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How does the limit of $U(x, y) = (ax^{-c} + by^{-c})^{-\frac{1}{c}}$ as c approaches 0 yield the Cobb-Douglas utlity function? [duplicate]

\begin{equation*} U(x, y) = (ax^{-c} + by^{-c})^{-\frac{1}{c}} \end{equation*} I ask this mainly because after logging both sides of the Utility equation (the first step to proving the assertion, I ...
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792 views

In the C.E.S. utility function do the parameters need to add up to unity to obtain the Cobb-Douglas utility function?

Consider the C.E.S. utility function $$U(x, y) = (ax^{-c} + by^{-c})^{-\frac{1}{c}}$$ Is it true that we must have $a+b=1$ in order to obtain a Cobb-Douglas utility function as $c\rightarrow 0$?
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Cobb-Douglas nested in CES model

Assume, using the following equation $Y=[((A_1L)^\alpha K^\beta)^\sigma+ (A_2X^\gamma)^\sigma]^{1/\sigma}$, we back out (obtain) the evolution of $A_1$ & $A_2$. Can we interpret $A_1$ as labour-...
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the difference between cobb-Douglass and leontief production technology [closed]

whatis the differences between cobb-Douglass and leontief production technology
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How can I prove $U(x) = [𝛼_1𝑥_1^𝜌+𝛼_2𝑥_2^𝜌]^{(1/𝜌)}$ is equal to Cobb-douglas Utility function when $𝜌\rightarrow0$ [closed]

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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Solving introductory microeconomics problems I have come across the following type of utility function: $$f(K,L) = (\alpha K^{\frac{\sigma - 1}{\sigma}} + (1 - \alpha) L^{\frac{\sigma - 1}{\sigma}})^{... 1answer 323 views What is the economic meaning of distribution parameter in a CES-production function? This is the production function (two input factors: x_1 and x_2)$$q=A[δx_1^ρ+(1-δ)x_2^ρ]^{\frac{1}{ρ}}  If distribution factor $δ$ is set to increase, what are the economic impacts on these ...
Consider a production process with two distinct capital types such that there is a capital aggregator. You could view $k_v$ as a more versatile capital (e.g. can be converted into many different ...