e. A firm in a given industry has an incentive to use the new technology if and only if the expected profits from adopting this technology are positive. i- Derive the condition under which no firm has an incentive to adopt the new technology when n=0. ii-Derive the condition under which firm has an incentive to adopt the new technology when n=1. f- Is it possible that these two equilibrium conditions are satisfied simultaneously? Which parameter is critical for this to be the case? g- Provide an example of a modern technology whose implementation, or the lack of its implementation, could be explained by this model. 2- Consequence of an Immigration Boom Consider an economy that is initially in a balance growth path. Assume that there is an immigration boom starting in period to that last until period t₁, t₁ > to. As a consequence of the immigration boom, the growth rate of the population is temporarily higher, n' > n for to t₁. Analyze the short and long-run implications of the immigration boom for the dynamics of technology, capital and output per-capita. To answer this question, use a graphical analysis of the model of endogenous technological progress described by the following equations: À(t)/A(t) = 0(S¸L(t)/A(t))¹-¢ and k(t)/k(t) = sk(k(t)/A(t))ª¯¹(1 − SR)¹-a — (d+n).

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1 E, F

e. A firm in a given industry has an incentive to use the new technology if and only if the
expected profits from adopting this technology are positive.
i-Derive the condition under which no firm has an incentive to adopt the new
technology when n=0.
ii- Derive the condition under which firm has an incentive to adopt the new
technology when n=1.
f- Is it possible that these two equilibrium conditions are satisfied simultaneously? Which
parameter is critical for this to be the case?
g- Provide an example of a modern technology whose implementation, or the lack of its
implementation, could be explained by this model.
2- Consequence of an Immigration Boom
Consider an economy that is initially in a balance growth path. Assume that there is an
immigration boom starting in period to that last until period t₁, t₁ > to. As a consequence
of the immigration boom, the growth rate of the population is temporarily higher, n' > n
for to < t < t₁, and reverts back to the initial value n after that, i.e., for t > t₁. Analyze
the short and long-run implications of the immigration boom for the dynamics of
technology, capital and output per-capita.
To answer this question, use a graphical analysis of the model of endogenous technological
progress described by the following equations: À(t)/A(t) = 0(SrL(t)/A(t))¹- and
k(t)/k(t) = Sk(k(t)/A(t))ª−¹(1 − Sr)¹−¤ − (d + n).
Transcribed Image Text:e. A firm in a given industry has an incentive to use the new technology if and only if the expected profits from adopting this technology are positive. i-Derive the condition under which no firm has an incentive to adopt the new technology when n=0. ii- Derive the condition under which firm has an incentive to adopt the new technology when n=1. f- Is it possible that these two equilibrium conditions are satisfied simultaneously? Which parameter is critical for this to be the case? g- Provide an example of a modern technology whose implementation, or the lack of its implementation, could be explained by this model. 2- Consequence of an Immigration Boom Consider an economy that is initially in a balance growth path. Assume that there is an immigration boom starting in period to that last until period t₁, t₁ > to. As a consequence of the immigration boom, the growth rate of the population is temporarily higher, n' > n for to < t < t₁, and reverts back to the initial value n after that, i.e., for t > t₁. Analyze the short and long-run implications of the immigration boom for the dynamics of technology, capital and output per-capita. To answer this question, use a graphical analysis of the model of endogenous technological progress described by the following equations: À(t)/A(t) = 0(SrL(t)/A(t))¹- and k(t)/k(t) = Sk(k(t)/A(t))ª−¹(1 − Sr)¹−¤ − (d + n).
1- Complementarities
and Industrialization
Consider the following variation of the model of industrialization and coordination
failures by Murphy, Shleifer and Vishny (1989) discussed in lectures 8.
Consumers: The economy is populated by N consumers, each of them demanding N
different goods. Individuals expend a constant fraction, 1/N, of their income in each
of the N goods.
Traditional Firms: In each sector, there are a large number of firms that can produce
using a traditional technology. Using the traditional technology, 1 unit of labor can be
used to produce 1 unit of the good, qold-1. Notice that the price of the good could never
exceed the wage w (why?). Therefore, traditional firms will earn zero profits.
Modern Firms: In each sector, there is a potential firm that must decide whether to use a
modern technology. To use the modern technology a firm must purchase yF/N units of
the goods produced by each of the N industries (including itself) and hire (1-y)F units of
labor, so that the total fixed cost is equal to F. If the modern technology is adopted by a
given firms in a sector, this firm produces using a superior technology that transform 1
unit of labor into a units of the good, qmodern=a*1, where a>1.
Labor Market: Traditional and modern firms compete in the same labor market, and
therefore, they must pay the same wage. Wages paid by traditional and modern firms is
normalized to 1, wold- wmodern =1.
a. Suppose that the expected sales in each industry are equal to q. Derive an expression
for
TT, the expected profits of using the new technology as a function of F, q, a.
b. The income per capita in this economy, y, is the sum of per capita labor income as well
as the profit income from the firms adopting the modern technology. Derive an
expression for y in terms of n, à and where n is the fraction of sectors using the modern
technology.
c. The expected sales of each industry, q, are the sum of the demand from consumers and
the demand from modern firms. The demand from modern firms is equal to nyF, the total
purchases by firms adopting the new technology. Therefore, the expected sales of an
industry are
q=y+nyF
Using this equation and your answer to a-b, derive an equation relating y with n, a, y and
F. Solve for y in terms of n, a, y and F.
d. Combining a-c, derive an expression for a in terms of n, a, y and F.
Transcribed Image Text:1- Complementarities and Industrialization Consider the following variation of the model of industrialization and coordination failures by Murphy, Shleifer and Vishny (1989) discussed in lectures 8. Consumers: The economy is populated by N consumers, each of them demanding N different goods. Individuals expend a constant fraction, 1/N, of their income in each of the N goods. Traditional Firms: In each sector, there are a large number of firms that can produce using a traditional technology. Using the traditional technology, 1 unit of labor can be used to produce 1 unit of the good, qold-1. Notice that the price of the good could never exceed the wage w (why?). Therefore, traditional firms will earn zero profits. Modern Firms: In each sector, there is a potential firm that must decide whether to use a modern technology. To use the modern technology a firm must purchase yF/N units of the goods produced by each of the N industries (including itself) and hire (1-y)F units of labor, so that the total fixed cost is equal to F. If the modern technology is adopted by a given firms in a sector, this firm produces using a superior technology that transform 1 unit of labor into a units of the good, qmodern=a*1, where a>1. Labor Market: Traditional and modern firms compete in the same labor market, and therefore, they must pay the same wage. Wages paid by traditional and modern firms is normalized to 1, wold- wmodern =1. a. Suppose that the expected sales in each industry are equal to q. Derive an expression for TT, the expected profits of using the new technology as a function of F, q, a. b. The income per capita in this economy, y, is the sum of per capita labor income as well as the profit income from the firms adopting the modern technology. Derive an expression for y in terms of n, à and where n is the fraction of sectors using the modern technology. c. The expected sales of each industry, q, are the sum of the demand from consumers and the demand from modern firms. The demand from modern firms is equal to nyF, the total purchases by firms adopting the new technology. Therefore, the expected sales of an industry are q=y+nyF Using this equation and your answer to a-b, derive an equation relating y with n, a, y and F. Solve for y in terms of n, a, y and F. d. Combining a-c, derive an expression for a in terms of n, a, y and F.
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