A respeito dos subconjuntos A, B, C definidos abaixo,no !$ \mathbb{R}^2 !$, responda V (verdadeiro) ou F (falso):

!$ A=\{(x,y) \in R^2:(x-1)^2+(y+1)^2 < \} !$

!$ B=\{(x,y) \in R^2 : xy \le 2\} !$

!$ C=\{(x,y) \in R^2:|x-2|+2|y+1| \le 2\} !$

Item 1 - !$ B\cap A = \varnothing !$

Indique se as afirmativa é falsa ou verdadeira:

Item 3 - A hipótese de expectativas racionais é o principal motivo de disputa entre os novos Keynesianos e os novos clássicos

Dadas a seguinte afirmativa sobre testes de hipóteses, é correto dizer que:

Item 2 - Quanto maior o p-valor, maior a credibilidade da hipótese alternativa.

THIRD TEXT

Keynes' largest influence came from a convoluted, badly organized and in places nearly incomprehensible tome published in 1936, during the depths of the Great Depression. It was called The General Theory of Employment, Interest and Money.

Keynes' basic idea was simple. In order to keep people fully employed, governments have to run deficits when the economy is slowing. That's because the private sector won't invest enough. As their markets become saturated, businesses reduce their investments, setting in motion a dangerous cycle: less investment, fewer jobs, less consumption and even less reason for business to invest. The economy may reach perfect balance, but at a cost of high unemployment and social misery. Better for governments to avoid the pain in the first place by taking up the slack.

The notion that government deficits are good has an odd ring these days. For most of the past two decades, America's biggest worry has been inflation brought by excessive demand. Inflation soared into double digits in the 1970s, budget deficits ballooned in the '80s, and now a Democratic President congratulates himself for a budget surplus that he wants to use to pay down the debt. But some 60 years ago, when 1 out of 4 adults couldn't find work, the problem was lack of demand.

Even then, Keynes had a hard sell. Most economists of the era rejected his idea and favored balanced budgets. Most politicians didn't understand his idea to begin with. In the 1932 presidential election, Franklin Roosevelt had blasted Herbert Hoover for running a deficit, and dutifully promised he would balance the budget if elected. Keynes' visit to the White House two years later to urge F.D.R. to do more deficit spending wasn't exactly a blazing success. "He left a whole rigmarole of figures," a bewildered F.D.R. complained to Labor Secretary Frances Perkins. "He must be a mathematician rather than a political economist." Keynes was equally underwhelmed, telling Perkins that he had "supposed the President was more literate economically speaking."

As the Depression wore on, Roosevelt tried public works, farm subsidies and other devices to restart the economy, but he never completely gave up trying to balance the budget. In 1938 the Depression deepened. Reluctantly, F.D.R. embraced the only new idea he hadn't yet tried, that of the bewildering British "mathematician." As the President explained in a fireside chat, "We suffer primarily from a failure of consumer demand because of a lack of buying power. "It was therefore up to the government to "create an economic upturn" by making "additions to the purchasing power of the nation."

Yet not until the U.S. entered World War II did F.D.R. try Keynes' idea on a scale necessary to pull the nation out of the doldrums - and Roosevelt, of course, had little choice. The big surprise was just how productive America could be when given the chance. Between 1939 and 1944 (the peak of wartime production), the nation's output almost doubled, and unemployment plummeted - from more than 17% to just over 1%.

Never before had an economic theory been so dramatically tested. Even granted the special circumstances of war mobilization, it seemed to work exactly as Keynes predicted. The grand experiment even won over many Republicans. America's Employment Act of 1946 - the year Keynes died - codified the new wisdom, making it "the continuing policy and responsibility of the Federal Government ... to promote maximum employment, production, and purchasing power."

Were Keynes alive today he would surely admire the vigor of the U.S. economy, but he would also notice that some 40% of the global economy is in recession and much of the rest is slowing down: Japan, flat on its back; Southeast Asia, far poorer than it was just two years ago; Brazil, teetering; Germany, burdened by double-digit unemployment and an economic slowdown; and declining prices worldwide for oil and raw materials.

