Consider an industry consisting of two firms named First and Next, both of which have the technology to manufacture a new type of computer chip. The inverse demand curve in this industry is P = 1 - qf - qn where P is the market price and qi is the output of firm i = F, N. Their cost functions are Cf = (1/2)qf - (3/4)qf^2 and Cn = (1/2)qn - (3/4)qn^2. Suppose that First is a Stackelberg leader. Derive Next's reaction function and then find the Stackelberg equilibrium quantities, the market price, and the profits of the firms. Show all work.