1) There are companies that produce two kinds of goods x and y. The government in the company country imposes a production quota for goods x and y so that the company has a production limit i.e: x + y = 42. The cost function owned by the company is: C (x; y) = 8x² - xy + 12y². Find the values of x, y and , which is can fill the government's quota criteria. Please find the formula for the approach: minimization or maximization. (use the Lagrange method to find your answer).

2) 1) Two firms have a market demand function:

QD = (600-P) / 2 and

TC = q2 + 30q

Question:

a) profit under no-cooperative conditions (cournot equilibrium);

b) profit in a collusion condition;

c) What are the conditions when the two firms can make choices for noncooperative and collusion? (find the profit value and create a payoff matrix from the results of points a, b and c);

d) what is the final equilibrium of the two firms? (find a solution with the game theory model) Was there prisoner's dillema?