countries would have the same cost of creating new technologies, whereas Country 1 has a higher value of γA than does Country 2. By contrast, if this ratio were infinite, then the cost of acquiring new technologies in Country 2 would be 0, and Country 2 would be experiencing faster technological growth than Country 1. Thus, at some ratio of A1/A2 between 1 and infinity, the two countries will have the same growth rates of A, and the ratio of the levels of technology in the two countries will remain constant. This will be the steady state.

103
Q

What’s an important note about the steady state technology ratio in the two-country model?

A

That this steady state is table: If the ratio A1/A2 starts off above the steady state, then A2 will grow faster than A1 and the ratio will fall. If the ratio starts off below the steady state, the opposite will occur.

104
Q

Write new equations given that, in a two-country model, A1^ = A2^

A

(γA1/μi)L1 = A1^ = A2^ = (γA2/μc)L2

105
Q

(γA1/μi)L1 = A1^ = A2^ = (γA2/μc)L2
Of these terms, the only one that can adjust is μc = (γA2/γA1)μi, where μc is the cost of copying. Thus, what do we know?

A

First, we know that in the steady state, the two countries must grow at the same rate. If Country 2 were growing faster than Country 1, then Country 2 would become the technology leader, an impossibility given that Country 2 spends less on RD than Country 1. If Country 1 were growing faster than Country 2, the technological gap between them would grow infinitely large, and the cost of copying for Country 2 would be 0 - in which case Country 2 would grow faster than Country 1. Given that the two countries grow at the same rate and that Country 2 devotes less effort to RD than Country 1, Country 2 must have a lower cost of technology acquisition than Country 1, and we can determine the specific cost by comparing the levels of RD effort in the two countries.

106
Q

Given that the two countries grow at the same rate and that Country 2 devotes less effort to RD than Country 1, Country 2 must have a lower cost of technology acquisition than Country 1, how can we determine the specific cost by comparing the levels of RD effort in the two countries?

A

For example, if Country 2 devotes half as much effort to RD as Country 1 (i.e., γA2./γA1 = 1/2), then the cost of technology copying in Country 2 must be half as large as the cost of invention in Country 1 (i.e., μc/μi = 1/2).
Once we know the value of μc in steady state, we can use the function that determines μc to figure out the steady-state value of A1/A2; that is, the relative level of technology in the two countries.

107
Q

Which interesting question arises as we examine the steady state of this model?

A

Is the technology-leading country necessarily better off than the follower? No

108
Q

Why isn’t the technology-leading country necessarily better off than the follower?

A

Although the technology leader is more productive, it also devotes a higher fraction of its labor force to RD and thus has fewer workers producing output.

109
Q

What will whether it is possible for the follower to have a higher level of income than the leader will depend on?

A

The cost of imitation relative to innovation.

110
Q

What happens if imitation is expensive?

A

Then the follower country either will have to devote almost as much of its labor force to RD as does the leader, in which case its level of technology will be close to the leader’s, or else will have a level of technology that is far behind that of the leader, if it devotes only a small part of its labor force to RD.

111
Q

What happens if imitation is inexpensive?

A

If imitation is inexpensive, then a follower country will have a level of productivity near that of the leader while devoting a much smaller share of its labor force to RD. In this case, it will be possible for the follower to have higher income than the leader.

112
Q

We can use this two-country model to think about the effects of changes in “policy”, here interpreted as changes in the parameter μ.These effects differ from what would be seen in the one-country model. Consider the following scenario. The two countries are in steady state, with γA1,< γA2. Suppose now that Country 2 raises its value of γA but that the new value is still below the value in Country 1. How does this change affect the steady-state levels of technology in the two countries?
Recall this graph has A^ on the y axis and A1/A2 on the x-axis. A1^ is a horizontal line. A2^ is an upward sloping curve (almost exponential). Where they cross (somewhere to the right of 1) is the steady state.

A

The curve representing A2 shifts upward. This shift means that for any given value of A1/A2 (and thus for any given cost of copying), Country 2 is growing faster than it would have grown before the increase in γA2. The new steady state occurs at a lower value of A1/A2; that is, a smaller gap in technology between the two countries.

113
Q

Figure 8.5 shows how the levels of A2 and y2 behave over time (ratio scale so that a variable growing at a constant rate appears as a straight line). Describe panel a).

A

Panel (a) shows that the growth rate of technology in Country 2 temporarily rises after γA2 increases (as seen by the increasing steepness o the line representing A2). Over time, however, as A2 moves closer to A1, technological growth in Country 2 returns to its old level.

114
Q

Why does technological growth in Country 2 return to its old level over time as A2 moves closer to A1?

A

The reason is that the steady-state growth rate of technology in Country 2 is determined by the growth rate of technology in Country 1, the technology leader.

115
Q

Figure 8.5 shows how the levels of A2 and y2 behave over time (ratio scale so that a variable growing at a constant rate appears as a straight line). Describe panel a).

A

Panel (b) shows that the immediate effect of an increase in γA2 is to reduce the level of output in Country 2, y2, because a smaller fraction of the labor force is involved in producing output. But the increase in RD effort leads to faster growth in A2 and thus in y2. Growth in Country 2 is temporarily high while the level of technology in Country 2 is moving toward the level in Country 1, but once the new steady-state ratio of A1/A2 has been reached, growth in Country 2 returns to its rate before the change in γA2.

