# 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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### Convexity/Uniqueness Marshallian demand Cobb Douglas case

Hi guys I have been asked to prove the 3 properties od the Walrasian/Marshallian demand function in the case of a Cobb-Douglas utility function.However, I am not sure how to prove that if the ...
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### Are prices part of total factor productivity?

I am trying to understand how production is related to income/profit and where do prices enter. Suppose there is a single firm with a Cobb-Douglas production technology: $$Y=AK^{\alpha}L^{\beta}$$ ...
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### How was the Cobb Douglas function derived?

In economics and econometrics, the Cobb–Douglas production function is a particular functional form of the production function, widely used to represent the technological relationship between the ...
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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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### Capital in terms of labor

I have a question that asks to find $\frac{\partial K}{\partial L}$ from $Q=cL^aK^b$, when $Q$ and $c$ are constants. It lists 4 answer choices but I’m just not sure how to approach it. Implicit ...
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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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### Are Cobb-Douglas preferences homothetic?

Our lecture defined a preference to be homothetic, if the following is true: $$(x_1, x_2) \thicksim (y_1, y_2) \Leftrightarrow (kx_1, kx_2) \thicksim (ky_1, ky_2)$$ Cobb-Douglas preferences can be ...
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### Derivation of demand function

Hello. I'm graduate student in Japan. This time, what I want to ask is how to solve the profit maximization problem using the image production function and derive the demand function. This ...
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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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### How to Calculate the productivity multiplier?

Given a Cobb Douglas $Y_t = A (K_t^\alpha L_t^{1-\alpha})$ $K_{t+1} = sY_t + (1-\delta) K_t$ How do we get the multiplier on productivity to be equal to $\frac{1}{1-\alpha}$? I understand ...
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### Optimizing Cobbs-Douglas given output

I am trying to find L$^*$ and K$^*$ (Labour and Capital respectively) given the following: Q = $K^{1/4}$ $L^{3/4}$ where Q = 120, w=$24, and r=$128 (Not sure if you need w and r) I know that if I ...
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### Given Cobb-Douglas production functions for 2 factories (same owner), how will the owner produce $y$?

So my question is this: A company owns two factories, A and B, each with the following production functions: $f_A(x_1,x_2)=x_1^{\alpha}x_2^{1-\alpha}$ $f_B(x_1,x_2)=x_1^{\beta}x_2^{1-\beta}$ Now ...
Given $$U(x,y)= x^\alpha y^{1-\alpha}$$ $\alpha \in (0,1)$, are Cobb Douglas goods (here $x$ and $y$) complements, substitutes, or neither? Why? An explanation with mixed partial derivatives would ...
### Interpreting how graphs of Cobb-Douglas utility functions. How does MRS vary as we vary $\alpha$?
Suppose I have the following Cobb-Douglas function $$U(x,y) = x^\alpha y^{1-\alpha} = 1$$ where $\alpha \in [0,1]$. $$MRS = -\frac{U_x}{U_y} = - \frac{\alpha}{1-\alpha} \frac{y}{x}$$ \frac{\...