May 22

Edgeworth duopoly

The Edgeworth duopoly model, also known as Edgeworth solution, was developed by Francis Y. Edgeworth in his work “The Pure Theory of Monopoly”, 1897. It is a duopoly model similar to the duopoly model developed by Joseph Bertrand, in which two firms producing the same good compete in terms of prices. Edgeworth’s model presents a slight modification as it also includes constraints in the production capacity of the firms. In this market structure, firms have two potential options, to collude or not.

As shown in the adjacent figure, when firms choose to collude they will split and share the market and the production of the good. Firm₁ will produce from O to F and firm₂ from O to G, in this way the supply is limited and prices will be set at p. Revenues of each firm correspond to the rectangle above FO and OG, and each firm would enjoy an equal share. Note that d₁ and d₂ are parts of total demand, each part being supplied by one of the firms.

Collusion is not always possible as firms have incentives to break cooperation in their search for higher profits. Collusion is also considered an illegal business practice in many countries. Eventually one of the firms will decide to lower their prices and increase production in order to gain market share from the other competitor. Consequentially the other firms will do the same. This process will escalade up to the point in which the maximum production of both firms is achieved. When this point is reached (OD for firm₁ and OE for firms₂), price will not be reduced any further and will remain at p’, as the increase in demand that follows price reduction will not be satisfied with a larger amount of production. On the contrary, prices will start to rise little by little so firms will be able once again to increase their profits. Overtime this process will be repeated and prices will oscillate from p to p’.

The following figure shows how all this translates into market demand (D), and how quantities sold will oscillate from Q and Q’.

Overall the Edgeworth’s solution is a more realistic one than Bertrand’s and it answers Bertrand’s paradox. However, it does not give a definitive solution.

May 17

Lope Gallego

Two-part tariff

A two-part tariff is a price discrimination technique that consists in charging consumers with a lump sum fee for the right to purchase the product and then a price per unit consumed. This practice is specially used in places such as golf clubs and amusement parks.

The firm must set the enrolment fee and the price per-unit of the product that maximises its profit. To maximise the amount of product purchased by consumers the firm must set a price that is equal to the marginal cost. Subsequently, the firm will appropriate consumer surplus by setting a fixed fee, A. The first tariff would be the entrance fee, A, which allows the monopoly to extract all consumer surplus. The second tariff is the price per unit, p*q, being this price equal to marginal cost, which means that there is no surplus, since the surplus cannot be extracted twice.

As it can be seen in the figure below, which shows two different demand curves for two types of consumers who have different willingness to pay, there are different ways to implement a two-part tariff. Monopolies can charge different entrance fee for each consumer according to their willingness to pay, extracting all the consumer surplus (grey area). However, since this is quite the same as first-degree price discrimination, it is hard to implement. When monopolies are unable to distinguish between different types of consumers, they can charge an entrance fee high enough so only the more exclusive, more willing to pay consumers get the product (green). The monopoly will extract all the consumer surplus of the first type of consumer, but won’t sell at all to the second type. Finally, the monopoly can charge the same entrance fee to both types, but that entrance fee will be that of the less willing consumer, A₂, charging the same to the other consumer, A₁ (blue). As it can be seen, in this case the monopoly will be able to extract more total consumer surplus by increasing prices from p to p’: it will extract less from the second type of consumer (area -) but will extract even more from the first type of consumer (area +).

May 16

Lope Gallego

First-degree price discrimination

First-degree price discrimination, or perfect discrimination, is the highest level of price discrimination, in which each unit of production is sold at the maximum price that the consumer is willing to pay for that specific unit. The firm will gain the entire market surplus it could possibly achieve, as it will sell all the units for the maximum price at which they could be sold.

This degree of price discrimination will always have as a result a Pareto efficient level of output as marginal willingness to pay will be equal to marginal cost. For this reason and even though monopolies are associated with this strategy, the production level of output will be the same as in a competitive market, and hence, the inefficiency associated to monopolies will be eliminated. As seen in the adjacent figure, the producer surplus equals total surplus (A+B). There is not deadweight loss, even though there is not consumer surplus (A, which was extracted by the monopoly), and at the end both quantity and price are equal to those that would result from perfect competition.

First-degree price discrimination is, however, quite unrealistic. On the one hand, income elasticity of demand should be equal to zero in order for perfect discrimination to work. On the other hand, there should be imperfect information in the market, since consumers knowing that the price would drop if they showed lower willingness to buy would make them show it, thus making impossible for the monopoly to practice first-degree price discrimination. Knowing the distribution of consumers’ preferences is almost impossible to determine and it is certainly expensive to research. Therefore, in real life, the closest thing there is to perfect discrimination is bargaining reductions in prices (known as second-degree price discrimination) or offering a two-part tariff.

