A block pricing monopoly sells electricity to identical customers. Each customer has a linear demand curve p = 180 - Q. The firm has a constant marginal and average cost of c = $60. There is no fixed cost.

(i) If the monopoly were required to set a single price that maximizes social welfare, what would be the price, and what would be the corresponding quantity supplied, denoted by QSW (2 marks).

(ii) Suppose that the monopoly is allowed to maximize profit, using declining block prices. Suppose for the moment that, according to the government's regulations, the firm can set only two block prices. The firm chooses Q1 and Q2 to maximize its profit, where the price per unit for the first block is p1 = 180 - Q1 and the price per unit for the second block is p2 = 180 - Q2. Write the firm's profit as a function of Q1 and Q2. (5 marks.) Next, find the profit-maximizing choice of Q1 and that of Q2. Derive the corresponding block prices, p1 and p2, and find the ratio (QSW - Q2) / QSW . (5 marks.)

(iii) Now, suppose the government changes its regulations, and allows the firm to set three blocks. Let Q1 denote the size of the first block, Q2 - Q1 the size of the second block, and Q3 - Q2 the size of the third block. Write the firm's profit as a function of Q1, Q2 and Q3, and solve for the optimal size of block 1, block 2, and block 3, and the corresponding per unit price for each block. Find the ratio (QSW - Q3) / QSW . (6 marks.)

(iv) How many units would be sold to each customer if the firm is allowed to set 60 different block prices? Find the ratio (QSW- Q60) / QSW . (2 marks)