10Um trabalhador pode realizar dois níveis de esforço quando contratado por uma fábrica, alto ou baixo. A probabilidade de ocorrerem erros de produção é condicional ao nível de esforço do trabalhador. Se o trabalhador realiza o esforço alto a probabilidade de erro é 0,25 e se o trabalhador realiza o esforço baixo a probabilidade de erro se eleva para 0,75. A função de utilidade do trabalhador é dada por: !$ U(w,e)=100-\dfrac{10}{w}-e !$, em que !$ w !$ é o salário do trabalhador e e o nível de esforço, que assume o valor !$ e=2 !$, no caso do trabalhador realizar o esforço alto, e e=0no caso do trabalhador realizar esforço baixo. A única oportunidade de trabalho existente no mercado é dada por este posto na fábrica. O valor do produto depende de seu estado, ou seja, se o produto estiver perfeito o fabricante consegue vendê-lo a R$ 20,00 a unidade e se o produto apresentar algum defeito, devido aos erros de produção, o produto não é vendido e, portanto, seu valor é zero. Sabendo que o fabricante é neutro ao risco e maximiza o lucro esperado conhecendo as restrições do trabalhador, assinale falso ou verdadeiro:

Item 3 - O salário pago para que o trabalhador realize o esforço baixo é dado por !$ w=\dfrac{10}{100} !$.

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 3 -American officials recorded faithfully the date of the last earthquake;

Com relação às escolhas ótimas dos consumidores, constata-se que:

Item 2 - A negatividade do Efeito Substituição decorrediretamente do Axioma Forte da Preferência Revelada.

Considere a expansão de Taylor para a função !$ y=f(x) !$ em torno do ponto !$ x=0 !$ julgue a afirmativa:

Item 4 - Se !$ f(x)=\dfrac{1}{1-x} !$, para !$ -1 < x < 1 !$, então !$ P(x)=1+\dfrac{4}{1!}x+\dfrac{4.3}{2!}x^2+\dfrac{4.3.2}{3!}x^3+\dfrac{4.3.2.1}{4!}x^4 !$ é o polinômio de Taylor de grau 4 da função !$ f !$.

Charlemagne

Choosing new friends

The European Union is struggling to help Arab revolutionaries

Apr 7th 2011 | from the print edition

IN ITS desire to surround itself with a “ring of friends”, Europe never really asked if it was rubbing shoulders with the right sort of chums. From Algeria to Belarus, it has been encircled for the most part by police states. The Arab revolts are belatedly overturning old assumptions. Take France: the same Rafale fighter jets it tried to sell to Colonel Muammar Qaddafi are now being sent into action against him.

The European Union, too, is revising its “neighbourhood policy” in the hope that its claim to be promoting economic and political reformin return for greater integration with the EU will no longer seem such a mockery. For years European officials negotiated action plans with countries and wrote reports bemoaning their lack of democracy, yet kept paying autocrats billions of euros. Until recently the EU was negotiating “deep and comprehensive” free-trade agreements with just two neighbours: Ukraine, even though it has been backsliding on civil liberties, and Libya.

Europe’s neighbourhood policy is a sort of enlargement-lite. It offers countries on the EU’s rim the prospect of integration short of full membership—“everything but institutions” went the early slogan. It was born from a wish to reassure Ukraine that it would not be cut off after the admission of eight ex-communist states (plus Malta and Cyprus) to the EU in 2004. But it was soon expanded to include other new neighbours (Belarus and Moldova), older Mediterranean neighbours and, for good measure, the Caucasus (Armenia, Azerbaijan and Georgia).

It has not all been cynical. To the east, the reforming government of Moldova is being rewarded with generous aid. Meanwhile, the EU has frozen assets and restricted visas for Belarus’s leaders after they rigged elections and suppressed protests. But in the south the promotion of democracy and the rule of law has been a fiction. As one Eurocrat puts it, “they pretended to implement the human rights commitment. We pretended to open up our programmes and policies.”

Last month the European Commission rushed out a revised Mediterranean policy insisting it would not be “a passive spectator”. Next month it will publish a more comprehensive review, including eastern neighbours. For Stefan Fule, one of the commissioners in charge, the first paper tried to answer “the easy question”: how to help Tunisia and Egypt after they had got rid of their dictators. The second will try to answer the harder questions: what to do about countries that have liberalised only partly (eg, Morocco and Jordan) or hardly at all (eg, Syria and Algeria).

(...)

It is tempting to draw a parallel between the fall of the Berlin Wall in 1989 and the Arab spring of 2011. But one big difference is that the ex-communist countries had a burning wish to “return” to Europe. Arab neighbours have no such ambition. And eastern neighbours, though eligible in theory, know the EU is not ready to expand beyond the Balkans. Without the lure of membership, the EU struggles to find effective foreign-policy tools.

Where does Europe’s interest lie?

As with its past inability to shift Arab dictators, the EU will struggle to shape the outcome of the Arab spring. But it should try, not least because its actions in the south influence the east. The neighbourhood is where the EU has the greatest chance of having an impact. As a union, it may not have military power, but it has useful economic and political tools.

Some officials worry that the emphasis on promoting democracy will tie Europe’s hands. What if Arab countries do not democratise? What if the Arab spring turns to winter? Europe will still have interests to pursue in energy security, fighting terrorism, managing migration and more. Such concerns are legitimate. But the Arab spring highlights another vital interest. The old Arab allies are falling; given the stability the EU wants, democracy offers abetter hope of taking radical Islam.

