The profit of firm 1 (the leader) is formula_16, where formula_17 is the follower's quantity as a function of the leader's quantity, namely the function calculated above. The best response is to find the value of formula_8 that maximises formula_19 given formula_17, i.e. given the best response function of the follower (firm 2), the output that maximises the leader's profit is found. Hence, the maximum of formula_19 with respect to formula_8 is to be found. First, differentiate formula_19 with respect to formula_8: