Seja A um conjunto qualquer. Indique a afirmativa verdadeira e a falsa:

Item 2 - Um ponto aderente é necessariamente um ponto de fronteira.

Quanto à desigualdade de Tchebyshev, supondo-se que uma variável aleatória tenha média e variância finita, ela assegura que a probabilidade:

Item 2 - da variável ultrapassar a média de um valor maior ou igual a n é menor ou igual ao inverso de n².

Sejam X, Y e Z variáveis aleatórias quaisquer. Então:

Item 1 - Var(2X + 4) = 4Var(X) + 16.

O Teorema Central do Limite (TCL), resultado maior dentre os teoremas da teoria da probabilidade, nas versões estudadas na graduação, estabelece condições que asseguram a convergência de somas de variáveis aleatórias, convenientemente padronizadas, à distribuição normal.

Item 0 - Esta convergência se dá em probabilidade, ou seja, é a mesma da Lei Fraca dos Grandes Números.

A respeito do modelo Keynesiano de equilíbrio agregativo a curto prazo, responda Verdadeiro ou Falso:

Item 1 - A política monetária não tem efeito sobre o nível de emprego no caso de os salários nominais serem flexíveis.

Public sectors, like attics, need occasional cleaning out. Employment in the public sector gets bloated because of patronage and poor accountability. Productivity can be raised sharply by reviewing labor requirements. The immediate savings - although not always as large as they would be in Brasil, for example, where public firm pay wages far above industry averages - generally are worthwhile in most developing economies. There is also ample room for privatization. Like fashions, ideological fads change, and one can benefit from the mood of the day to sell off steel mills, airlines, or telephone companies - none of which are considered to occupy the commanding heights of capitalism (p.24).

It can be understood in that same text that:

Item 4 - Retrenchment of public servants is strongly advocated.

A função utilidade de um trabalhador U(x,1), depende do consumo de um bem x e lazer 1. Este último é definido como a quantidade de horas disponíveis para o trabalho que o indivíduo não vende no mercado. Se um aumento da taxa de salário resulta em uma diminuição na quantidade de trabalho que ele está disposto a vender no mercado então:

Item 0 - lazer é um bem de Giffen.

The “Lucas critique” became the rallying cry for those young turks intent on destroying the consensus. Defenders of the consensus argued that users of macroeconometric models were already aware of the problem Lucas defined so forcefully, that the models were nonetheless informative if used with care and judgement, and that the Lucas critique was right in principle but not important in practice. These defenses were not heeded.

According to the paragraph above:

Item 1 - The Turks responded to Lucas’ rallying cry.

Sejam X, Y e Z variáveis aleatórias quaisquer. Então:

Item 3 - Cov(X,Y) = E(XY) - E(X).E(Y).

PART I

Rudiger Dornbusch, Policies to Move from Stabilization to Growth. Proceedings of the World Bank Annual Conference on Development Economics 1990, pages 19-48.

The typical stabilization program for an economy emerging from high inflation involves freezing wages and prices and making little fiscal adjustment. For the first month of two this program is successful, partly because expectations of a freeze will have led to prior price hikes. Soon the freeze wears off, however, and the deferred rise in public sector prices, the lifting of export taxes, and real appreciation combine to erode the budget position. Then, in phase two, policy-makers implement tight money. This gives an unsustainable program another few months of life, but of course it also increases public indebtedness sharply. Next, in phase three, the problems with the program become widely perceived, and debtors plead distress due to high real interest rates. When tight money goes, the house of cards collapses; the exchange rate collapses, inflation surges, and real interest rates turn very negative. Soon, another stabilization is under construction, ready for spring, tottering in the summer, and blown away by fall.

The important lesson to draw is this: tight money is not a substitute for a balanced budget. Real interest rates ultimately should be low, and the only way such a situation is sustainable is by basically sound fiscal and real exchange rate policies. Here we note that tight monetary policy is a signal of serious misalignment in the budget, the real exchange rate, or both. Realized real interest rates of 30 or 40 percent, in the presence of domestic debt, soon give rise to fiscal problems (p.26).

According to the same text:

Item 2 - Unorthodox anti-inflationary programs usually start in the spring fade way by fall.