Suponha uma economia caracterizada pelas seguintes relações:

C = 200 + 0,8Yd I = 300
T = 0,1Y M = 0,2Yd G = 240 X = 180
Em que:
Y = renda total; Yd = renda disponível após pagamento de impostos;
C = consumo, I = investimento, G = gasto do governo,
X = exportações, M = importações, T = imposto.

Indique se o item abaixo a respeito desta economia é certo ou errado:

Item 1 -

Suponha uma economia caracterizada pelas seguintes relações:

C = 200 + 0,8Yd I = 300
T = 0,1Y M = 0,2Yd G = 240 X = 180
Em que:
Y = renda total; Yd = renda disponível após pagamento de impostos;
C = consumo, I = investimento, G = gasto do governo,
X = exportações, M = importações, T = imposto.

Indique se o item abaixo a respeito desta economia é certo ou errado:

Item 3 - Um aumento do gasto governamental no valor de $92 levará a uma piora das contas do governo da ordem de $72 e uma piora do saldo comercial da ordem de $36.

De 50.000 válvulas fabricadas por uma companhia, retirou-se uma amostra aleatória de 400 válvulas e verificou-se que a vida média era de 800 horas, com um desvio-padrão de 100 horas.

Item 3 - O nível de confiança na estimação por intervalo (por exemplo 95%) significa que, construídos todos os intervalos possíveis, 95% dos casos conterão o parâmetro populacional.

Quanto ao modelo de regressão linear simples da forma

!$ Y_i=\alpha+bX_1+u_i !$

em que !$ Y !$ representa a produção de parafusos; !$ X !$ a quantidade de trabalho, medida em homens/hora de trabalho; e !$ u !$ a perturbação aleatória; podemos afirmar que:

Item 2 - O pressuposto de homocesticidade significa que cada perturbação tem a mesma variância cujo valor é desconhecido.

Com relação à teoria da Probabilidade pode-se afirmar que:

Item 1 - Se A, B e C são eventos quaisquer com P(C) !$ ≠ !$ 0, então: !$ P(A \cup B \mid C)=P(A \mid C)+P(B \mid C) !$

Indique se o item abaixo é certo ou errado, com base no texto a que se refere.

PART II

Cambridge versus Cambridge

In most universities today, economics is booming. To undergraduates and businesspersons it spells money-making; to graduate students it offers a lucrative slot in a bank or a confortable billet in a university; to governments it promises technical wheezes for balancing the books and boosting industries. The dismal science, it seems, can do no wrong.

Harvard and Cambridge are ideally placed to exploit this boom. They can both lay claim to some of the most illustrious names in the history of the subject. And they both boast well-connected alumni and high-powered students. But nobody inside the profession doubts that Harvard is having a far better boom than Cambridge. An Oxford professor admits that Harvard has probably the best economics department in the world. A Princeton professor ranks Cambridge along, say, Phennsylvania State University. cambridge graduates frequently go on to Harvard’s graduate school; the compliment is rarely returned. What is wrong with Cambridge?

The decline of its economics department dates from its defeat in one of the noisiest battles in post-war economics - the so-called Cambridge versus Cambridge controversy. In the early 1960s a group of Cambridge economists led by Joan Robinson mounted a furious assault on neoclassical orthodoxy. The Massashusetts Institute of Technology (MIT) took up the case for the defense (Harvard being a gentlemanly backwater).

At stake was nothing less than the soul of the subject. Robinson et al. argued that neoclassical economics was interested in the wrong thing (the optimal allocation of given resources) and based on a false assumption (that man is a rational “utility maximizer.”) In the Cambridge view, the hottest subjects were te accumulation of capital and the distribution of income. To add spice to the debate, the Cambridges disagreed about method and ideology. MIT preferred mathematics and markets; Cambridge favoured elegant prose and state intervention. To the likes of Robinson, the paddy fields of China were far preferable to the skyscrapers of Manhattan.

The world went the Massachusetts way. Neoclassical economics is now international orthodoxy; the Cambridge tradition is taken seriously only in East Anglia and the Italian provinces. Economics is an over more mathematical subject. And state planning is dead.