Even without membership, the EU could offer reformers more in areas of particular interest like energy. Southern Europeans should allow freer trade: if they keep out Tunisian oranges, they must expect more Tunisian immigrants. The Union for the Mediterranean, a failed talking shop, needs to reform. Policies should be better tailored for each neighbour. Europe cannot change geography, so it will have to deal with all the countries on its rim, democratic or autocratic. But in its circle of neighbours, it must always demonstrate that its best friends are the democrats.

from the print edition | Europe

The text remarks that

According to the text, due to its “neighbourhood policy”, Europe

Item 4 - Expelled Malta and Cyprus from the EU in 2004.

Julgue o item:

Item 4 - Seja !$ f:R^2\rightarrow R\ !$ diferenciável, tal que !$ f \ne 0 !$ e !$ \dfrac{\delta f}{\delta x}+\dfrac{\delta f}{\delta y}=0 !$ Se !$ g(x,y)=\dfrac{x}{f(x,y) !$, então !$ f(\dfrac{\delta g}{\delta x} + \dfrac{\delta g}{\delta y})=2 !$.

Charlemagne

Choosing new friends

The European Union is struggling to help Arab revolutionaries

Apr 7th 2011 | from the print edition

IN ITS desire to surround itself with a “ring of friends”, Europe never really asked if it was rubbing shoulders with the right sort of chums. From Algeria to Belarus, it has been encircled for the most part by police states. The Arab revolts are belatedly overturning old assumptions. Take France: the same Rafale fighter jets it tried to sell to Colonel Muammar Qaddafi are now being sent into action against him.

The European Union, too, is revising its “neighbourhood policy” in the hope that its claim to be promoting economic and political reformin return for greater integration with the EU will no longer seem such a mockery. For years European officials negotiated action plans with countries and wrote reports bemoaning their lack of democracy, yet kept paying autocrats billions of euros. Until recently the EU was negotiating “deep and comprehensive” free-trade agreements with just two neighbours: Ukraine, even though it has been backsliding on civil liberties, and Libya.

Europe’s neighbourhood policy is a sort of enlargement-lite. It offers countries on the EU’s rim the prospect of integration short of full membership—“everything but institutions” went the early slogan. It was born from a wish to reassure Ukraine that it would not be cut off after the admission of eight ex-communist states (plus Malta and Cyprus) to the EU in 2004. But it was soon expanded to include other new neighbours (Belarus and Moldova), older Mediterranean neighbours and, for good measure, the Caucasus (Armenia, Azerbaijan and Georgia).

It has not all been cynical. To the east, the reforming government of Moldova is being rewarded with generous aid. Meanwhile, the EU has frozen assets and restricted visas for Belarus’s leaders after they rigged elections and suppressed protests. But in the south the promotion of democracy and the rule of law has been a fiction. As one Eurocrat puts it, “they pretended to implement the human rights commitment. We pretended to open up our programmes and policies.”

Last month the European Commission rushed out a revised Mediterranean policy insisting it would not be “a passive spectator”. Next month it will publish a more comprehensive review, including eastern neighbours. For Stefan Fule, one of the commissioners in charge, the first paper tried to answer “the easy question”: how to help Tunisia and Egypt after they had got rid of their dictators. The second will try to answer the harder questions: what to do about countries that have liberalised only partly (eg, Morocco and Jordan) or hardly at all (eg, Syria and Algeria).

(...)

It is tempting to draw a parallel between the fall of the Berlin Wall in 1989 and the Arab spring of 2011. But one big difference is that the ex-communist countries had a burning wish to “return” to Europe. Arab neighbours have no such ambition. And eastern neighbours, though eligible in theory, know the EU is not ready to expand beyond the Balkans. Without the lure of membership, the EU struggles to find effective foreign-policy tools.

Where does Europe’s interest lie?

As with its past inability to shift Arab dictators, the EU will struggle to shape the outcome of the Arab spring. But it should try, not least because its actions in the south influence the east. The neighbourhood is where the EU has the greatest chance of having an impact. As a union, it may not have military power, but it has useful economic and political tools.

Some officials worry that the emphasis on promoting democracy will tie Europe’s hands. What if Arab countries do not democratise? What if the Arab spring turns to winter? Europe will still have interests to pursue in energy security, fighting terrorism, managing migration and more. Such concerns are legitimate. But the Arab spring highlights another vital interest. The old Arab allies are falling; given the stability the EU wants, democracy offers abetter hope of taking radical Islam.

Even without membership, the EU could offer reformers more in areas of particular interest like energy. Southern Europeans should allow freer trade: if they keep out Tunisian oranges, they must expect more Tunisian immigrants. The Union for the Mediterranean, a failed talking shop, needs to reform. Policies should be better tailored for each neighbour. Europe cannot change geography, so it will have to deal with all the countries on its rim, democratic or autocratic. But in its circle of neighbours, it must always demonstrate that its best friends are the democrats.

from the print edition | Europe

The text remarks that

According to the text, due to its “neighbourhood policy”, Europe

Item 0 - Never complained about the undemocratic practices of somecountries on its rim;

Os acontecimentos econômicos e políticos de 1930, internacionais e domésticos, permitem que vários autores considerem este ano um marco na periodização da História Econômica do Brasil. Caracteriza (m) a década de 1930:

Item 2 - o crescimento industrial com baixas taxas nos três primeiros anos da década, mas que posteriormente acelerou-se, registrando-se taxas superiores a 10% em vários anos da mesma década.

Considere a expansão de Taylor para a função !$ y=f(x) !$ em torno do ponto !$ x=0 !$ julgue a afirmativa:

Item 2 - Seja !$ k !$ uma constante positiva. Se !$ f(x)=e^{kx} !$ e os coeficientes dos termos de 2ª e 3ª ordem são iguais, então !$ k=3 !$.