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 4 - Sejam !$ u_1,u_2, v !$ vetores em V tais que !$ u_1.v=D_1,u_2.v=D_2 !$ e o vetor !$ u_1-u_2 !$ é paralelo ao vetor !$ v !$. Então, !$ \lVert u_1 - u_2 \lVert = \dfrac{|D_2-D_1|}{\lVert v \lVert} !$

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 3 - Up to this day, Keynes never succeeded in bringing Republicans to his side.

Assinale V (verdadeiro) ou F (falso):

Item 1 - Se !$ f(x,y) !$ é o menor valor entre !$ x !$ e !$ y !$, então !$ f(x,y)=\dfrac{x+y-|x-y|}{2} !$

Com relação aos conceitos de bem público e externalidades, é correto afirmar que:

Item 1 - Caso as preferências dos consumidores sejam quase lineares, as consequências distributivas da especificação dos direitos de propriedade são eliminadas.

A respeito da chamada "fase espontânea” de substituição de importações, é correta a afirmativa:

Item 0 - As duas guerras mundiais, especialmente a Segunda, estimularam a substituição de importações por causa das dificuldades impostas ao transporte marítimo.

O II Plano Nacional de Desenvolvimento (II PND), empreendido pelo governo Geisel, visava à reestruturação industrial como forma de superar os estrangulamentos de cadeias produtivas e a redução da dependência externa da economia. Sobre as políticas de desenvolvimento adotadas naquele período, é correto afirmar que:

Item 3 - O endividamento externo por parte de empresas públicas foi importante no financiamento do desequilíbrio do balanço de pagamentos.

Indique se as afirmativa é falsa ou verdadeira:

Item 0 - De acordo com os novos Keynesianos, a não neutralidade da moeda é uma conseqüência da rigidez dos salários reais.

Considere uma economia de trocas na qual dois agentes A e B possuem 5 unidades de cada um de dois bens x e y. Assim, existem 10 unidades de cada um dos bens x e y na economia. A função de utilidade do agente A é U(x, y) = x + 2y e a do agente B é V(x, y) = min{2x, y}.

Item 3 - Se os agentes puderem negociar livremente suas alocações iniciais, o agente B jamais aceitará uma troca que lhe deixe com menos de 4 unidades de x.

Considere o seguinte modelo de regressão linear clássico, relacionando as variáveis quantidade demandada (Q) e preço do produto (P). Admita que as duas variáveis sejam medidas em Reais, e que a estimação será efetuada por MQO (ln é logaritmo natural)

!$ ln=Qi=\beta_1+\beta_2 lnPi+u_i\,\,\,\,\,\,\, i=1,2,..., 100 !$

É correto afirmar que:

Item 4 - Se o coeficiente R² ajustado da regressão com a variável ln Y for maior do que o coeficiente R² ajustado da regressão original, então necessariamente, o coeficiente de ln Y é estatisticamente significante, ao nível de significância de 5%, em um teste bi-lateral.

Assinale V (verdadeiro) ou F (falso):

Item 4 - Os pontos de inflexão de !$ f(x)=\dfrac{x^3}{6}+2sen(x)-x\,cos(x) !$ no intervalo!$ [-2\pi,2\pi] !$ são !$ -\pi, 0,\pi !$.