== Let f(x1, x2)=xx be a Cobb-Douglas production technology where a, ß > 0 and a +ẞ<1. (i) Show that the technology satisfies monotonicity, diminishing marginal product, diminishing TRS, and diminishing returns to scale. (ii) Which of these properties are invariant to arbitrary increasing transfor- mations of the technology? That is, which properties remain true for oof(x1, x2), where o can be any strictly increasing function? You can assume that is differentiable for convenience.

== Let f(x1, x2)=xx be a Cobb-Douglas production technology where a, ß > 0 and a +ẞ<1. (i) Show that the technology satisfies monotonicity, diminishing marginal product, diminishing TRS, and diminishing returns to scale. (ii) Which of these properties are invariant to arbitrary increasing transfor- mations of the technology? That is, which properties remain true for oof(x1, x2), where o can be any strictly increasing function? You can assume that is differentiable for convenience.

ENGR.ECONOMIC ANALYSIS

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Chapter1: Making Economics Decisions

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Question

Let f(x1,x2)=xxx be a Cobb-Douglas production technology where a, ẞ> 0
and a+B< 1.
(i) Show that the technology satisfies monotonicity, diminishing marginal
product, diminishing TRS, and diminishing returns to scale.
(ii) Which of these properties are invariant to arbitrary increasing transfor-
mations of the technology? That is, which properties remain true for
oof(x1, x2), where can be any strictly increasing function? You can
assume that is differentiable for convenience.
2. Solve for the short-run profit maximization problem for f(x1, x2) = 2x1 + x2
and f(x1, x2) = min{2x1, x2}, holding x2 at 2, and taking real factor prices wi
and w2 as given.

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