Question

N firms are competing by producing the same product. The quantity of production by firm i is denoted by q_{i .} Each firm chooses the quantity (any positive number) without knowing the other firms’ choices. The profit of each firm depends on the market price and the cost of production. The market price is given by P=100-∑q_i, and the cost of producing quantity q_i is C(q_i)=40qi. When N=1, it is the case of monopoly. What is the optimal quantity of production? What about for N=2?

Answer 1