Cost Function Exponents Simplification

Watch
FishFullofRum
Badges: 0
Rep:
?
#1
Report Thread starter 6 years ago
#1
Hi everyone,

I'm working through an aspect of differential equation for an economics course and am stuck on a simplification aspect of it. The professor is assuming quite a bit of background mathematics knowledge, which is just slightly beyond my current level of understanding. If someone more skilled at these things could break down the following simplification on a variable by variable basis I'd be very grateful.


0 = r-\frac{a}{B} \times w \times A^{-\frac{1}{B}} \times {K}^{-\frac{a}{B}-1} \times Q^{\frac{1}{B}}

Solving for K:

{K}^{-\frac{a+B}{B}} = A^{\frac{1}{B}} \times \frac{B}{a} \times \frac{r}{w} \times Q^{-\frac{1}{B}}

Clearly, there's more to this problem than I've posted here but this is the part that I'm stuck on. I'm figuring this pretty much involves inverting the signs but if someone could give me a bit more of a detailed breakdown that would be great.

Thanks in advance for any replies.
0
reply
Ateo
Badges: 9
Rep:
?
#2
Report 6 years ago
#2
This is just the rules of indicies..

\displaystyle K^{-\frac{a}{B} - 1} = \frac{r}{\frac{a}{B} \cdot w \cdot A^{-\frac{1}{B}} \cdot Q^{\frac{1}{B}}}

\Rightarrow \displaystyle K^{-\frac{a + B}{B}} = \frac{B}{a} \cdot \frac{r}{w} \cdot A^{\frac{1}{B}} \cdot Q^{-\frac{1}{B}}
0
reply
FishFullofRum
Badges: 0
Rep:
?
#3
Report Thread starter 6 years ago
#3
Thanks for the response, but I was rather hoping for an explanation of the particulars of how those rules are applied in the above instance.
0
reply
davros
  • Study Helper
Badges: 16
Rep:
?
#4
Report 6 years ago
#4
(Original post by FishFullofRum)
Thanks for the response, but I was rather hoping for an explanation of the particulars of how those rules are applied in the above instance.
Well your first step should be to move all the terms except r to one side so that you have an equation that starts r = ....

Now see what factors you can multiply by that will help you to isolate the term with K in it.
0
reply
X

Quick Reply

Attached files
Write a reply...
Reply
new posts
Back
to top
Latest
My Feed

See more of what you like on
The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

Personalise

Are you travelling in the Uni student travel window (3-9 Dec) to go home for Christmas?

Yes (96)
28.24%
No - I have already returned home (44)
12.94%
No - I plan on travelling outside these dates (65)
19.12%
No - I'm staying at my term time address over Christmas (34)
10%
No - I live at home during term anyway (101)
29.71%

Watched Threads

View All