# Tag Info

Accepted

### 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 ...
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### 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 ...

### 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 ...
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### 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 ...
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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 ...
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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 ...
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### 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 ...
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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 ...
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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 ...
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### 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 $A:= \prod_i \alpha_i^{\alpha_i}$ ...
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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 $p_1x_1$...
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### 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.
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### 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-...
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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: $$\alpha p_2 x_2 - ... • 12.5k 4 votes Accepted ### Is cross-price elasticity a Cobb-Douglas production function? As stated in the comments, there is no economic connection between a demand function and a production function. The only connection between the two functional forms is that both of them are log-linear.... • 12.5k 3 votes Accepted ### Growth Accounting with variable factor shares Interesting question. In effect, while factor shares were thought to have remained fairly stable over a long time (the first of the Kaldor's facts), more recently they have varied, particularly in the ... • 8,591 3 votes ### Profit maximization with Cobb-Douglas function Should I solve for L^∗ by separating K^∗ from the equation and plugging into pMP_{L} Yep, that's about it. Wouldn't this yield a very complicated solution? Somewhat. The math is available ... 3 votes ### Indirect changes in Marshallian Demand You correctly derived the Marshallian demand function for Cobb-Douglas utility, you notice that the optimal level of consumption of x or y is a function only of the individual's income and the ... • 871 3 votes Accepted ### Demand derived from Cobb-Douglas utility, interpretation, check From (1) and (2) you get$$\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 ...
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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 ...