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== 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.

Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)
Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)
14th Edition
ISBN:9781305506381
Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Chapter9: Applications Of Cost Theory
Section: Chapter Questions
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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.
Transcribed Image Text: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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