Assinale C (certo) ou E (errado):

Item 4 - O produto !$ AB !$ dos operadores auto-adjuntos !$ A !$, !$ B !$ é auto-adjunto se, e somente se, !$ AB = BA !$.

A evolução da economia brasileira na década de 1950 e até meados dos anos 1960 foi marcada por modificações profundas na política cambial, e cada uma dessas alterações constitui um marco decisivo no processo de desenvolvimento econômico. Assim, é correto afirmar:

Item 1 - A Instrução 70 da SUMOC, de outubro de 1953, introduziu o monopólio cambial do Banco do Brasil e instituiu o regime de leilões de câmbio em bolsa de fundos públicos do país.

Há mais de uma década a economia brasileira vem se abrindo ao exterior. A abertura iniciou-se timidamente no final da década de 1980, transformou-se em estratégia oficial no início da década de 1990 e continua a ocorrer, com adaptações, até o presente. A natureza e os impactos da abertura nos permitem afirmar que:

Item 0 - Há uma transição da indústria brasileira para um novo regime de comércio. Ficaram para trás pelo menos quatro décadas de forte proteção que, embora favorecendo a diversificação da estrutura produtiva, gerou acentuadas distorções.

Assinale C (certo) ou E (errado):

Item 0 - Seja !$ A !$ uma matriz não-singular com autovalores !$ r_1 !$, !$ r_2 !$ e !$ r_3 !$, com !$ r_1 < r_2 < r_3 !$. Se !$ r_1 = 1 !$ e !$ traço (A) = det (A) = 6 !$, então !$ { \large r_2 \over r_1} -r_3 = -2 !$.

Considerando apenas dois produtos (x, y) e dois fatores (K, L), disponíveis em quantidades fixas, e utilizando-se a caixa de Edgeworth para analisar a eficiência na produção, pode-se afirmar:

Item 2 - A fronteira de possibilidades de produção não pode ser linear.

Em relação às distribuições de probabilidade contínuas:

Item 0 - Se X tem distribuição Normal !$ (μ, σ^2) !$, então a função densidade de probabilidade de X, f(x), atinge o seu valor máximo quando !$ x = μ !$ e nesse ponto !$ f(x) = { \large 1 \over σ \sqrt {2\pi}} !$.

É correto afirmar a respeito do modelo de regressão linear clássico multivariado: !$ Y = Xγ + ε !$, com n observações e k > 2 variáveis explicativas, incluindo-se o intercepto.

Item 2 - Quando os coeficientes !$ γ \ 's !$ estimados forem altamente significativos, individualmente, mas a estatística F e o R² indicarem que o modelo como um todo tem um baixo poder explicativo, pode-se desconfiar da presença de multicolinearidade.

BASED ON YOUR INTERPRETATION OF THE TEXT THAT FOLLOWS, DETERMINE IF EVERY STATEMENT IS RIGHT OR WRONG.

FIRST TEXT

At length, in 1776, our illustrious countryman, Adam Smith, published the “Wealth of Nations” – a work which has done for Political Economy what the Essay of Locke did for the philosophy of mind. In this work, the science was, for the first time, treated in its fullest extent; and the fundamental principles on which the production of wealth depends, established beyond the reach of cavil and dispute. In opposition to the Economists, Dr. Smith has shown that labor is the only source of wealth, and that the wish to augment our fortunes and to rise in the world – a wish that comes with us from the womb, and never leaves us till we go into the grave – is the cause of wealth being saved and accumulated: he has shown that labor is productive of wealth when employed in manufactures and commerce, as well as when it is employed in the cultivation of the land; he has traced the various means by which labor may be rendered most effective; and has given a most admirable analysis and exposition of the prodigious addition made to its powers by its division among different individuals and countries, and by the employment of accumulated wealth, or capital, in industrious undertakings. He has also shown, in opposition to the commonly received opinions of the merchants, politicians, and statesmen of his time, that wealth does not consist in the abundance of gold and silver, but enjoyments of human life; that it is in every case sound policy to leave individuals to pursue their own interest in their own way; that in prosecuting branches of industry advantageous to themselves, they necessarily prosecute such as are, at the same time, advantageous to the public; and that every regulation intended to force industry into particular channels, or to determine the species of commercial intercourse to be carried on between countries, is impolitic and pernicious – injurious to the rights of individuals – and adverse to the progress of real opulence and lasting prosperity.

