How can I prove $U(x) = [_1_1^+_2_2^]^{(1/)}$ is equal to Cobb-douglas Utility function when $\rightarrow0$

Question

This is the question, I have problem with part b, I don't know what function should I use to reach the result thanks in forward

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Possible duplicate of How can I obtain Leontief and Cobb-Douglas production function from CES function? — Herr K., Nov 25 '19 at 18:35

score 3 · Answer 1 · answered Nov 26 '19 at 19:04

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Hint: find $\ln(U(x))$ and then use L'Hopital's rule to find the limit as $\rho\rightarrow0$.

answered Nov 26 '19 at 19:04

Hal_Incandenza

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score 2 · Answer 2 · answered Nov 25 '19 at 12:22

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hint: you are supposed to show the utility function represents the same preferences not that the utility functions are exactly same. Recall that any monotonic transformations of function preserves the original order of preferences. So you only need to show that in the limit one function is monotonic transformation of the other.

answered Nov 25 '19 at 12:22

1muflon1

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well actually I tried to use ln to show it but I couldn't find the relation that's what I asked it here, I guess I asked the wrong question – Aisa.Imn Nov 25 '19 at 13:18

How can I prove $U(x) = [_1_1^+_2_2^]^{(1/)}$ is equal to Cobb-douglas Utility function when $\rightarrow0$

2 Answers2