Question is attached. Please show working for calculations. Explanation in words not necessary!

A block pricing monopoly sells electricity to identical customers. Each cus tomer has a linear demand curve p = 180 Q. The rm has a constant marginal and average cost of c = $60. There is no xed 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 prot, using declining block prices. Suppose for the moment that, according to the government's regu lations, the rm can set only two block prices. The rm chooses Q1 and Q2 to maximize its prot, where the price per unit for the rst block is p1 = 180 Q1 and the price per unit for the second block is p2 = 180 Q2. Write the rm's prot as a function of Q1 and Q2. (5 marks.) Next, nd the protmaximizing choice of Q1 and that of Q2. Derive the corresponding block prices, 191 and p2, and nd the ratio (st Q2) g. (5 marks.) (iii) Now, suppose the government changes its regulations, and allows the rm to set three blocks. Let Q1 denote the size of the rst block, Q2 Q1 the size of the second block, and Q3 Q2 the size of the third block. Write the rm's prot 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 Qsl/st- (6 marks.) (iv) How many units would be sold to each customer if the rm is allowed to set 60 different block prices? Find the ratio (st Q60)g. (2 marks.)