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 = P1x1 + P2x2 + λ[U - xαy1-α] First order conditions L'(x) = P1 - λαxα-1y1-α = 0 L'(y) = P2 - λ(1-a)xαy-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: P1/P2 = λαxα-1y1-α / λ(1-a)xαy-α 3. The attempt at a solution Here is where I get confused. How did the we arrive at the next step: P1/P2 = α/(1-α) . x/y Please explain you get x/y from the tangency condition.