My Math Forum Question on Derivative (Consumer Theory)

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 July 8th, 2012, 08:03 PM #1 Newbie   Joined: Jul 2012 Posts: 14 Thanks: 0 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!
 July 8th, 2012, 08:19 PM #2 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 522 Math Focus: Calculus/ODEs 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: $U=x^{0.6}y^{0.4}$ $\frac{\delta U}{\delta x}=0.6x^{-0.4}y^{0.4}$ $\frac{\delta^2 U}{\delta x^2}=-0.4\cdot0.6x^{-1.4}y^{0.4}=-0.24x^{-1.4}y^{0.4}$
 July 8th, 2012, 08:32 PM #3 Newbie   Joined: Jul 2012 Posts: 14 Thanks: 0 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.
 July 8th, 2012, 08:38 PM #4 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 522 Math Focus: Calculus/ODEs 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."
 July 8th, 2012, 08:43 PM #5 Newbie   Joined: Jul 2012 Posts: 14 Thanks: 0 Re: Question on Derivative (Consumer Theory) I will definitely look into it. I really appreciate your help. Thank you!
July 8th, 2012, 08:47 PM   #6
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Re: Question on Derivative (Consumer Theory)

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 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!

 July 8th, 2012, 08:54 PM #7 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 522 Math Focus: Calculus/ODEs Re: Question on Derivative (Consumer Theory) Glad to help, and welcome to the forum!

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