Responda C ou E:

Item 2 - !$ \int\limits_{-\pi}^{\pi} |x| sen \ x \ dx = 0 !$

Considere a distribuição de probabilidade conjunta de (X,Y), de acordo com a tabela abaixo:

Pode-se afirmar que :

Item 3 - As variáveis aleatórias X e Y apresentam uma relação linear.

Classifique como certo ou errado a afirmativa abaixo:

Item 0 - A área compreendida entre a curva !$ x . y = 3 !$ e a reta !$ y = 4 - x !$ é menor do que 1.

Uma matriz A, quadrada de dimensão n é dita ortogonal quando A^tA= AA^t = I_n , onde o superescrito ^t denota transposição e I_n é a identidade de dimensão n. Considere uma matriz ortogonal A de ordem n. Classifique como certo ou errado s afirmação (sobre A) abaixo:

Item 4 - O produto interno de Ax por Ay é igual ao produto interno de x por y multiplicado pelo determinante de A.

A respeito das funções !$ f: \Re^2 \rightarrow \Re !$ definidas abaixo, responda C ou E.

Item 0 - O valor mínimo da função !$ f(x, y) = xy^2 !$ sujeito à restrição !$ |x| + 9|y| ≤ 9 !$ é inferior a -1 (menos um);

Based on your interpretation of the text you are about to read, determine whether each statement is right or wrong.

Part-I

“Trade, Jobs, and Wages” in Pop Internationalism, by Paul Krugman, Chapter 3, pp.-35-37.

The MIT Press, 1996.

The real wage of the average American worker more than doubled between the end of World War II and 1973. Since then, however, those wages have risen only 6 percent. Furthermore, only highly educated workers have seen their compensation rise; the real earnings of blue-collar workers have fallen in most years since 1973.

Why have wages stagnated? A consensus among business and political leaders attributes the problem in large part to the failure of the U.S. to compete effectively in an increasingly integrated world economy. This conventional wisdom holds that foreign competition has eroded the U.S. manufacturing base, washing out the high-paying jobs that a strong manufacturing sector provides. More broadly, the argument goes, the nation's real income has lagged as a result of the inability of many U.S. firms to sell in world markets. And because imports increasingly come from Third World countries with their huge reserves of unskilled labor, the heaviest burden of this foreign competition has ostensibly fallen on less educated American workers.

Many people find such a story extremely persuasive. It links America's undeniable economic difficulties to the obvious fact of global competition. In effect, the U.S. is (in the words of President Bill Clinton) "like a big corporation in the world economy" -- and, like many big corporations, it has stumbled in the face of new competitive challenges.

Persuasive though it may be, however, that story is untrue. A growing body of evidence contradicts the popular view that international competition is central to U.S. economic problems. In fact, international factors have played a surprisingly small role in the country's economic difficulties. The manufacturing sector has become a smaller part of the economy, but international trade is not the main cause of that shrinkage. The growth of real income has slowed almost entirely for domestic reasons. And -- contrary to what even most economists have believed -- recent analyses indicate that growing international trade does not bear significant responsibility even for the declining real wages of less educated U.S. workers.

The fraction of U.S. workers employed in manufacturing has been declining steadily since 1950. So has the share of U.S. output accounted for by value added in manufacturing. (Measurements of "value added" deduct from total sales the cost of raw materials and other inputs that a company buys from other firms.) In 1950 value added in the manufacturing sector accounted for 29.6 percent of gross domestic product (GDP) and 34.2 percent of employment; in 1970 the shares were 25.0 and 27.3 percent, respectively; by 1990 manufacturing had fallen to 18.4 percent of GDP and 17.4 percent of employment.

Before 1970 those who worried about this trend generally blamed it on automation -- that is, on rapid growth of productivity in manufacturing. Since then, it has become more common to blame deindustrialization on rising imports; indeed, from 1970 to 1990, imports rose from 11.4 to 38.2 percent of the manufacturing contribution to GDP.

Yet the fact that imports grew while industry shrank does not in itself demonstrate that international competition was responsible. During the same 20 years, manufacturing exports also rose dramatically, from 12.6 to 31.0 percent of value added. Many manufacturing firms may have laid of workers in the face of competition from abroad, but others have added workers to produce for expanding export markets.

To assess the overall impact of growing international trade on the size of the manufacturing sector, we need to estimate the net effect of this simultaneous growth of exports and imports. A dollar of exports adds a dollar to the sales of domestic manufacturers; a dollar of imports, to a first approximation, displaces a dollar of domestic sales. The net impact of trade on domestic manufacturing sales can therefore be measured simply by the manufacturing trade balance -- the difference between the total amount of manufactured goods that the U.S. exports and the amount that it imports. (in practice, a dollar of imports may displace slightly less than a dollar of domestic sales because the extra spending may come at the expense of services or other nonmanufacturing sales. The trade balance sets an upper bound on the net effect of trade on manufacturing.)

Item 0 - The dynamic forces of the American Firms were fundamental in maintaining the wage level and preserving jobs for highly skilled labor in the manufacturing sector.