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Analysis of Financial Time Series (Wiley Series in by Ruey S. Tsay

By Ruey S. Tsay

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From this figure we can see that neither an all-cabbage nor an all-potato diet will minimize cost, given the assumed prices. 425). 4 Monotonous in the extreme, the diet was nonetheless deemed nutritionally adequate and might have seemed luxurious to people caught in the Irish potato famine of the 1840s. The minimum-cost combination of cabbage and potatoes depends on the price of potatoes relative to that of cabbage. 5. 5. The calorie 4 The diet satisfies G. Stigler’s (1945) full list of nine nutritional requirements, not just the three discussed above.

1, we can see immediately that the protein constraint is satisfied wherever the calorie and vitamin A constraints are satisfied. In other words, the protein requirement will never be a binding constraint on the solution to this diet problem. Because the protein constraint is redundant, it can be henceforth ignored. 425). The calorie constraint is binding below this point; the vitamin A constraint is binding above it. 2. Any point on or above this curve satisfies all the nutrient requirements. This curve is an isoquant for feeding one man for one day.

Letting √ p denote plowing depth in centimeters, suppose the revenue derived from a field is R = 256 p, and the cost of √ 2 2 cultivating it is C = p . The profit derived from the field is π = R − C = 256 p − p . If you have studied calculus, √ you can see that the first and second derivatives are dπ/dp = 128/ p − 2p and d 2 π/dp 2 = −64p −3/2 − 2. Setting the first derivative equal to zero and solving for p, we find that π attains an extreme value when p = 16. Noting that the second derivative is negative, we conclude that this extreme value is a maximum.

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