In light of all this, Keynes would be mystified that the International Monetary Fund is requiring troubled Third World nations to raise taxes and slash spending, that "euro" membership demands budget austerity, and that a U.S. President wants to hold on to budget surpluses. You can bet Keynes wouldn't be silent. Dapper and distinguished as he was, he'd enter the fray with both fists and a mighty roar (Reich, R. B. “Joyn Maynard Keynes”. Time, Latin American Edition, March 29, 1999, p.76).

According to the text:

Item 2 - Before the War, Roosevelt sharply refused to pull the American economy out of its doldrums.

BASED ON YOUR INTERPRETATION OF THE TEXTS THAT FOLLOW, DETERMINE IF EACH STATEMENT IS TRUE OR FALSE.

FIRST TEXT

An Indian newsweekly featured Amartya Sen on the cover of a late October 1998 issue with the headline “The Prophet we ignore.” The scholar of poverty has spent decades devising novel approaches to solving India’s woes – and the government of his native country has often chosen to forgo his advice, the magazine contends.

Nevertheless, Sen’s work has not gone unnoticed. The Royal Swedish Academy of Sciences chose to award Sen a Nobel for his contributions to welfare economics, the study of the way societies make fair choices about allocating resources. His work deals with fundamental questions such as how income inequality should be measured and what the conditions that lead to famines are. The academy noted that Sen’s melding of tools from philosophy with economics “restored an ethical dimension to the discussion of vital economic problems.”

In May 1993 Sen wrote an article in Scientific American called “The Economics of Life and Death.” In the following excerpt Sen discusses the genesis of a famine:

Economic explanations of famine are often sought in measures of food production and availability. And public policy is frequently based on a country’s aggregate statistics of the amount of food available per person, an indicator made prominent by Thomas Robert Malthus in the early 1800s. Yet contrary to popular belief, famine can result even when that overall indicator is high. Reliance on such simple figures often creates a false sense of security and thus prevents governments from taking measures to avert famine.

A more adequate understanding of famine requires examining the channels through which food is acquired and distributed as well as studying the entitlement of different sections of society. Starvation occurs because a substantial proportion of the population loses the means of obtaining food. Such a loss can result from unemployment, from a fall in the purchasing power of wages or from a shift in the exchange rate between goods and services sold and food bought. Information about these factors and the other economic processes that influence a particular group’s ability to procure food should form the basis of policies designed to avoid famine and relieve hunger.

The Bangladesh famine of 1974 demonstrates the need for a broader appreciation of the factors leading to such a calamity. That year, the amount of food available per capita was high in Bangladesh: indeed, it was higher than in any other year between 1971 and 1976. But floods that occurred from late June until August interfered with rice transplantation ... and other agricultural activities in the northern district. Those disruptions, in turn, caused unemployment among rural laborers, who typically lead a hand-to-mouth existence. Bereft of wages, these workers could no longer buy much food and became victims of starvation...

[The situation was exacerbated by precautionary hoarding and speculative stockpiling, which caused prices to rise and hurt the food-buying ability of poor Bangladeshis.] When food prices peaked in October, so also did the death toll...

The occurrence of this famine illustrates how disastrous it can be to rely solely on food supply figures. Food is never shared equally by all people on the basis of total availability. In addition, private and commercial stocks of produce are offered to or withdrawn from the market in response to monetary incentives and expectation of price changes.

There are several ways to prevent famine. In Africa and Asia, growing more food would obviously help, not only because it would reduce the cost of food but also because it would add to the economic means of populations largely employed in producing food. Augmenting food production, however, is not the only answer. Indeed, given the variability of the weather, concentrating too much of a nation’s resources on growing more food can increase the population’s vulnerability to droughts and floods. In sub-Saharan Africa, in particular, there is a strong need for diversification of production, including the gradual expansion of manufacturing.

No matter how successful the expansion of production and diversification may be in many African and Asian countries, millions of people will continue to be devastated by floods, droughts and other disasters. Famine can be averted in these situations by increasing the purchasing power of the most affected groups – those with the least ability to obtain food. Public employment programs can rapidly provide an income. The newly hired laborers can then compete with others for a share of the total food supply. The creation of jobs at a wage does, of course, raise prices: rather than letting the destitute starve, such a practice escalates the total demand for food. That increase can actually be beneficial, because it brings about a reduction in consumption by other, less affected groups. This process distributes the shortage more equitably, and the sharing can deter famine. (Gibbs, W. W., Nemeck, S. and Stix, G. The 1998 Nobel Prizes in Sciences. Scientific American. January 1999, p 11).