May 16

Lope Gallego

Second-degree price discrimination

Second-degree price discrimination, or nonlinear pricing, involves setting prices subject to the amount bought, in an attempt to capture part of the consumer surplus. Revenues collected by the firm in this matter will be a nonlinear function. A bulk sale strategy, such as quantity discounts, will be applied and consumers will choose the block that better suits them.

Consider the adjacent figure: a monopoly will be able to implement this type of price discrimination to a certain consumer by offering discounts for buying a higher quantity. Note that d corresponds to the consumer’s demand curve, not the market’s. By offering a lower price, p2, for quantity q2, the monopoly is able to extract part of the consumer surplus. This price discrimination works similarly to a two-part tariffs. However, in this case, the monopoly won’t charge an entrance fee, but will hide this entrance fee into part of the discounted price offered to the consumer.

May 16

Lope Gallego

Third-degree price discrimination

Third-degree price discrimination, also referred to as market segmentation of price discrimination, consists of varying prices depending on what segment of the market the consumer belongs to. Each consumer will be charged with a different price, but it will remain constant whatever the amount bought. This degree of discrimination is the most commonly used by firms and it includes examples such as students or third age discounts.

As shown in the figure above, the firm will disaggregate the global demand, and it will charge each market segment the price that will maximise its profit. Higher prices will be charged to those segments where the elasticity of demand is lower. In this case, we have

May 16

Lope Gallego

Price discrimination

Price discrimination, also referred to as price differentiation, occurs when a firm sells the same product at different prices, either to the same or different consumers. The study of this strategy comes naturally when dealing with monopolies as these seek to sell additional output to consumers without lowering the price of the units that are already being sold so as to maximise their profits. Good examples of price discrimination are transportation or storage costs. To optimise price discrimination, firms will have to control and prevent reselling, and they will also have to sort consumers depending on their willingness to pay. The former does not generally imply complications, but sorting consumers is a more complex process.

Arthur C. Pigou made a distinction between different levels of price discrimination in his book “The Economics of Welfare”, 1920. The first degree or perfect discrimination is given when the monopolist charges each unit with a price that is equal to the consumer’s maximum willingness to pay for that unit. The second degree or nonlinear price fixing is given when price depends on the amount bought by the consumer as in quantity discounts. Finally, the third degree or market segmentation of price discrimination occurs when there are several differentiated market segments to which the firm will apply different prices, e.g. student or third age discounts.

May 13

Lope Gallego

Natural monopoly

Natural monopolies occur in those industries in which the total costs of production are lower if a single firm produces the whole output instead of having production divided amongst more than one firm. Although this is the usual definition, which is attributed to William Baumol, who provided it in his article “On the Proper Cost Tests for Natural Monopoly in a Multiproduct industry”, 1977, natural monopolies have been studied since the time of John Stuart Mill and Alfred Marshall. In 1923, economist J.M. Clark greatly contributed to the understanding of natural monopolies in his book “Studies in the Economics of Overhead Costs”, explaining how in manufacturing industries, since overhead costs are a significant fraction of total costs, a high number of firms will not mean lower prices.

Natural monopolies are brought by economic and technical reasons, such as high capital costs, economies of scale and other barriers to entry, and not by legal imperatives. Public utilities such as electricity and water services are some of the most common examples. Natural monopolies are characterized by subadditivity of a representative firm’s cost function. Subaddititvity will exist when

which is the essence of the idea behind natural monopolies. The demand function plays a key part in subadditivity and hence, the existence of natural monopolies depends on its position, and whether it will be more or less efficient, to have a single firm or more in the market.

However, subadditivity is considered a necessary but insufficient condition for a natural monopoly to be considered optimal, whereas if economies of scale exist, this is a sufficient but not necessary condition for a natural monopoly to be sustainable. Consider the figure below. The cyan demand curve, within the economy of scale region, indicates a viable natural monopoly. The red line would indicate a non-sustainable natural monopoly. The black line indicates the frontier of a profit generating monopoly (which would attract competitors) and the green line indicates a viable duopoly.

As in most imperfect competition market structures and especially in monopolistic ones, a firm who is in a position of natural monopoly may practice an abusive behaviour, which will translate into a loss of welfare. In such cases, government intervention will be praised both by consumers and those firms that seek for lower prices and a profitable share of the market. Regulations such as price setting, taxation or subsidies may be used in order to restore and maximise the initial efficiency of natural monopolies.

Nevertheless, the government must be cautious when setting and applying regulations, as an incorrect comprehension of the market structure may bring a higher cost to the total social welfare instead of the expected benefits. In order to achieve an optimal regulation level, governments should analyse and determine if natural monopolies can be sustained whenever they ensure a lower total cost. If this is the case, the government will have to guarantee that the firm earns no excessive revenues, and that fair prices are maintained. If on the contrary, the total costs of the industry would diminish if new firms entered the market, the government should regulate their entrance. Essentially, what governments should do is to correctly balance the conflict between the industry’s efficiency and its profitability.

