Considere uma economia com função de produção dada por !$ Y=C\cdot K^\alpha\cdot L^{1-\alpha} !$,em que !$ Y !$ é o produto, !$ K !$ é o estoque de capital, !$ L !$ é o número de trabalhadores, !$ C !$ representa o nível tecnológico da economia e !$ \alpha !$ é um parâmetro. As firmas são perfeitamente competitivas e escolhem seus respectivos níveis de capital e trabalho tomando como dado o nível tecnológico !$ C !$. Este, porém, depende dos níveis agregados de !$ K !$ e !$ L !$ na economia, da seguinte forma: !$ C=A\cdot K^{1-\alpha}\cdot L^{\beta-1} !$,em que !$ A !$ é uma constante positiva e !$ \beta !$ é um parâmetro.

A equação de acumulação de capital na economia é !$ K=sY-dK !$, em que !$ s !$ é a taxa de poupança e !$ d !$ a taxa de depreciação do capital.

Com base nessas informações, indique se a seguinte afirmativa é Verdadeira (V) ou Falsa (F):

Item 2 - Se !$ \beta = \alpha !$ e !$ 0 < \alpha < 1 !$, a taxa de crescimento de !$ Y !$ depende da taxa de crescimento de !$ L !$.

Considere uma economia com função de produção dada por !$ Y=C\cdot K^\alpha\cdot L^{1-\alpha} !$,em que !$ Y !$ é o produto, !$ K !$ é o estoque de capital, !$ L !$ é o número de trabalhadores, !$ C !$ representa o nível tecnológico da economia e !$ \alpha !$ é um parâmetro. As firmas são perfeitamente competitivas e escolhem seus respectivos níveis de capital e trabalho tomando como dado o nível tecnológico !$ C !$. Este, porém, depende dos níveis agregados de !$ K !$ e !$ L !$ na economia, da seguinte forma: !$ C=A\cdot K^{1-\alpha}\cdot L^{\beta-1} !$,em que !$ A !$ é uma constante positiva e !$ \beta !$ é um parâmetro.

A equação de acumulação de capital na economia é !$ K=sY-dK !$, em que !$ s !$ é a taxa de poupança e !$ d !$ a taxa de depreciação do capital.

Com base nessas informações, indique se a seguinte afirmativa é Verdadeira (V) ou Falsa (F):

Item 4 - Se !$ \beta = 1 !$ e !$ 0 < \alpha < 1 !$, a taxa de crescimento de !$ Y !$ independe da taxa de crescimento de !$ L !$.

Based on your interpretation of the texts that follow, determine if each statement is true or false.

Text 1

Excerpts from:

Earthquake preparations

The curse of complacency

Americans are neither shaken nor stirred

Apr 7th 2011 | LOS ANGELES | from the print edition

SOONER or later, America will suffer an earthquake as devastating as the one that has wreaked havoc on northern Japan. It could happen next week, next year or next century; it has happened on numerous occasions in the past, and will happen again. The best that can be done is to prepare for the inevitable, adopting measures that will help emergency teams rescue the victims and allow the recovery to proceed as rapidly as possible. But the chaos that ensued in the aftermath of Hurricane Katrina shows how unprepared America can be for disasters.

Earthquakes about as powerful as the magnitude 9.0 quake that shattered the coastal towns of northern Japan before drowning them with a 30ft tsunami have struck along the Oregon coast at least seven times during the past 3,500 years. The last time was on January 26th 1700. The precise date is known thanks to records kept by Japanese officials, who witnessed the devastation caused by the subsequent tsunami when it inundated their shores.

Dia6America’snext mega-disaster is likely to be a smaller earthquake, but one much closer to a major conurbation than has occurred of late. That could happen almost anywhere—from Alaska and California in the west to Massachusetts, Missouri and South Carolina to the east. All have suffered considerable death tolls and damage as a result of large earthquakes in the past.,

(...)

Geologists in America fear that the lack of serious shaking in recent times has lulled those living in seismically active parts of the country intobelieving that their local building codes and disaster preparations are adequate. A computer simulation, called “ShakeOut”, undertaken by the United States Geological Survey in 2008—involving over 5,000 emergency responders and 5.5m citizens—indicated that a magnitude 7.8 earthquake unleashed on the lower end of the San Andreas Fault, some 40 miles east of Los Angeles, would cause 1,800 deaths, $113 billion in damage and nearly $70 billion in business interruption.

Partly in response to ShakeOut, the National Earthquake Hazards Reduction Programme (set up by Congress in 1977 to mitigate the effects of earthquakes) commissioned a body of scientists in 2008 to draw up a 20-year action plan for reducing the hazard of earthquakes in America. The National Research Council (NRC), which was charged with developing the plan, reported last week on the 18 tasks it reckons are crucial if the country’s earthquake resilience is to be improved. Implementing the plan is expected to cost $6.8 billion over 20 years. That seems cheap. According to the California Emergency Management Agency, every dollar spent on preparation saves four dollars on reconstruction after a disaster.

