Two companies are producing widgets It costs the first company q 1 2 dollars to produce q 1 widgets and the second company 0 5q 2 2 dollars to produce q 2 widgets If a total of q widgets are produced, consumers will pay 200 q dollars for each widget If the two companies want to collude in an attemp...

Collusive duopoly Cost for each firm to produce q units is of form ...

Two companies are producing widgets. It costs the first company q 1 2 dollars to produce q

Question:

Two companies are producing widgets. It costs the first company q₁²dollars to produce q₁ widgets and the second company 0.5q₂² dollars to produce q₂ widgets. If a total of q widgets are produced, consumers will pay 200 – q dollars for each widget. If the two companies want to collude in an attempt to maximize the sum of their profits, how many widgets should each company produce?