Consider a Cournot duopoly with two firms with production cost of 2 per unit of some product. Consider that the investment decision of firm 1 on whether or not to install a new technology which allows a production cost of 0 per unit is common knowledge, but installing the technology costs c, which is also common knowledge. The output levels q1 and q2 are as in the Cournot model where the price per unit the firm can get is

p(q1,q2) = 14 -(q1 + q2): Compute, for which values of c firm 1 is better off investing in the new technology.