Question

Using an appropriate diagram, carefully explain why a natural monopoly cannot sell the socially optimal quantity of output at a single price. Also, explain how second-degree price discrimination can allow for optimal output without the need to subsidize the firm. Be sure to identify total revenue.

Answer 1

Natural Monopoly:

Monopoly market refers to a market with only one seller and many buyers. A natural monopoly is one where monopoly exists because of high fixed or start up costs due to unique raw materials or technology required. High start-up costs deter firms from entering the industry which results in a natural monopoly due to presence of natural barriers to entry. Fig 1 drawn below shows why natural monopoly cannot produce a socially optimal level of outcome. A natural monopoly has a downward sloping average revenue curve (AR) and a similar marginal revenue curve (MR) that is half of the AR curve. The profit maximizing condition requires marginal revenue to be equal to marginal cost (MC). Therefore the natural monopoly’s output is at the intersection of the MC and MR curve, denoted by Qm. The price charged by the monopolist is Pm, which represents the AR curve corresponding to Qm level of output. Since the monopolist charges this single price (and does not go for price discrimination), the quantity of monopoly output also remains the same.

The socially optimum level of output is produced when the market is in perfect competition. At that level, the price (P) is equal to MC i.e., P=MC. Thus Qs, the socially optimum level of output is at the intersection of the AR curve and MC. This is because, the AR curve (total revenue divided by quantity) is nothing but the price itself. Thus, when a natural monopolist is producing and selling at a single price and not practicing price discrimination, there is no way that it can produce a socially optimum level of output. It’s output level will be way below that of the socially optimum level.

Second Degree Price Discrimination:

Price discrimination refers to the act of charging different prices for the same product or service, to different customers, in order to maximize sales and also profit. Clearly, price discrimination is the opposite of charging a single price where the monopolist is in fact charging different prices as opposed to one particular price.

There can be three degrees or types of price discrimination. Among them, the second degree price discrimination is where the monopolist charges different prices for different quantities of goods or services consumed. The segregation of prices is done on the basis of quantities consumed. Unlike grouping of consumres as in the case of third degree price discrimination, here the quantities produced/sold are grouped and different prices are charged for different groups. The most common example is ‘bulk discounts’ where a consumer buying in bulk will get more discount and pay less price. That is, the same consumer buying more of the same good/service would have to pay less price for it. There is a ‘self selection constraint’ in this type of price discrimination where the consumer ‘self selects’ the price group he wants to place himself in, on the basis of quantity consumed.

This is shown in figure 2 where a monopolist practices second degree price discrimination. The MR and AR curves are identical to that shown above. The only difference is that the monopolist doesn’t charge a single price, but charges different prices for different blocks of quantity. The socially optimal level is again Qs which is at the intersection of the AR and MC curves.

The monopolist practicing second degree price discrimination charges price P’ for block 1 of quantity Q’. When Q’ rises to Q’’ to represent block 2, the price falls to P’’. Total revenue rises from triangle AB’C’ to AB”C”. When quantity further rises to block 3 at Q”’, the price falls to P”’. Total revenue rises to AB”’C”’. Finally, a price of P* makes the consumer buy Q* level of output which coincides with the socially optimal level of output at Qs. Thus, second degree price discrimination does allow for optimal output. Had this been the case of natural monopoly, then the ridiculously high start-up costs would have to be heavily subsidized to provide an incentive to the producer to produce that socially optimal level of output, at a single price. However, for the same monopolist practicing second degree price discrimination, the consumers self select their groups and the ones buying at P* allow the monopolist to produce and sell the socially optimum quantity level, without subsidizing it. In fig 2, the total revenue (TR) at socially optimum level is denoted by triangle ABC.