Under a single-rate electricity tariff for households and small businesses in Australia, a flat usage rate is charged for "blocks" of electricity consumed. The rate for the first block is higher than that for the second, and the lowest rate applies to electricity usage in excess of the second block. Suppose the inverse demand curve for a typical consumer is \(p=30-Q / 3\), where \(p\) is cents per kilowatt hour \((\mathrm{kWh})\) and \(Q\) is \(\mathrm{kWh}\) per day, and the profitmaximizing monopoly has a constant marginal and average cost of 20 cents per \(\mathrm{kWh}\).

a. What is the quantity where price equals marginal cost?

b. What would be the optimal quantity and price and the firm's profit, consumer surplus, and deadweight loss if the monopoly could set only a single price?

c. What would be the firm's profit, consumer surplus, and deadweight loss if the consumer uses \(20 \mathrm{kWh}\) of electricity per day when the monopoly charges 26.67 cents/kWh on the first block of \(10 \mathrm{kWh} /\) day, 23.33 cents/ \(\mathrm{kWh}\) on the second block of \(10 \mathrm{kWh} /\) day, and 20 cents/ \(/ \mathrm{Wh}\) on the remaining usage?

d. Comparing your answers to parts \(\mathrm{b}\) and \(\mathrm{c}\), would the typical consumer be worse off with declining block pricing?