J. R. McCulloch, on Adam Smith and Laissez-Faire from The Principles of Political Economy, 1830. Reprinted

in: Charles Dickens, Hard Times. W.W. Norton & Co, 1990: 318-319.

The text permits us to conclude that:

Item 0 - The individuals’ and society’s interests coincide.

BASED ON YOUR INTERPRETATION OF THE TEXT THAT FOLLOWS, DETERMINE IF EVERY STATEMENT IS RIGHT OR WRONG.

SECOND TEXT

Sir, - Allow a working man to thank you for your able article on “strikes” in The Times of yesterday, and to avoid waste of your valuable space, I will proceed at once to give you a case in point.

I was three months ago at work for a good master in a good shop, one among 200, and quite content, as was the majority, with the remuneration received – viz., 5s per day. About this time trade meetings were convened to discuss the propriety of demanding an advance of 10 per cent, or 5s. 6d. per day, and a few of our men attended. A deputation was appointed and awaited on our employer, with an intimation that, unless their demand was complied with, a “strike” would be the result. The master plainly stated that, having contracts on hand to a very great amount, the completion of which in a few months was insured by heavy penalties, he could not, without great pecuniary loss, - indeed, not without risk of failure, - at once grant their request, but that, if his men would remain at their work on the then terms, he would endeavor to make such arrangements as would enable him to meet their demand when a portion of his present contracts were worked out, - say, in five or six month; but, no; the deputation were not inclined to entertain anything so reasonable as this. Other meetings were called, at which some half-dozen “speakers” and “grand movers” used all their eloquence to prove employers tyrants and workmen slaves. The result was a “turn-out”; the great majority going out because they were afraid to be marked men, and because they had no confidence in each other, although they were convinced they were thereby doing their employer an injustice and running a risk of gaining a questionable advantage for themselves. After remaining idle some time the contracts pressed so much that our employer was compelled to succumb, and we all returned with the advance demanded. But mark the sequel. I and a great many others were in a short time discharged, and arrangements were made to extend the time for several large contracts, thereby dispensing with our services. Another result is, that the high rate of wages in town has drawn so many hands from the country, although there was no lack of workmen before the advance, that I have not been able since to procure a job at the new rate of wages; and, Sir, my case is the case of hundreds besides. To keep myself from starving, I offered to work in a large shop at the old rate of 5s., but as soon as this became known I was literally hunted out of the shop, and I am now, no doubt, what is so much dreaded by all my class – a marked man.

I am not allowed to work for what my own conviction tells me is a fair remuneration, and cannot procure employment at the advanced rate, as no master is inclined to set on more workmen, under present circumstances, than will just complete what he is compelled by heavy penalties to finish in a given time. Thus, Sir, you see that numbers may remain out of employment- a burden to themselves and to society – that those who are so lucky as to be retained may exult in having obtained a trifling advantage, which they are all along afraid (and nor without reason) of losing every day. At the same time it is certain that had the “supply and demand” been duly considered, a strike or a rise would not have taken place, to throw us into this uncomfortable and ruinous state of affairs.

Your willingness to give ear to a poor man’s grievances, and my cause to complain, must be my apology for troubling you with so long a letter.

I am, Sir, your obedient servant,

A Sufferer.

An Ostracized Workman to the Editor of the Times (Letter to The Times, October 10, 1853). Published in:

Charles Dickens, Hard Times. W.W. Norton & Co, 1990: 281-282.

According to the text the majority of the workers supported the strike because:

Item 3 - They trusted each other.

Assinale C (certo) ou E (errado):

Item 1 - !$ \int_0^4 { \large x^2 - 4 \over x + 2} dx = 0 !$.