May 10

Lope Gallego

Lerner index

The Lerner index measures a firm’s level of market power by relating price to marginal cost. When either exact prices or information on the cost structure of the firm are hard to get, the Lerner index uses price elasticity of demand in order to measure market power: the Lerner index is equivalent to the inverse of the elasticity in its absolute value faced by the firm when price is set to maximise profits. Both formulas are equivalent:

Economist Abba Lernerdeveloped this relationship in his article “The Concept of Monopoly and the Measurement of Monopoly Power”, 1934. This was Lerner’s first major article on welfare economics, in which he introduced the idea that monopolies are a matter of degree, stating that their power depend on the excess of price over marginal costs, discussing also Pareto optimality and loss of total welfare in monopolies.

The extent to which a firm can take advantage of its monopolistic condition will highly depend on the flexibility of its demand curve. If it is more rigid (steeper), it will only have to reduce its production in order to achieve a higher price. However the more flexible (flatter) the demand curve is, the less market power the firm has to increase prices.

Therefore, Lerner index will always be between 0 and 1: the closer it is to 0, the closer it is to perfect competition; the closer it is to 1, the higher market power the seller has and hence closer to a monopoly. A monopolist seeking to maximise profits will never be on the inelastic part of the demand curve, E < 1, which is why elasticity will always be such as ∞ ≥ E ≥ 1.

May 9

Lope Gallego

Bilateral monopoly

Bilateral monopoly is a market structure in which there is only a single buyer (monopsony) and a single seller (monopoly). Game theory is frequently used when analysing this kind of market structure. Analysing bilateral monopolies becomes relevant when analysing factor markets, specially when analysing the labour market.

Depending on which side has greater negotiation power there can be different outcomes that resemble more or less its two extreme possibilities, as shown in the adjacent figure. The obvious and antagonistic scenarios that can result in this market are monopsony and monopoly. When the demand side holds all the negotiation power we will be dealing with a monopsony-like situation such as m, where price P_m is lower than the monopolist price (P_M) and the price of a perfectly competitive market (P_PC). When negotiation power is held by the supply side, the monopolistic firm will sell less quantity (Q_M) than the monopsonist would buy if it had more power (Q_m). However, when the bargain power is equally shared between the two sides there may be joint profit maximisation, which can be done by colluding, or even vertical integration may occur if both firms merge, which would get both firms to jointly get an equilibrium corresponding to perfect competition (C). A bilateral monopoly, however, will have worse results for both firms. The quantity sold will be very low (Q_BC) at a rather low price (P_BC).

A bilateral monopoly can also be considered as a firm that has high negotiation power with its clients, which would get the firm to be considered as a monopoly, and high negotiation powers with its suppliers, which would mean the firm is also a monopsony. Consider as an example Standard Oil, back in the days before its breakup. In 1911, the United States Supreme Court ruled that the company was an illegal monopoly. However, Standard Oil could also be considered as a monopsony: being the biggest oil corporation in the US, it had incredible power when negotiating prices with its suppliers when acquiring parts for its refining factories.

May 8

Lope Gallego

Multiproduct monopoly

Multiproduct monopolies are those monopolistic firms that sell, at least, more than one product. The firm will have to take into account how a change in the price of one of its products affects the demand of the rest of them, especially when they are complementary or substitutive goods. The magnitude of the cross elasticity of demand will be of great importance as it will measure this effect. The multiproduct monopoly will maximise its profits as:

It is noteworthy to comment the different effects that an increase in price of one product will have in the rest of the products depending if they are substitute or complementary goods. For substitute goods the loss of demand in the market when prices are raised will be balanced by the increase of demand of the other good as consumers will just switch to the other product. However, for complementary goods the loss of demand will be amplified in the other market. To understand this second effect let’s think of petrol and cars. When price of petrol increases, demand for cars will be negatively affected as their overall cost will be increased.

Multiproduct monopolies can set prices to each of its products either jointly, or by division, each division setting the price for the product it sells. If the goods are substitutes, and each division sets the price, prices will be low, since each firm has an incentive to lower the price and steal some sales from other divisions, thus behaving as oligopolists. This is commonly known as cannibalization. Therefore, a multiproduct monopoly producing substitute goods must set its prices jointly.

If the multiproduct monopoly sells goods that are perfect complements, it must take into account the necessity of setting the right price in order to sell both products. When each division sets these products’ prices separately, these divisions will have an incentive to increase the price, acting as a regular monopoly, which will increase the total price of both products. If set jointly, the price of each product will be lower, but total profits will be higher. Therefore, for both complementary and substitute goods the multiproduct monopoly should set its prices jointly.