Question 1 (20 p) Consider a market with 2 firms where the inverse demand function is given by P a-bO, where O=q,+q . Each firm has a cost function given by 7C(q.)=cq, where i=/1,2). 1) derive the marginal revenue functions of firms in accordance with the models of Cournot and Stackelberg (4 p.); 2) compare price level and quantities in this market calculating the Cournot equilibrium and the Stackelberg equilibrium (3 p.); 3) calculate the profits of the duopolists according to the models of Cournot and Stackelberg (3p); 4) draw a graph with best response functions and illustrate the Cournot solutions in the graph (3p.); 5) compare your results regarding price level, quantities and profits to the result under perfect competition and collusion (monopoly) respectively and illustrate these solutions in your graph (4p.); 6) determine the parameters of market equilibrium and profits of duopolists according to Bertrand's model (3p.)