Problem 1 Two firms produce the same good; y1 denotes the output of firm 1 and yz the output of firm 2. Production is free up to a maximum determined by capacity constraints. Producing above that level requires heavy investment and is therefore exceedingly expensive. Specifically, the total cost functions faced by the firms are 0 if y1 $ 7. C1(y1) = 1 100 if y1 > 7 for firm 1 and C2 (32) = 1 0 if yz $ 2. 100 if yz > 2 for firm 2. Note that firm 2 faces a tighter capacity constraint. The market inverse demand function is p = 12 - y1 - 92. The firms choose their production levels simultaneously and independently. (a) Write down the profit functions of the two firms. (b) Compute their best reply functions. (c) Determine the Cournot-Nash equilibrium production levels