The Cambridge controbersy did more than marginalise the dominant faction in the Cambridgeshire fens. It also divided the faculty and politicised appointments. Some senior figures, like Frank Hahn and James Meade, did the unpatriotic thing and sided with the other Cambridge. The result was civil war. It was impossible to change the syllabus or appoint a lecturer without an ideological feud. The divided faculty made a number of light-weight appointments. It also lost a generation of stars. Just three of the dozen or so who fled - Amartya Sen, Christopher Bliss and Jim Mirrlees - would make the nucleus of a world-class department.

That was almost two decades ago. Why has Cambridge taken so long to repair the damage? Partly because the place is so enthralled by its glorious past. Naming a road ofter Sidgwick, a building after Marshall and a seminar room after Keynes is dangerously close to ancestor worship. But even more important than its over-developed sense of history is its underdeveloped appetite for competition. While Cambridge sank into faction fighting, Harvard challenged MIT for the position as the best department in the world. To understand their different fates, you need to examine their rival philosophies of academic life.

(The Economist, Dec. 1991 - Jan. 1992, p.43).

According to the text:

Item 2 - According to the Cambridge school, accumulation of capital and distribuition of income are what should matter most to economists.

Indique se o item abaixo é certo ou errado, com base no texto a que se refere.

PART III

THE MANDARIN REVOLUTION

When the Great War came, Keynes was not attracted to the trenches. He went to the Treasury, where his job was to take British earnings from trade, proceeds from loans floated in the United States and returns from securities conscripted and sold abroad and make them cover all possible overseas war purchases. And he helped the French and the Russians do the same. No magic was involved, as many have since suggested. Economic skill does not extend to getting very much for nothing. but an adept and resourceful mind was useful, and this Keynes had. In the course of time Keynes received a notice to report for military service. He sent it back. When the war was over, he was a natural choice for the British delegation to the Peace Conference. That, from the official view, was an appalling mistake.

The mood in Paris in the early month of 1919 was vengeful, myopic, indifferent to economic realities, and it horrified Keynes. So did his fellow civil servants. So did the politicians. In June he resigned and came home, and, in the next two month, he composed the greatest polemical document of modern times. It was against the reparations clauses of the Treaty and, as he saw it, the Carthaginian peace.

Europe would only punish itself by exacting, or seeking to exact, more from the Germans than they had the practical capacity to pay. Restraint by the victors was not a matter ot compassion but of elementary self-interest. The case was documented with figures and written with passion. In memorable passages Keynes gave his impressions of the men who were writing the peace. Woodrow Wilson he called “this blind and deaf Don Quixote.” Of Clemenceau he said: “He had one illusion - France; and one desillusion, mankind ...” On Lloyd George he was rather severe: “How can I convey to the reader, who does not know him, any just impression of this extraordinary figure of our time, this syren, this goat-footed bard, this half-human visitor to our age from the hag-ridden magic and enchanted woods of Celtic antiquity.”

Alas, no man is of perfect courage. Keynes deleted this passage on Lloyd George at the last moment.

The Economic Consequences of Peace was published before the end of 1919. The judgement of the British Establishment was rendered by The Times: “Mr. Keynes may be a clever economist. He may have been a useful Treasury official. But in writing this book, he has rendered the Allies a disservice for which their enemies will, doubtless, be grateful. “In time there would be a responsible view that Keynes went too far - that in calculating the limits on Germany’s ability to pay, he was excessively orthodox. Perhaps he contributed to the German’s sense of persecution and injustice that Hitler so effectively exploited. But the technique of The Times attack should also be noticed. It was not that the great men of the Treaty and the Establishment were suffering under the onslaught, although that, of course, was the real point. Rather, the criticism was causing rejoicing to the nation’s enemies. It is a device to which highly respectable men regularly resort. “Even if you are right, it is only the Communists who will be pleased.” (John Kenneth Galbraith, 1977. The Age of Uncertainty. Houghton Mifflin Company, Boston, p.198-200).

According to the text:

Item 4 - Keynes rendered a service to Hitler.

Marque como certo ou errado o item abaixo:

Item 4 - A série !$ \sum\limits^{∞}_{n-1}(1/n^2) !$ é convergente.

Assinale se o item é certo ou errado:

Item 3 - !$ \textstyle \lim_{x \rightarrow 0}(e^x+x)^{1/x}=1 !$.

Assinale o item certo ou errado:

Item 4 - !$ \int\limits_{3}^{∞} {\large{1 \over x^2}}dx=1/3 !$.

Assinale o item certo ou errado:

Item 3 - !$ \int\limits_{1}^{∞}{\large{1 \over x^3}}dx=1/2 !$.