116
Q

The finding that an increase in RD in the follower country causes a temporary increase in the growth rate of output is in stark contrast to the result of the one-country model, in which an increase in RD produced a permanent increase in growth. As far as the follower country is concerned, this model of growth through technology creation shares which property of the models of factor accumulation that we studies in Chapters 3, 4, and 6?

A

A change in “policy” (such as the investment rate, γ, in the Solow model, or the level of RD spending γA2, in this model) will lead to a transitory change in the growth rate of output. Eventually, the growth rate of output will return to its level preceding the change in policy, although the level of output will differ from what it would have been without the policy change.

117
Q

Why does the result that a change in RD spending will lead to only a transitory change in the growth rate of output not hold true for the leader country in this two-country model?

A

Because the leader country does not have the option to imitate technology from abroad, it is effectively in the same situation described in the one-country model: A change in RD will lead to a permanent change in its growth rate of output.

118
Q

The scenario of one country leading the world in every technology, with every other country playing catch-up, might have been nearly correct at some points in history. How has it changed since?

A

In the world today, technological superiority is much more diffuse, with many countries crowding the “technological frontier” and different countries leading in industries.

119
Q

The lack of a single “technology leader” in the world today does not mean that the model fails to serve a useful purpose. Rather, what does it suggest?

A

That we should focus on the model’s general lesson instead of the particular results.

120
Q

The general lesson of the model is that increased RD spending within a given country will have two effects. What’s the first?

A

It will change that country’s relative position in the world technological hierarchy and thus bring a period of transitory growth in both technology and income within the country.

121
Q

The general lesson of the model is that increased RD spending within a given country will have two effects. What’s the second?

A

Increased RD spending in a given country will lead to faster growth in technology for the world as a whole.

122
Q

Following Y^ = ê from the appendix to this chapter, total output grows at the growth rate of e. We can rewrite this equation in terms of our original measure of productivity,A, by starting with the definition of e, taking logs, and differentiating with respect to time, What do we get?

A

ê = (1/(1-α))A^
and thus
Y^ = (1/(1-α))A^

123
Q

yss = kss^(α) = (γ/(ê + δ))^(α/(1-α)), which shows the steady-state level of output per effective worker, says raising the growth rate of technology, ê, will lower the steady-state level of output per effective worker. At first, this result seems counter intuitive in that we would expect an increase in technological progress to raise the level of output. What is the resolution to this mystery?

A

That faster technological progress does raise the level of output per worker, even as it lowers the level of output per effective worker because it raises the number of effective workers per worker - that is, e.

124
Q

Raising the growth rate of technology, ê, will lower the steady-state level of output per effective worker. We see this effect by tracing through the chain of events that follows from an increase in the growth rate of technology, that is, in ê
Previously we derived the equation Y^ = y^ + ê which says that the growth rate of total output is the sum of the growth rate of output per effective worker and the growth rate of effective worker per actual worker. In the steady state, y^=0. Now consider an economy that is in steady state. Suppose that there is an increase in the growth rate of technology - that is, ê rises. Two forces will be acting on the growth rate of total output. What are they?

A

On the one hand, ê has risen. On the other hand, because the steady-state level of output per effective worker has fallen, y^ will become negative (having been 0 in the steady state).

125
Q

Suppose that there is an increase in the growth rate of technology - that is, ê rises. Two forces will be acting on the growth rate of total output. On the one hand, ê has risen. On the other hand, because the steady-state level of output per effective worker has fallen, y^ will become negative (having been 0 in the steady state). Which of these effects will dominate?

A

To answer this, rewrite kdot = (Kdot/eL) - (L^ + ê)k
= γk^(α) - (ê + δ)k by dividing both sides by k:

k^ = dotk/k = γk^(α-1) - (ê + δ)
In the steady state, k^ is 0. Let the increase in ê be denoted Δê. Because the right side of the preceding equation is equal to 0 before the increase in e, we that following the increase:
k^ = -Δê
The relationship between the growth rates of y and k can be derived by starting with the production function in per-effective worker terms, taking logs, and differentiating with respect to time. y^ = αk^. Combining the two preceding equations:
y^ = -αΔê
The growth rate of total output will thus be Y^ = y^ + ê + Δê = ê + (1-α)Δê
so the initial effect of a rise in the growth rate of technology by some amount Δê will be to raise the growth of total output by (1-α)Δê

126
Q

The initial effect of a rise in the growth rate of technology by some amount Δê will be to raise the growth of total output by (1-α)Δê. What happens over time however?

A

As the economy moves to a new steady state, y will fall and y^ will approach 0. In the new steady state, the growth rate of total output will have risen by the full amount Δê.

127
Q

Describe the graph of effective workers per actual worker, e (ratio scale) on the y-axis and time on the x-axis after an increase Δê.

A

Straight upward sloping line before increase, straight and steeper line after the increase.

128
Q

Describe the graph of output per effective workers, y (ratio scale) on the y-axis and time on the x-axis after an increase Δê.

A

Straight horizontal line before increase, downward sloping with upward curl after the increase until it converges to a new horizontal line (bow-shaped).

129
Q

Describe the graph of total output, Y (ratio scale) on the y-axis and time on the x-axis after an increase Δê.

A

Straight upward sloping line before increase, steeper line with an upward curl after the increase.

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