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8 votes
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Is the Cobb-Douglas Utility Function Locally Non-Satiated at (0,0)?

No. Cobb-Douglas utility is monotonic and monotonicity implies L.N.S. The issue here is that you're only considering edge cases. You've correctly reasoned that edge points are not more desirable that ...
123's user avatar
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8 votes

CobbDouglas: Constant marginal costs and constant returns to scale

Since the exponents add to one the production function has constant returns to scale, which means that, given factor prices, total cost is linear, which means that it's derivative (= marginal cost) is ...
Mark Machina's user avatar
7 votes

How was CES utility function derived?

To understand the CES utility functions, which I guess is your question, a good starting point is the Wikipedia page on constant elasticity of substitution. In particular, The CES aggregator is also ...
emeryville's user avatar
  • 6,990
6 votes

How was CES utility function derived?

The C.E.S functional has been introduced in Economics in the context of production theory, by Arrow, K. J., Chenery, H. B., Minhas, B. S., & Solow, R. M. (1961). Capital-labor substitution and ...
Alecos Papadopoulos's user avatar
5 votes
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Are Cobb-Douglas preferences homothetic?

Note that the wikipedia article is very specific: [...] defined a preference to be homothetic, if they CAN be represented by A utility function [...] You chose a specific utility function to ...
Giskard's user avatar
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5 votes
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Notation of a Cobb-Douglas function printed in 1989

Seems to be the second one, so $$ Q_t = A_t*(K_t^\alpha N^\beta_t T_t^\rho). $$ Two clues: This is the usual specification. On the top of page 14 it is written that $$ w_t = \beta Q_t/N_t. $$ Given ...
Giskard's user avatar
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5 votes

Is Cobb-Douglas the only output function corresponding to a competitive economy?

Let $a+b<1,\;\; a,b>0$. Pay the factors of production their marginal product: $$rK = \frac {aQ}{K} K= aQ,\;\;\ wL=\frac {bQ}{L} L=bQ$$ So total payments to factors of production will be $$rK ...
Alecos Papadopoulos's user avatar
5 votes
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Interpretation of Interesting Utility Function

This is the CES production function, where CES stands for constant elasticity of substitution. The parameter $\sigma$ captures the (constant) elasticity of substitution and $\alpha$ is the share ...
Herr K.'s user avatar
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5 votes
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How was the Cobb Douglas function derived?

What is the proof of this formula? There is actually no proof for what the production function should be. There are infinite many possible production functions and to discover which one is the most ...
1muflon1's user avatar
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5 votes
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Deriving a demand curve from a Cobb-Douglas utility

If you take the general class of CES utility functions, of which Cobb-Douglas is a special case, you do indeed get a demand function that depends on other prices. Specifically, the CES utility ...
Herr K.'s user avatar
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5 votes
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Cobb–Douglas utility maximized by spending a "fixed fraction of income on each good"?

A "fixed fraction" doesn't mean an "equal fraction", or at least that's not the intended meaning. It can be easily verified that the solution to \begin{equation} \max_{x_1,x_2}\;...
Herr K.'s user avatar
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5 votes
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CES First order Condition with two labour types

Simply multiply and divide one $\left(a_{F} \boldsymbol{F}\right)^{\frac{(\sigma-1)}{\sigma}}$ in the bracket and then take one outside the bracket. And by the way your FOC is incorrect in that $\frac{...
Alalalalaki's user avatar
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5 votes
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Cobb-Douglas Production Function - Finding units of labour to maximise production

If your aim is to maximize the production then your approach is correct. But if the aim is to find the optimal number of units of labor, then you should solve it as a profit maximization problem with ...
Macosso's user avatar
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5 votes

Cobb Douglas Production: Identification issues for technical change

Maybe the following is useful: Sato (1970), The Estimation of Biased Technical Progress and the Production Function, International Economic Review, 11, 179-208 JSTOR link
tdm's user avatar
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5 votes
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Calculating cost-minimizing inputs with 3 inputs in production function

The production function $$F(x) = x_1^{\alpha_1}x_2^{\alpha_2}x_3^{\alpha_3},$$ has the derivative with respect to $x_j$ where for sake of example I choose $j=1$ $$\frac{\partial F(x)}{\partial x_1} = \...
Jesper Hybel's user avatar
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4 votes

How was the Cobb Douglas function derived?