One of the NRC’s most important (and certainly most expensive) recommendations is a national earthquake warning system like the one Japan installed in 2007. Thanks to its network of 1,000 seismic stations around the country, Japanese authorities had nearly a minute to halt bullet trains in northern Japan (none was derailed) and warn local employers to stop lifts and switch off dangerous machinery. The seismographs detect the Dia7burst of “P-waves” emitted by an earthquake that travel at twice the speed of the more destructive “S-waves”, giving valuable seconds of warning depending on the distance from the epicentre.

But seismologists fear a national earthquake warning system is unlikely to be built in America because of complacency and the spending squeeze. Finding just the $50m needed to complete California’s pilot network is proving hard enough—and Californians need no reminding how valuable such a system would be. Unlike the wary Japanese, when it comes to earthquake mitigation the majority of Americans remain unshaken and unstirred.

from the print edition | United States

The text remarks that:

Item 0 - The National Research Council (NRC) had the task of developing a plan for reducing the hazards of earthquakes in America;

Julgue a afirmativa:

Item 3 - Sejam !$ P=(3,-1,2) !$ e !$ Q=(4,-2,-1) !$. A equação do plano que passa por !$ P !$ e é perpendicular ao vetor !$ \vec{PQ} !$ é !$ x-y-3z+2=0 !$.

Based on your interpretation of the texts that follow, determine if each statement is true or false.

Text 1

Excerpts from:

Earthquake preparations

The curse of complacency

Americans are neither shaken nor stirred

Apr 7th 2011 | LOS ANGELES | from the print edition

SOONER or later, America will suffer an earthquake as devastating as the one that has wreaked havoc on northern Japan. It could happen next week, next year or next century; it has happened on numerous occasions in the past, and will happen again. The best that can be done is to prepare for the inevitable, adopting measures that will help emergency teams rescue the victims and allow the recovery to proceed as rapidly as possible. But the chaos that ensued in the aftermath of Hurricane Katrina shows how unprepared America can be for disasters.

Earthquakes about as powerful as the magnitude 9.0 quake that shattered the coastal towns of northern Japan before drowning them with a 30ft tsunami have struck along the Oregon coast at least seven times during the past 3,500 years. The last time was on January 26th 1700. The precise date is known thanks to records kept by Japanese officials, who witnessed the devastation caused by the subsequent tsunami when it inundated their shores.

Dia6America’snext mega-disaster is likely to be a smaller earthquake, but one much closer to a major conurbation than has occurred of late. That could happen almost anywhere—from Alaska and California in the west to Massachusetts, Missouri and South Carolina to the east. All have suffered considerable death tolls and damage as a result of large earthquakes in the past.,

(...)

Geologists in America fear that the lack of serious shaking in recent times has lulled those living in seismically active parts of the country intobelieving that their local building codes and disaster preparations are adequate. A computer simulation, called “ShakeOut”, undertaken by the United States Geological Survey in 2008—involving over 5,000 emergency responders and 5.5m citizens—indicated that a magnitude 7.8 earthquake unleashed on the lower end of the San Andreas Fault, some 40 miles east of Los Angeles, would cause 1,800 deaths, $113 billion in damage and nearly $70 billion in business interruption.

Partly in response to ShakeOut, the National Earthquake Hazards Reduction Programme (set up by Congress in 1977 to mitigate the effects of earthquakes) commissioned a body of scientists in 2008 to draw up a 20-year action plan for reducing the hazard of earthquakes in America. The National Research Council (NRC), which was charged with developing the plan, reported last week on the 18 tasks it reckons are crucial if the country’s earthquake resilience is to be improved. Implementing the plan is expected to cost $6.8 billion over 20 years. That seems cheap. According to the California Emergency Management Agency, every dollar spent on preparation saves four dollars on reconstruction after a disaster.

One of the NRC’s most important (and certainly most expensive) recommendations is a national earthquake warning system like the one Japan installed in 2007. Thanks to its network of 1,000 seismic stations around the country, Japanese authorities had nearly a minute to halt bullet trains in northern Japan (none was derailed) and warn local employers to stop lifts and switch off dangerous machinery. The seismographs detect the Dia7burst of “P-waves” emitted by an earthquake that travel at twice the speed of the more destructive “S-waves”, giving valuable seconds of warning depending on the distance from the epicentre.

