# Basic Algebra - Economics

• Jan 11th 2012, 04:42 AM
dukethyduke
Basic Algebra - Economics
Hey!

I guess these problems that bother me are rather simple to you. Hopefully I can get these fundamental algebraic problems out of my way, with a little bit of help by you.

First of, I'm solving a problem concerning Edgeworths box ( Yea I know, completely worthless in real life).

The thing is the following, I have the following equation that I'm supposed to solve for Y1:

(3Y1/X1) = (Ny - Y1) / (Nx - X1)

The answer is supposed to be: Y1(X1) = NyX1/(3Nx-2X1)

I can see NyX1, but where did Y1 go?
I can see 3Nx, but where did 2X1 come from?

Secondly I have the following problem in a MRS equation;

Q(L,K) = 12L^(1/3)K^(1/2) = Q
L = 4,5K
Solve for K.

The answer is supposed to be:K = Q^(6/5)/36

W.R

/ Duke
• Jan 11th 2012, 02:33 PM
MarceloFantini
Re: Basic Algebra - Economics
Can you show your attempts so far at manipulating the terms to arrive at the solution? Perhaps we can spot where things went wrong.
• Jan 12th 2012, 12:30 AM
dukethyduke
Re: Basic Algebra - Economics
Quote:

Originally Posted by MarceloFantini
Can you show your attempts so far at manipulating the terms to arrive at the solution? Perhaps we can spot where things went wrong.

Thank you!

Yes sure. Regarding the first problem, when I'm supposed to solve for Y1:

To get Y1 alone on the lefthand side I move X1 up to the numerator on the righthand side, getting (Ny - Y1)*X1. Then, the same procedure for the numerator on the lefthand side, 3, moving it down to the denominator on the right hand side, getting (Nx-X1)*3.

So, Y1 = (NyX1 - Y1X1) / (3Nx - 3X1)

Here I get stuck. I don't now what to do with "Y1X1" and "3X1".

Regarding the second problem I use L = 4,5K so I don't fool around with two unknowns, implying = 12*(4,5*K)^(1/3)K^(1/2)
--› Q=19.812K^(1/3)K^(1/2)
--› Q=19.812K^(5/6)
--› Q^(6/5)=36K
--› Q^(6/5)/36 = K
--› BOOM! I solved it!

But, the first question is still a mystery

Thankful for help,

With regards,
Duke
• Jan 12th 2012, 05:15 AM
skeeter
Re: Basic Algebra - Economics
Quote:

(3Y1/X1) = (Ny - Y1) / (Nx - X1)
I assume the 1 , 2, and lower case x and y are subscripts ...

$\frac{3y_1}{x_1} = \frac{N_y - y_1}{N_x - x_1}$

cross multiply ...

$3y_1N_x - 3y_1x_1 = x_1N_y - x_1y_1$

since you're solving for $y_1$ , get all the terms with $y_1$ as a factor on the same side of the equation ...

$3y_1N_x - 3y_1x_1 + x_1y_1 = x_1N_y$

factor out $y_1$ from each term on the left side ...

$y_1(3N_x - 3x_1 + x_1) = x_1N_y$

combine like terms ...

$y_1(3N_x - 2x_1) = x_1N_y$

divide to isolate $y_1$ ...

$y_1 = \frac{x_1N_y}{3N_x - 2x_1}$