# Maximizing two codependant profit equations for Bertrand Model Oligopolies

For this problem I was given the Fixed Cost, Marginal cost, and demand curves for two firms (x and y). So far, from this information I derived the profit (π) function for each firm.

π(x)=-0.01x^2+70x+0.005xy-10y-120000

π(y)=-0.01y^2+520y+0.005xy-10x-1020000

Normally, when maximizing profit, we would use LaGrange. However, the λ constraint was something like cost or budget.

My second guess is to simply take the first partial derivative of each to maximize, but I dont think that will account for the fact that each profit function is dependent on outcome of the other.

Can someone point me in the right direction?

(apologies for format)

• So It looks like my 2nd guess was correct. Taking the partial of each maintains the dependent variables. – Ocasta Eshu Apr 25 '11 at 1:45