According to the text:

Item 2 - Sen was referred to as “The Prophet We Ignore” on the cover of a magazine because his work is not well known in India.

Seja X₁, X₂ , ..., X_n uma amostra aleatória da densidade Normal(0,!$ \theta !$) e seja !$ \sum_{i=1}^n X^2_i !$. É correto afirmar que:

Item 2 - A variável aleatória !$ \sum_{i=1}^n X^2_i/\theta !$ tem distribuição qui-quadrado com n graus de liberdade.

SECOND TEXT

Kosovo has given the European Union a chance to forge elements of a new common foreign policy in the cauldron of war. Last week. More quietly and with far less sense of urgency, came a chance to do so in peace. At a landmark summit in Rio de Janeiro, 46 leaders from Europe and Latin America agreed on a broad range of political, cultural and trade initiatives to build a “strategic partnership” between the regions – and challenge the United States’ longstanding hegemony in South and Central America.

“The end of the North American century “trumpeted the daily Folha de São Paulo after the meeting. But even if words are followed by deeds, that proclamation seems premature. At present, E. U. trade with Latin America and the Caribbean is less than that with Switzerland. The U. S., on the other hand, claims that by 2010 it will export more to the region than to Japan and the E. U. combined.

Export markets are what Latin America needs most, but market access hasn’t been the E. U’s strong suit. The Old World has focused on development aid (Europe contributes mores than half of the region’s total aid receipts) and cultural links. Change will be grudging. Before the summit European governments squabbled over giving the European Commission a mandate for trade liberalization talks with the Mercosur bloc – Argentina, Brazil, Paraguay, Uruguay and associate member Chile. France in particular, as the prime beneficiary of the E. U’s lavish and protectionist agricultural policy, was loath to make any concessions ahead of the upcoming World Trade Organization negotiating round. The Commission did get its mandate, but the timetable for talks won’t be set until November and formal negotiations are unlikely to start before mid 2001.

“We had hoped the conference would have gone further,” said Prime Minister Antonio Guterres of Portugal, which along with Spain has been the principal advocate of greater trade with the region. Andrew Crawley, deputy-director of the Institute for European-Latin American Relations in Madrid, claims the Rio summit sill set the stage for a new trade era. “We essentially got Europe’s fast track,” he says, referring to the negotiating mandate denied to President Clinton by the U. S. Congress, thus complicating Washington’s efforts to secure a Free Trade Area of the Americas.

Even so, the E.U.’s protectionist farm tariffs are as much an obstacle to free trade as a fickle U. S. Congress. Latin America has greatly liberalized its trade regimes over the last decade, but Europe still discriminates against South American farm products, which make up 40% of Mercosur’s exports. Partly as a result, sales to Europe accounted for only 13.5% of Latin America’s exports in 1997, compared to 24% in 1990.

Brazilian President Fernando Cardoso has argued that if Europe can’t reform its agricultural regime, South America will gravitate more to the U. S. If that sparks a genuine competition between the U. S. and Europe to open their markets further to Latin American products, so much the better for South and Central America (Graff, J.L. “Europe Discovers America.” Time, July 12, 1999, p.25).

According to the text:

Item 1 - Latin American governments still face stiff domestic opposition to proposals to lower tariffs.

Sendo V o espaço vetorial de dimensão 3 sobre o corpo R, munido do produto interno Euclidiano!$ (.):x.y\equiv x_1 y_1 + x_2 y_2 + x_3 y_3; x,y \in V !$, define-se uma norma !$ \lVert .\lVert !$ pelo produto interno: !$ \lVert x \lVert = \sqrt{x.x,x \in V} !$. Assinale V (verdadeiro) ou F (falso):

Item 1 - Se todos os vetores de V são combinações lineares de 2k+1 vetores de V (para qualquer k, inteiro positivo) então 2k vetores neste espaço são LI;

Alguns mercados se caracterizam pela existência de informação assimétrica. É correto afirmar que:

Item 1 - Segundo Akerlof, no mercado de bens usados o resultado esperado é um preço médio uniforme para todos os bens vendidos, na ausência de garantias ou instrumentos similares.

