Regulation

Assume a natural monopoly with total costs C = 500 + 20Q and the firm tries to maximize its profit. Market demand is Q = 100 – P . There are six “rich” consumers with each having inverse demands: p = 100 – 6.3q; also, there are four “pour” consumers, each with demands: p = 100 – 80q. The regulator bans third-degree price discrimination but allows any two-part tariff system. The monopolist will find the optimal two-part tariff that applies equally to both types (that is, only one pair of fixed fee and usage fee for both groups). To find the optimal two-part tariff, one possible approach is to exclude poor consumers. The other possibility is to keep all consumers in the market.

(a)  Find the optimal two-part tariff and profit for the case where the poor are excluded. Compute the sum of consumer and producer surplus minus the $500 fixed cost (that is, the find total surplus)

(b)  Find the profit and total surplus for the case of all consumers retained in the market. What is the optimal two-part tariff where all are retained in the market?

(c)  Compare the efficiency of the tariffs in parts (a) and (b). Hint: efficiency is measured in total surplus, not in profit.

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