(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

When attempting to divide the following equality (a "tangency condition" in microeconomic consumer theory), I'm puzzled by the solution derived here, please explain the procedure for arriving at the solution. Many thanks!

2. Relevant equations

I differentiated the Lagrangian wrt x and y:

L = P_{1}x_{1}+ P_{2}x_{2}+ λ[U - x^{α}y^{1-α}]

First order conditions

L'(x) = P_{1}- λαx^{α-1}y^{1-α}= 0

L'(y) = P_{2}- λ(1-a)x^{α}y^{-α}= 0

The "tangency condition" requires that we divide L'(x) by L'(y): Doing so, and carrying the second half of each function to the other side, we get:

P_{1}/P_{2}= λαx^{α-1}y^{1-α}/ λ(1-a)x^{α}y^{-α}

3. The attempt at a solution

Here is where I get confused. How did the we arrive at the next step:

P_{1}/P_{2}= α/(1-α) . x/y

Please explain you get x/y from the tangency condition.

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# Homework Help: Dividing with exponential functions

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