Two companies produce luxury clothing, Pradi and Gucca. Each firm has the following cost function: C(q)=30q+1.5q2

The demand for luxury clothing is represented by the following inverse demand equation: P=300-3Q Where Q=Q1+Q2 is total production.

a) If each firm maximizes its profits by taking the output of its rival as given (i.e. if the firms behave as in the Cournot model), what will be the equilibrium production quantities chosen by each firm? What is the total production and market price? What are the profits made by each company?

b) The leaders of Pradi and Gucca realize that they would benefit from entering into collusion. If the two firms collide, what will be the optimal amount of production? What will the market price be? What will be the quantity and profit of each firm in this case?