Thread: 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

I'm thankful for answers.

W.R

/ Duke

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

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

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

I assume the 1 , 2, and lower case x and y are subscripts ...

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

cross multiply ...

$\displaystyle 3y_1N_x - 3y_1x_1 = x_1N_y - x_1y_1$

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

$\displaystyle 3y_1N_x - 3y_1x_1 + x_1y_1 = x_1N_y$

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

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

combine like terms ...

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

divide to isolate $\displaystyle y_1$ ...

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