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July 8th, 2012, 07:03 PM   #1
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Question on Derivative (Consumer Theory)

Hello everyone,

I am currently doing some consumer theory and one of the questions basically asks to verify Diminishing Marginal Utility.

Here it is : For (a)-(d), which of the utility functions exhibit diminishing marginal utility for good X?
I understand what the question is asking for and intuition behind the answer, however for this equation:

U = (x^.6)(y^.4)

how is the marginal utility of X = MUx/x = (-0.24x^(-1.4))(y^(0.4))

I've been taking partial derivatives of the Cobb-Douglas equations in order to find MUx and MUy in order to solve these problems, however when I take the partial derivative for this I get : MUx = .6x^(-.4)y^(.4). I haven't taken calculus for a while so it may be that I am over looking something obvious.

I don't know what is being done in order to obtain the answer above. I tried product rule, but then I end up wit an awkward Y term and since it's in respect to X , it just ends up floating about.

Anything help would be greatly appreciated. Thank you all!
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July 8th, 2012, 07:19 PM   #2
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Re: Question on Derivative (Consumer Theory)

You want to take the second partial with respect to x, as diminishing marginal utility is taken to correspond to this.

Given:





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July 8th, 2012, 07:32 PM   #3
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Re: Question on Derivative (Consumer Theory)

It seems I don't understand the intuition

If you take the first derivate , you are able to deduce how much more utility is gained per each unit of x correct?

By taking the 2nd derivative , we are able to see deduce what? I am confused as to why the 2nd derivative is necessary. Evidently your answer is correct, however I thought that the first derivate allowed us to see DMU by observing whether MUx increased when X increased or if it decrease when X increased. If you could please elaborate, I would greatly appreciate it. Thank you.
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July 8th, 2012, 07:38 PM   #4
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Re: Question on Derivative (Consumer Theory)

I'm sorry, economics is not a subject with which I am very familiar (I only took macro and micro two decades ago and those courses used no calculus).

I simply googled "diminishing marginal utility" and found this is how it is defined.

Here is the article I used:

http://en.wikipedia.org/wiki/Margina...rginal_utility

Look under "Quantified marginal utility."
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July 8th, 2012, 07:43 PM   #5
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Re: Question on Derivative (Consumer Theory)

I will definitely look into it.

I really appreciate your help. Thank you!
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July 8th, 2012, 07:47 PM   #6
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Re: Question on Derivative (Consumer Theory)

Quote:
Originally Posted by edwinh
I will definitely look into it.

I really appreciate your help. Thank you!
I just figured it out. Thank you very much. Your push towards the right direction is what I needed!
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July 8th, 2012, 07:54 PM   #7
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Re: Question on Derivative (Consumer Theory)

Glad to help, and welcome to the forum!
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