BASED ON YOUR INTERPRETATION OF THE TEXTS THAT FOLLOW, DETERMINE IF EACH STATEMENT IS TRUE OR FALSE.

FIRST TEXT

An Indian newsweekly featured Amartya Sen on the cover of a late October 1998 issue with the headline “The Prophet we ignore.” The scholar of poverty has spent decades devising novel approaches to solving India’s woes – and the government of his native country has often chosen to forgo his advice, the magazine contends.

Nevertheless, Sen’s work has not gone unnoticed. The Royal Swedish Academy of Sciences chose to award Sen a Nobel for his contributions to welfare economics, the study of the way societies make fair choices about allocating resources. His work deals with fundamental questions such as how income inequality should be measured and what the conditions that lead to famines are. The academy noted that Sen’s melding of tools from philosophy with economics “restored an ethical dimension to the discussion of vital economic problems.”

In May 1993 Sen wrote an article in Scientific American called “The Economics of Life and Death.” In the following excerpt Sen discusses the genesis of a famine:

Economic explanations of famine are often sought in measures of food production and availability. And public policy is frequently based on a country’s aggregate statistics of the amount of food available per person, an indicator made prominent by Thomas Robert Malthus in the early 1800s. Yet contrary to popular belief, famine can result even when that overall indicator is high. Reliance on such simple figures often creates a false sense of security and thus prevents governments from taking measures to avert famine.

A more adequate understanding of famine requires examining the channels through which food is acquired and distributed as well as studying the entitlement of different sections of society. Starvation occurs because a substantial proportion of the population loses the means of obtaining food. Such a loss can result from unemployment, from a fall in the purchasing power of wages or from a shift in the exchange rate between goods and services sold and food bought. Information about these factors and the other economic processes that influence a particular group’s ability to procure food should form the basis of policies designed to avoid famine and relieve hunger.

The Bangladesh famine of 1974 demonstrates the need for a broader appreciation of the factors leading to such a calamity. That year, the amount of food available per capita was high in Bangladesh: indeed, it was higher than in any other year between 1971 and 1976. But floods that occurred from late June until August interfered with rice transplantation ... and other agricultural activities in the northern district. Those disruptions, in turn, caused unemployment among rural laborers, who typically lead a hand-to-mouth existence. Bereft of wages, these workers could no longer buy much food and became victims of starvation...

[The situation was exacerbated by precautionary hoarding and speculative stockpiling, which caused prices to rise and hurt the food-buying ability of poor Bangladeshis.] When food prices peaked in October, so also did the death toll...

The occurrence of this famine illustrates how disastrous it can be to rely solely on food supply figures. Food is never shared equally by all people on the basis of total availability. In addition, private and commercial stocks of produce are offered to or withdrawn from the market in response to monetary incentives and expectation of price changes.

There are several ways to prevent famine. In Africa and Asia, growing more food would obviously help, not only because it would reduce the cost of food but also because it would add to the economic means of populations largely employed in producing food. Augmenting food production, however, is not the only answer. Indeed, given the variability of the weather, concentrating too much of a nation’s resources on growing more food can increase the population’s vulnerability to droughts and floods. In sub-Saharan Africa, in particular, there is a strong need for diversification of production, including the gradual expansion of manufacturing.

No matter how successful the expansion of production and diversification may be in many African and Asian countries, millions of people will continue to be devastated by floods, droughts and other disasters. Famine can be averted in these situations by increasing the purchasing power of the most affected groups – those with the least ability to obtain food. Public employment programs can rapidly provide an income. The newly hired laborers can then compete with others for a share of the total food supply. The creation of jobs at a wage does, of course, raise prices: rather than letting the destitute starve, such a practice escalates the total demand for food. That increase can actually be beneficial, because it brings about a reduction in consumption by other, less affected groups. This process distributes the shortage more equitably, and the sharing can deter famine. (Gibbs, W. W., Nemeck, S. and Stix, G. The 1998 Nobel Prizes in Sciences. Scientific American. January 1999, p 11).

According to the text:

Item 2 - Welfare economics deals with the way societies decide about how to allocate their resources in a fair way.