Talk:Cobb–Douglas production function

The difficulties section
The difficutlies section is not good. The fact that cobb douglas does not have constant returns to scale in general is not a difficulty and does not necessarily clash with proper microfoundations. It is just a property of its general form.

128.112.41.155 (talk) 18:40, 8 September 2009 (UTC)

Origin
Lloyd (2001) claims that the Cobb-Douglas function was proposed by von Thünen, Mill, and Pareto even before it was proposed by Wicksell.

Lloyd, Peter John (2001): The Origins of the von Thunen-Mill-Pareto-Wicksell-Cobb-Douglas Function. History of Political Economy - Volume 33, Number 1, pp. 1-19, http://muse.jhu.edu/login?uri=/journals/history_of_political_economy/v033/33.1lloyd.pdf —Preceding unsigned comment added by 188.179.72.230 (talk) 18:31, 24 January 2011 (UTC)

Help
I cannot understand why it is that when α + β = 1 there are constant returns to scale. Does anybody know how to derive this?

Sure. First of all, if α + β = 1, then β = 1 - α, so we'll substitute that in. Also, let's say that n is the factor that we're scaling by. So our initial setup is

$$A({\color{Blue}n}L)^\alpha\,({\color{Blue}n}K)^{1-\alpha\,}$$

$$A{\color{Blue}n}^\alpha\,L^\alpha\,{\color{Blue}n}^{1-\alpha\,}K^{1-\alpha\,}$$ // distribution of exponents

$${\color{Blue}n}^\alpha\,{\color{Blue}n}^{1-\alpha\,}AL^\alpha\,K^{1-\alpha\,}$$ // just reordering things

$${\color{Blue}n}^{\alpha\,+1-\alpha\,}AL^\alpha\,K^{1-\alpha\,} $$ // multiplication with exponents

$${\color{Blue}n}^1AL^\alpha\,K^{1-\alpha\,} $$

$${\color{Blue}n}AL^\alpha\,K^{1-\alpha\,} $$

so the result of scaling up both inputs by n is that the final answer is also scaled up by n. --152.23.101.108 02:30, 2 September 2006 (UTC)

(Or, more abstractly, scaling up both inputs by n results in the output being scaled up by $$n^{\alpha\,+\beta\,}$$)

The above might be too specific to put on the page, but maybe we could say something about how the function exhibits homogeneity of degree 1 when the exponents sum to 1? That way we can link to the mathematics article that explains the concept a bit more succinctly (thus avoiding those sort of derivations when unnecessary). Bsdlite (talk) 21:31, 14 May 2008 (UTC)

This seems a bit unclear: "A, α and β are the output elasticities of labor and capital, respectively. These values are constants determined by available technology. " —Preceding unsigned comment added by 61.230.54.247 (talk) 19:30, 18 May 2008 (UTC)

Q=AKL?
In my econometrics class, we're taught Q=A*K^alpha*L^beta 149.4.115.3 (talk) 14:12, 28 October 2010 (UTC)

Quick Question
In the section Difficulties and criticisms / Lack of microfoundations; it begins with the text...

''The Cobb–Douglas production function was not developed on the basis of any knowledge of engineering, technology, or management of the production process. It was instead developed because it had attractive mathematical characteristics, such as diminishing marginal returns to either factor of production and the property that expenditure on any given input is a constant fraction of total cost.''

If any of the contributors can respond with a source citation for this, it would be appreciated! — Preceding unsigned comment added by Nklapper (talk • contribs) 23:10, 13 December 2012 (UTC)

This is just wrong. When the function was proposed by Wicksell in "A mathematical analysis of Dr. Åkerman's problem", the micro foundations was thoroughly discussed (together with constant returns to scale). — Preceding unsigned comment added by 80.202.79.220 (talk) 19:12, 1 August 2015 (UTC)

I read this article and was horrified at its terrible quality. It's now September 2018 (three years after this issue was identified) and nobody has corrected it yet! — Preceding unsigned comment added by 2601:405:4400:DF50:BC95:2F7B:C0DD:2707 (talk) 18:00, 27 September 2018 (UTC)

Quick STATEMENT FOR FURTHER ANALYSIS
Jay -- I was trying to understand the fundamental assumption basis based on mathematical characteristics v/s technological changes or advancements .My belief is always based on one fundamental statement "LAWS OF DIMINISHING RETURNS".Hence a constant output of Cobb–Douglas production function contradicts my fundamental belief.I am now finding that we are very quick to admit benefits or loss based on different models.A scientific study across the macroeconomic models would be beneficial in the complex era of globalized world for all the nations and its citizens. Upon searching I found an interesting analysis http://faculty.chicagobooth.edu/brent.neiman/research/KN.pdf

suppose that an economy,s production function is cobb douglas with parameter ∞ =0.3. what fractions of income do capital and labor receive?

suppose that an economy,s production function is cobb douglas with parameter ∞ =0.3. what fractions of income do capital and labor receive?

verra nice
It is unusual to see such a technical subject explained so well; my only minor complain is in the intro, when you have the equation, before explaining the algebra, you need a pre algebra explanation for the gen public something like, the outpput of an economy depends on labor (hours worked), capital (buildings, equipment); the Cobb Douglas is a mathematical expression that gives a particular form to this. well, that is n't very good, but perhaps you get the point ?? I esp liked the explanation of what a1% elasticity means; that is outstanding - congrats and please, don't let them tell you it is to simple; it isn't it is just right — Preceding unsigned comment added by 50.245.17.105 (talk) 00:19, 17 December 2014 (UTC)

economists are bad mathematicians
economists can only add, multiply, take logarithms, and (sometimes, very rarely) $$e^{\alpha x}$$, indeed they obtain such stupid equations, meaning nothing except that their model (comparable to the worst climatics models) is meaning-less.

this is what I understand from this article : stop thinking economists are smart.

Why is the function measured in terms of dollars?
In my economics course we don't have Y in terms of Dollars nor any inputs. We typically use units for both Y, L, and K i.e. L man hours, Y units produced. — Preceding unsigned comment added by Nieblham (talk • contribs) 02:09, 11 May 2020 (UTC)

Deleting unsourced texts
This part of the article seems to have no sources and to be original research :

"The Cobb–Douglas production function was not developed on the basis of any knowledge of engineering, technology, or management of the production process. This rationale may be true given the definition of the Capital term. Labor hours and Capital need a better definition. If capital is defined as a building, labor is already included in the development of that building. A building is composed of commodities, labor and risks and general conditions. It was instead developed because it had attractive mathematical characteristics, such as diminishing marginal returns to either factor of production and the property that the optimal expenditure shares on any given input of a firm operating a Cobb–Douglas technology are constant. Initially, there were no utility foundations for it. In the modern era, some economists try to build models up from individual agents acting, rather than imposing a functional form on an entire economy. The Cobb–Douglas production function, if properly defined, can be applied at a micro-economic level, up to a macro- economic level."

Can we delete it ? Tucopu (talk) 11:47, 1 November 2023 (UTC)