Consider two firms that produce the same good and compete setting quantities. The firms face a linear demand curve given by P(Q) = 1 Q, where the Q is the total quantity offered by the firms. The cost function for each of the firms is c(qi) = cqi , where 0 < c < 1 and qi is the quantity offered by the firm i = 1, 2.

1. What is the Nash equilibrium output choices of the firms?