Suponha que se tenha usado dados de 12 plantações para estimar a função de produção:

Y = 2,10 + 0,32 X
(0,3) (0,08)

em que Y é medido em toneladas de café por hectare de X em centenas de quilo de fertilizante por hectare. O erro-padrão das estimativas s_b0 e s_b1 são dados entre parênteses.

Pode-se afirmar que:

Item 3 - Se o café custar $15 por tonelada e o fertilizante $3 por 100 quilos, não vale a pena ao fazendeiro usar mais fertilizante para aumentar a produção, pois o custo marginal excede a receita marginal.

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 text:

Item 1 - Tight money is a complement, not a substitute for tight budget.

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).

Still according to the same text:

Item 4 - Fiscal policy is more effective than monetary policy.

O vetor aleatório (X,Y) toma valores com probabilidade 1 no quadrado [0,1]x[0,1] do R² , segundo a seguinte densidade:

!$ f( x,y) = { \begin{cases} 4\,\,se\,( x \le 1/2\,e\,y \le x)\,\,\,ou\,\,( x \ge 1/2\,\,e\,y \ge x)\\0\,\,nos\,outros\,pontos\,do\,quadrado \end{cases}} !$

pode-se afirmar que:

Item 0 - E(X) = E(Y) e Var(X) = Var(Y).

The breakdown of the Phillips curve and the prescience of Friedman and Phelps made macroeconomics ready for Robert Lucas’ (1976) more comprehensive attack on the consensus view. Lucas contended that many of the empirical relations that make up the large-scale macroeconometric models were no better founded on microeconomic principles than was the Phillips curve. In particular, the decisions that determine most macroeconomic variables, such as consumption and investment, depend crucially on expectations of the future course of the economy. Macroeconometric models treated expectations in a cavalier way, most often resorting to plausible but arbitrary proxies. Lucas pointed out that most policy interventions change the way individuals form expectations about the future. Yet the proxies for expectations used in the macroeconometric models failed to take account of this change in expectation formation. Lucas concluded therefore, that these models should not be used to evaluate the impact of alternative policies.

According to the paragraph above:

Item 0 - Macroeconometric models treated expectations in a haughty way.

Dada uma população de 10 elementos, se dela se tirar, com reposição, todas as amostras aleatórias de tamanho três possíveis, pode-se afirmar que:

Item 4 - A média amostral é um estimador eficiente da média da população.

Classifique como Verdadeira ou Falsa a afirmativa abaixo:

Item 0- Se numa economia o investimento é superior à poupança doméstica, o saldo total do balanço de pagamentos é necessariamente negativo.

O vetor aleatório (X,Y) toma valores com probabilidade 1 no quadrado [0,1]x[0,1] do R² , segundo a seguinte densidade:

!$ f( x,y) = { \begin{cases} 4\,\,se\,( x \le 1/2\,e\,y \le x)\,\,\,ou\,\,( x \ge 1/2\,\,e\,y \ge x)\\0\,\,nos\,outros\,pontos\,do\,quadrado \end{cases}} !$

pode-se afirmar que:

Item 3 - P[1/4 < Y < 3/4] = P[X < 1/2].

PART II

Pichon, F. S.A. Vosti, and J. Witcover, “Determinants of Land-Use Practices in the Humid Tropics: Farm-Level Evidence from Ecuador.” The International Food Policy Research Institute, Washington, DC, 1992.

Farmers in the humid tropics, it is often suggested, move through roughly the same progression of land-use patterns over time, constrained by a “straitjacket” of ecological determinism. Occupation of forest lands necessarily requires some initial deforestation to establish ownership; using the land for annual food crops meets immediate food needs. As soils deplete, the argument runs, farmers must clear additinal forest for annual crop production, and dedicate previously cleared lands to perennial crops. As soil nutrient levels continue to fall on all cropped land, farmers shift both perennial and annual crops onto more recently deforested lands, leaving initially deforested acres to pasture and/or fallow. In this way, farmers, driven by environmental constraints and survival needs, and the absence of affordable and/or available technology, supposedly have little choice but to encroach more and more on forested land (p.10).

Still according to the same text:

Item 3 - Farmers depend on perennial food crops for nutrition.

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 2 - Se as variáveis aleatórias, atendendo às hipóteses do TCL, tem a mesma média !$ \mu !$ e variância !$ \sigma^2 !$ , o teorema garante que a soma das n primeiras, subtraídas de !$ n\,\mu !$, e dividida por !$ n\,\sigma !$, converge para uma distribuição normal com média 0 e variância 1 (N(0,1)).