But seismologists fear a national earthquake warning system is unlikely to be built in America because of complacency and the spending squeeze. Finding just the $50m needed to complete California’s pilot network is proving hard enough—and Californians need no reminding how valuable such a system would be. Unlike the wary Japanese, when it comes to earthquake mitigation the majority of Americans remain unshaken and unstirred.

from the print edition | United States

The text implies that:

Item 2 - Oregon has been the only place in America affected by powerful earthquakes so far;

Considere uma função de produção representada por !$ Y=K^\alpha(NA)^{1-\alpha} !$, em que !$ Y !$ é o produto, !$ K !$ é o estoque de capital, !$ N !$ é o número de trabalhadores, !$ A !$ é a tecnologia e !$ 0 < \alpha < 1 !$. Defina !$ W !$ como o salário por trabalhador e !$ r !$ como a taxa de juros. Com base no modelo de Solow, avalie se a afirmativa abaixo é Verdadeira (V) ou Falsa (F):

Item 4 - A razão capital-produto cresce à mesma taxa que o progresso técnico.

Based on your interpretation of the texts that follow, determine if each statement is true or false.

Text 1

Excerpts from:

Earthquake preparations

The curse of complacency

Americans are neither shaken nor stirred

Apr 7th 2011 | LOS ANGELES | from the print edition

SOONER or later, America will suffer an earthquake as devastating as the one that has wreaked havoc on northern Japan. It could happen next week, next year or next century; it has happened on numerous occasions in the past, and will happen again. The best that can be done is to prepare for the inevitable, adopting measures that will help emergency teams rescue the victims and allow the recovery to proceed as rapidly as possible. But the chaos that ensued in the aftermath of Hurricane Katrina shows how unprepared America can be for disasters.

Earthquakes about as powerful as the magnitude 9.0 quake that shattered the coastal towns of northern Japan before drowning them with a 30ft tsunami have struck along the Oregon coast at least seven times during the past 3,500 years. The last time was on January 26th 1700. The precise date is known thanks to records kept by Japanese officials, who witnessed the devastation caused by the subsequent tsunami when it inundated their shores.

Dia6America’snext mega-disaster is likely to be a smaller earthquake, but one much closer to a major conurbation than has occurred of late. That could happen almost anywhere—from Alaska and California in the west to Massachusetts, Missouri and South Carolina to the east. All have suffered considerable death tolls and damage as a result of large earthquakes in the past.,

(...)

Geologists in America fear that the lack of serious shaking in recent times has lulled those living in seismically active parts of the country intobelieving that their local building codes and disaster preparations are adequate. A computer simulation, called “ShakeOut”, undertaken by the United States Geological Survey in 2008—involving over 5,000 emergency responders and 5.5m citizens—indicated that a magnitude 7.8 earthquake unleashed on the lower end of the San Andreas Fault, some 40 miles east of Los Angeles, would cause 1,800 deaths, $113 billion in damage and nearly $70 billion in business interruption.

Partly in response to ShakeOut, the National Earthquake Hazards Reduction Programme (set up by Congress in 1977 to mitigate the effects of earthquakes) commissioned a body of scientists in 2008 to draw up a 20-year action plan for reducing the hazard of earthquakes in America. The National Research Council (NRC), which was charged with developing the plan, reported last week on the 18 tasks it reckons are crucial if the country’s earthquake resilience is to be improved. Implementing the plan is expected to cost $6.8 billion over 20 years. That seems cheap. According to the California Emergency Management Agency, every dollar spent on preparation saves four dollars on reconstruction after a disaster.

One of the NRC’s most important (and certainly most expensive) recommendations is a national earthquake warning system like the one Japan installed in 2007. Thanks to its network of 1,000 seismic stations around the country, Japanese authorities had nearly a minute to halt bullet trains in northern Japan (none was derailed) and warn local employers to stop lifts and switch off dangerous machinery. The seismographs detect the Dia7burst of “P-waves” emitted by an earthquake that travel at twice the speed of the more destructive “S-waves”, giving valuable seconds of warning depending on the distance from the epicentre.

But seismologists fear a national earthquake warning system is unlikely to be built in America because of complacency and the spending squeeze. Finding just the $50m needed to complete California’s pilot network is proving hard enough—and Californians need no reminding how valuable such a system would be. Unlike the wary Japanese, when it comes to earthquake mitigation the majority of Americans remain unshaken and unstirred.

from the print edition | United States

According to the text:

Item 1 - We have no idea how many times powerful earthquakes have struck along the Oregon coast during the past 35 centuries;

Classifique a afirmativa a seguir como Verdadeira (V) ou Falsa (F):

Item 2 - Suponha que: (i) o investimento em uma unidade de capital no ano T gere um fluxo de lucros esperados a partir de T+1; (ii) o lucro real esperado por unidade de capital seja constante e igual a $20 por ano; (iii) a taxa de depreciação do capital seja de 5% ao ano, a partir de T+2; (iv) a taxa real de juros seja constante e igual a 5% ao ano; (v) o custo de aquisição de uma unidade de capital no ano T seja $215. Logo, conclui-se que o investimento em capital no ano T não vale a pena.