4. [20 points] There are n firms in a competitive industry. The market demand function is given by p = 50 -2Q. A firm's cost function is C (q) = q'. The total surplus is given by S1 = 1(n+1)' 50'n . Suppose the government imposes a per-unit tar t > 0 on consumers. That is, for each unit of goods purchased, the consumer pays p + t. As a result, the market demand function becomes p +t =50-20. The tax goes to the government and firms only receive p for each unit of output sold. So the profit of a firm is pq - q2. Derive the total surplus, denoted by S2. Is S2 > S,? Explain the intuition of your