Another problem sorry

B

bensmyname

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Aug 6, 2010
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Hey, another problematic question, where i probably need atleast a good point in the right direction is this:
A consumers preference over food(X) and other goods (Y) are given by U(X,Y).
With marginal utilities MUx=Y and MUy=x. The consumers income is 32400.
Calculate the optimal basked when Px=40 and Py=10.


Quite stuck on this one tbh. Not thinking right.
Any help appreciated,
Thanks
Ben.
 
bensmyname said:
Hey, another problematic question, where i probably need atleast a good point in the right direction is this:
A consumers preference over food(X) and other goods (Y) are given by U(X,Y).
With marginal utilities MUx=Y and MUy=x. The consumers income is 32400.
Calculate the optimal basked when Px=40 and Py=10.


Quite stuck on this one tbh. Not thinking right.
Any help appreciated,
Thanks
Ben.
Click to expand...

Ben

This is a math site. People here will help you with math, but they do not necessarily know how to translate a problem in microeconomics into math unless you lay the problem out in good math notation.

I think you mean that you have two goods, X and Y. You have a utility function U(x, y) where x and y are quantities of X and Y respectively. I have no clue what MUx = Y means; can a marginal utility be the name of a good? I mean I am even guessing that MUx is intended to mean marginal utility of x.

If this is as I strongly suspect a problem in maximization subject to a constraint, then the solution involves Lagrangian multipliers, a very frequent method in economics. But no one here can help you unless you specify the problem carefully. Capitals and parentheses and such are important. If part of your problem is translating economics into math, I can help with that, but then I need a very careful description of the problem, ideally a word-for-word quotation so I can figure out what is being asked. Sorry if I sound unfriendly, but your questions are too vague to permit answers.

PS It is possible to insert subscripts on this site. Px is a lot different than is P[sub:a74ksr7d]x[/sub:a74ksr7d].
 
Thank you for your reply. Didn't realise the subscript was there, and i will use from now on.

I think you mean that you have two goods, X and Y. You have a utility function U(x, y) where x and y are quantities of X and Y respectively. I have no clue what MUx = Y means; can a marginal utility be the name of a good? I mean I am even guessing that MUx is intended to mean marginal utility of x
Click to expand...
MU[sub:2axmnyko]x[/sub:2axmnyko]=Y and MU[sub:2axmnyko]y[/sub:2axmnyko]=X i take to mean that they have the same Marginal Utilities, but not sure. But yes it was meant to mean Marginal Utility of X.
I am going to have another go at it now, and hopefully work something out.
Thank you for your help.
PS you dont sound unfriendly i get what your saying, and appreciate help.
 
Not even sure im going right way but i get to this and then stuck: (don't know how to do all symbols so make & mean partial differentiation, L=Lagrangian, and #=Lambda

L=XY-#(32400-40X-10Y)
Then partially differentiating each one..
&L/&X = Y-40# = 0
&L/&Y = X-10# = 0
&l/&# = 32400-40X-10Y = 0

Then i'm basically stuck, Do you know a next step? or is this the wrong way to go..?
 
Think i worked it out.
went (y-40#)-(4x-40#) = 0
Which y-4x=0
which y=4x

put that in lagrangian
32400 - 80x = 0
gets you 405 for x then putting that in got me 1620 for y
gets U= 405*1620=656100.

I think. Haha. But thank you for any help once again. No doubt have more to ask soon =P
 
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