If one reads the original article by Cobb and Douglas (1928), https://www.aeaweb.org/aer/top20/18.1.139-165.pdf , one will find at the end of page 152 that the authors stress that they took into ...
Alecos Papadopoulos's user avatar
4 votes
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Is Cobb-Douglas the only output function corresponding to a competitive economy?

Any constant returns to scale function is compatible witha competitive economy. Cobb-Douglas is not the only one. Google CES production function. Also, product can be wasted or be an externality, so ...
chatGPT's user avatar
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4 votes
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Consumer preference and price in the Cobb-Douglas function

No, preferences are stable. That is not to say that the quantity demanded or marginal utility obtained at the new price level is the same though. If we'd allow the exponent of the utility function ...
Maarten Punt's user avatar
  • 2,373
4 votes

Marginal cost given (Cobb-Douglas) production

The Cobb Douglas production function with constants returns to scale $$y = \prod_i x_i^{\alpha_i} = A \prod_i \left(\frac{x_i}{\alpha_i}\right)^{\alpha_i} ,$$ where $A:= \prod_i \alpha_i^{\alpha_i}$ ...
Jesper Hybel's user avatar
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4 votes
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Finding restrictions on parameters for a demand function

Demand is positive, so $A>0$. If $p_1$ goes to $\infty$, $x_1$ has to go to 0, since $p_1x_1$ is bounded by $M$. Thus $\alpha < 0$. If $p_2$ goes to 0, $x_1$ cannot go to $\infty$, since $p_1x_1$...
VARulle's user avatar
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4 votes

Is it true that for Cobb-Douglas preferences, the demand function is always iso-elastic?

Yes. I have to include at least 30 characters in an answer, so let me repeat: Yes.
VARulle's user avatar
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4 votes

Does global maximum of CRS Cobb-Douglas profit exist

It is generally true that a profit-maximizing firm with a constant-returns to scale technology can produce a positive output only if the profit is zero. Output prices are pinned down by the zero-...
Michael Greinecker's user avatar
4 votes

Confusion on deriving Walrasian price changes using IFT

First, there is a slight mistake in your first order condition as $x_2$ needs to be in the numerator and $x_1$ in the denominator. The two first order conditions can be written as: $$ \alpha p_2 x_2 - ...
tdm's user avatar
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4 votes
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Is cross-price elasticity a Cobb-Douglas production function?

As stated in the comments, there is no economic connection between a demand function and a production function. The only connection between the two functional forms is that both of them are log-linear....
tdm's user avatar
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3 votes
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Growth Accounting with variable factor shares

Interesting question. In effect, while factor shares were thought to have remained fairly stable over a long time (the first of the Kaldor's facts), more recently they have varied, particularly in the ...
luchonacho's user avatar
  • 8,591
3 votes

Profit maximization with Cobb-Douglas function

Should I solve for $L^∗$ by separating $K^∗$ from the equation and plugging into $pMP_{L}$ Yep, that's about it. Wouldn't this yield a very complicated solution? Somewhat. The math is available ...
android16.5's user avatar
3 votes

Indirect changes in Marshallian Demand

You correctly derived the Marshallian demand function for Cobb-Douglas utility, you notice that the optimal level of consumption of $x$ or $y$ is a function only of the individual's income and the ...
Sunhwa's user avatar
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3 votes
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Demand derived from Cobb-Douglas utility, interpretation, check

From (1) and (2) you get $$\frac{x_j}{x_i}=\frac{a_j p_i}{a_i p_j},$$ or equivalently, $$x_j =\frac{a_j p_i}{a_i p_j} x_i.$$ Substituting this into equation 3 for $j=2,...,n$ and $i=1$ (solving for ...
dlnB's user avatar
  • 595
3 votes
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Is an income tax always more favourable for consumers compared to ad valorem/quantity tax?

You question can be answered using a revealed preference argument. Let $B = \{q \in \mathbb{R}^n_+| p' q \le m\}$ be some budget set of a consumer (i.e. $B$ gives all possible bundles that the ...
tdm's user avatar
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