# Questions tagged [cobb-douglas]

The Cobb-Douglas function is a commonly used functional form for a firm's production function or for consumers' utility, with a variety of convenient properties.

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### How can I obtain Leontief and Cobb-Douglas production function from CES function?

In most Microeconomics textbooks it is mentioned that the Constant Elasticity of Substitution (CES) production function, $$Q=\gamma[a K^{-\rho} +(1-a) L^{-\rho} ]^{-\frac{1}{\rho}}$$ (where the ...
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### Cobb-Douglas and Logarithm Utility Functions

Suppose I have a consumer with a utility function $U(x,y) = x^\alpha y ^{1-\alpha}$ where $a \in (0,1)$. Suppose this consumer has wealth $w$ and the prices for $x$ and $y$ are $p_x$ and $p_y$ ...
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### Is the Cobb-Douglas Utility Function Locally Non-Satiated at (0,0)?

My understanding of local non-satiation is that increasing your allocation of one good by a marginal amount increases utility. Suppose your utility takes the following form: $$U(x,y)=x^\alpha y^\beta$$...
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### Demand derived from Cobb-Douglas utility, interpretation, check

I derived demand, given a Cobb-Douglas utility function but I am not really sure if I did it correctly. I am especially struggling with the sum signs and the subscripts of $i$ & $j$. It would be ...
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### Indirect changes in Marshallian Demand

Suppose we have a Cobb-Douglas utility function: $$U(x,y)=x^\alpha y^\beta$$ and a budget constraint: $$p_{x}x+p_{y}y=I$$ where $\alpha+\beta=1$. It can be shown that the Marshallian demand for $x$ ...
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### 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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### Marginal product of capital net of depreciation

I am trying to understand how marginal product of capital net of depreciation is the following: Given that the production function is quite standard I understand the first term of the marginal ...
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### Stochastic frontier analysis in a unit out put production function. Taking logs is causing issues?

I wish to perform stochastic frontier analysis to calculate inefficiency of firms, but for a unit output isoquant ( imp) now y'=1, k'=k/y and l'=l/k. Now, these values lie between 0 and 1 (including 0)...
I have $U(x,y)=xy$, $p_1=4$ and $p_2=1$. Income is unknown. Where do I start?
Suppose that a competitive firm receives a price of $P$ for its output, and pays prices of w, r and v for its labor $(L)$, capital $(K)$ and natural resources $(R)$ inputs, respectively. The firm ...