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# How can you tell if MUx is positive but diminishing? watch

1. The question asks "Show that MUx is positive but diminishing". In the picture below, I have taken the derivative, and taken the second derivative.

So from there, how can I know if it is less than or greater than 0? My lecture notes say that the left hand side is negative and the right hand side is negative, therefore there should be a positive diminishing marginal utility, but I'm not sure how he worked out that both the LHS and RHS are negative?

Could anyone shine any light on this please? Thank you.

2. (Original post by ImNotSuperman)
The question asks "Show that MUx is positive but diminishing". In the picture below, I have taken the derivative, and taken the second derivative.

So from there, how can I know if it is less than or greater than 0? My lecture notes say that the left hand side is negative and the right hand side is negative, therefore there should be a positive diminishing marginal utility, but I'm not sure how he worked out that both the LHS and RHS are negative?

Could anyone shine any light on this please? Thank you.

Well, x and y cannot be negative, simply because you can't have negative goods... So, putting any number greater than 0 as x and y, will show you that MUx is positive, and that then the second differential is negative... Hope that makes sense.
3. (Original post by ImNotSuperman)
The question asks "Show that MUx is positive but diminishing". In the picture below, I have taken the derivative, and taken the second derivative.

So from there, how can I know if it is less than or greater than 0? My lecture notes say that the left hand side is negative and the right hand side is negative, therefore there should be a positive diminishing marginal utility, but I'm not sure how he worked out that both the LHS and RHS are negative?

Could anyone shine any light on this please? Thank you.

Just a note on notation, you're doing partial differentiation when you're holding constant so you want to use rather than .

I think you may have misunderstood what the lecturer meant by LHS and RHS. The condition for a diminishing marginal utility is that both second order partial differentiations of and are negative. In other words, you've done some of the steps (by proving that the second order partial derivative for is negative), just missing the last bit.
4. (Original post by mobbsy91)
x
(Original post by The Financier)
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Thanks for the quick replies. Wasn’t expecting that on a Saturday morning.

So just to clarify, if MUx is positive, then it has a positive marginal utility.

But what if MUX is positive, and MUy is negative?

And if both second order partial derivatives of x and y are negative, then it is diminishing marginal utility. But what if x is negative and y is positive?
5. (Original post by ImNotSuperman)
Thanks for the quick replies. Wasn’t expecting that on a Saturday morning.

So just to clarify, if MUx is positive, then it has a positive marginal utility.
Yep.

But what if MUX is positive, and MUy is negative?
This means that good is an economic bad and therefore brings negative marginal utility. The marginal utility of good is still positive.

And if both second order partial derivatives of x and y are negative, then it is diminishing marginal utility. But what if x is negative and y is positive?
Then you cannot confirm that it has diminishing marginal utility. The positive factor of may outweigh the negative factor of for some values. Only when both second order partial derivatives are negative can you confirm that it is diminishing.
6. Thank you TF. I'd rep you but I've already repped you recently.
7. (Original post by ImNotSuperman)
Thank you TF. I'd rep you but I've already repped you recently.
No problem man. Happy to help

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