# 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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### Cobb Douglas relation with uncompensated law of demand

Does a Cobb Douglas or homothetic function satisfy the uncompensated law of demand? 1 vote
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### Is it true that for Cobb-Douglas preferences, the demand function is always iso-elastic?

As we know that $Q*P=const.$ for Cobb-Douglas preferences, we can thus conclude that $\frac{dQ/Q}{dP/P}$ is always $-1$: $$QP=const. \implies 0=d(PQ)=Q\ dP+P\ dQ \implies \frac{dQ}{Q}=-\frac{dP}{P}$$...
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### Is an income tax always more favourable for consumers compared to ad valorem/quantity tax?

I'm studying the optimal choice of consumers with regards to taxation. I read that for consumers, income tax is generally (for Cobb-Douglas preferences) preferred compared to ad valorem tax: If the ...
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### Finding restrictions on parameters for a demand function

I have a question that asks: Let $x_1$ be the quantity of a good 1, $p_1$ the price of good 1, $p_2$ the price of good 2, and $M$ is income. Let $𝑥_1(𝑝_1, 𝑝_2, 𝑀; 𝐴) = 𝐴𝑝_1^𝛼𝑝_2^𝛽𝑀^𝛾$ ...
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### Values of A,K,N,a in Cobb-Douglas function expressing GDP

In many basic macroeconomics textbooks a Cobb-Douglas production function with constant returns to scale is used to express the output of the economy as a function of labor and capital: $Y=AK^aN^{1-a}$...
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### CES First order Condition with two labour types

I am struggling to derive a first order in this model with Cobb-Douglas production function and CES labour aggregator with two types labour (here male and female, but could be equally low and high ...
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### What's special about Cobb–Douglas utility relative to the rest of the CES family?

My question concerns CES utility functions, which have the form $$u(x) = \left(\sum_{j=1}^n a_j x_j^{\rho} \right)^{1/\rho}$$ for utility parameters $a_j$, an elasticity parameter $\rho$, and some ...
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### Cobb–Douglas utility maximized by spending a "fixed fraction of income on each good"?

Consider a Cobb–Douglas utility function having the form $$u(x) = \prod_{j=1}^n x_j^{a_j}$$ where $x$ is an allocation vector and $a_j$ are utility parameters with $\sum a_j = 1$. My question has to ...
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### References on Cobb-Douglas Function

I am wondering why everybody uses Cobb-Douglas production functions? Nowadays they are so standard that they are just written down without further discussion. Does anybody know more about this and can ...
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### Labor Supply- how to do comparative statics?

Consider an economy with a competitive industry where the representative firm's production function takes the form of a Cobb Douglas production function $Y=z K^{\theta} L^{1-\theta}$. $z$ is an index ...
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### Neoclassical Two-Sector Model of Endogenous Growth: Getting the consumption growth rate

I'm struggling to derive the growth of consumption from a two-sector model with the traditional Cobb-Douglas function. The model I am speaking about incorporates the fractions used by physical and ...
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### CobbDouglas: Constant marginal costs and constant returns to scale

A company has a production function: $$y=x_1^{\alpha}x_2^{1-\alpha}$$ where $0<\alpha<1$. Factor input 1 costs $w_1> 0$ and factor input 2 costs $w_2> 0$. The company wants to minimize its ...
1 vote
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Let $y=x_1^\alpha x_2^\beta$ where $\beta=1-\alpha$ be a Cobb-Douglas production function. Find the elasticity of the optimal demand functions (for minimizing production cost) for both goods wrt. $w_2/... 0 votes 1 answer 79 views ### Isn't the parameter A denoting technological progress from Cobb-Douglas already included in alpha and beta? Does it not follow that if capital is better performing than labor it would be used more frequently? What exactly does parameter A actually mean, then? 0 votes 1 answer 788 views ### Marginal cost given (Cobb-Douglas) production My function is$y=x_1^\alpha x_2^\beta$with$\beta={1-\alpha}$. I found: the minimization problem for demand to be$x_1^{*}(w_1,w_2,y)=\left ( \frac{w_2}{w_1}\frac{\alpha}{\beta} \right )^{\frac{\... 1 vote
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### Utility functions and positive monotone transformations

We let $g(z)$ be a strictly monotonous function so: $$\frac{dg(z)}{dz}>0$$ Consumer 1 has preferences given by the utility function $u(x_1,x_2)=ln(x_1)+2ln(x_2)$, while consumer 2 has preferences ...
1 vote
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### Compare taxes Cobb-Douglass and more

Let a utility function for a consumer be defined as $u(x_{1},x_{2})=x_{1}^{1/2} x_{2}^{1/2}$. With the budget $x_{1}p_{1}+x_{2}p_{2}=m$. With values $p_1=p_2=1, m=32$. The state now adds a tax of unit ... 1 vote
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### Estimating $TFP$ using Cobb-Douglas production function

Suppose we want to estimate total factor productivity (TFP) under time series framework. Let assume that the production function is given in the Cobb-Douglas form, i.e. $$Y_t=A_tK_t^\alpha L_t^\beta,$$...
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### How was CES utility function derived?

Is there any book/papers that I can refer to the proof (derivation) of the CES utility function? Or if anyone could help me with the derivation, I will be so much grateful to you.
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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 ...
1 vote
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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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1 vote
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### Regression on derived consumer preference

I have a data set with some demographics of consumers who bought a product that can be used to imply their preference (beta) using Cobb-Douglas (see comments of original question). I’d like to check ...
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### Consumer preference and price in the Cobb-Douglas function

I believe I’m using the most basic version of Cobb-Douglas: $U(x,y)=x^\beta * y ^{(1-\beta)}$. The question I have is: in this example would a consumer’s preference ($\beta$) change if the price of ...
Consider two countries: Home and Foreign that produce two goods, cars and wheat. The production technologies are such that: $q_{c} = K_{c}^{0.5} L_{c}^{0.5}$ and $q_{w} = 0.5 K_{w}^{0.5}L_{w}^{0.5}$ ...
I have the utility function $U^A=\alpha ln(x^A)+\beta ln(y^A)$ for consumer $A$ and $U^B=\gamma ln(x^B)+\phi ln(y^B)$ for consumer $B$. They are endowed with $\omega^h_x$ and $\omega^h_y$ of $x$ and \$...