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).

According to the text:

Item 2 - Land use in the tropics is a rough ordeal.

Uma firma oligopolística tem um custo variável médio igual a Cm = 20$, constante para um intervalo de produção entre 200 e 1.000 unidades. O valor do estoque de capital investidos na firma é igual a $100.000. Para determinar o seu preço de venda, esta firma fixa uma taxa de mark-up m sobre o custo variável médio da seguinte forma:

P = (1 + m)Cm. Desta maneira:

Item 3 - entre 200 e 1.000 unidades produzidas, uma mesma taxa de mark-up gera uma única taxa de retorno do capital.

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 1 - Se o desvio-padrão da variável X (sX ) é 1 e o desvio-padrão da variável Y (sY ) é 1 então o coeficiente de correlação entre X e Y, r, é 0,32.

Assinale a afirmação verdadeira e a falsa:

Item 3 - O conjunto das soluções de um sistema de equações lineares é um espaço vetorial.

Madame Pompidou economizou 10.000 francos e planeja gastar esse dinheiro com uma viagem ao Brasil. A utilidade da viagem é uma função do logaritmo de seus gastos no Brasil e é dada por U = ln (gastos). Nesta viagem existe uma probabilidade de 25% de que ela venha a perder 1.000 francos. Para evitar esse risco de perda de 1.000 francos, ela pode fazer um seguro pagando um prêmio de 250 francos. Pode-se afirmar que:

Item 1 - fazendo o seguro, a utilidade esperada da viagem será menor do que sem fazê-lo.

Assinale como verdadeira ou falsa a afirmativa abaixo:

Item 1 - !$ \int_{ - \infty}^{ \infty} x^2\,e^{-x} dx =3 !$

Sobre o modelo de crescimento de longo prazo de Solow, responda Verdadeiro ou Falso:

Item 0 - Quanto maior a taxa de poupança, maior a taxa de crescimento do produto no longo prazo.

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 0 - It is argued that farmers fall new forest for annual crop production while leaving previously cleared area to perennial crops.

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 4 - Crop retation is a standard practice in tropical agriculture, or so it is argued.

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 4 - Para cada y, a densidade condicional de x dado y é sempre a distribuição uniforme no intervalo [0,1].