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Nov 7

Hotelling’s linear city

Hotelling’s linear city model was developed by Harold Hotelling in his article “Stability in Competition”, in 1929. In this model he introduced the notions of locational equilibrium in a duopoly in which two firms have to choose their location taking into consideration consumers’ distribution and transportation costs. Hotelling’s model has been source of inspiration for a great amount of fruitful literature which does not only constrain to industrial organization theory but also to other sciences, such as politics, as some of its conclusion can be directly applied to them.

Initially the model was developed as a game in which firms first chose a location and after a selling price for their products. In order to set their business in the best location to maximize profits, the firms will have to evaluate three key variables: competitors’ location, customers’ distribution and transportation costs.

However, this model includes two different approaches, the first one being a static model consisting of a single stage were firms choose their location and prices simultaneously, and a dynamic model in which price is set after determining the location. The model is based on a linear city that consists of only a single straight street. For a better comprehension, Hotelling’s model is sometimes explained by using the example of a beach were two ice cream stands are trying to decide the best location.

Static model

In a beach going from west to east, of size [0,1] where consumers are distributed evenly, two identical ice cream stands (A and B) with a marginal cost of production, c > 0, try to determine their best location. A is located at a distance a from point 0, while B is located at a distance b from point 1.

It is indifferent for customers whether to go to one or the other stand, as long as their utility is maximized. For this reason, we must assume that both ice cream stands offer the exact same ice creams, and therefore consumers’ utility will be given only by the price of the ice cream and the distance to the stand. Despite differences in prices, the stand with the lowest prices will not necessary attract all the demand since consumers will also consider the distance to the stand.

If both stands’ prices were equal, the differential factor would be how close consumers are to each stand. All consumers located to the left of a would go to stand A, and all consumers located to the right of 1-b would go to stand B. The remaining consumers, located between both stands would go to whichever is the closest. In this first model, is the exact middle of that beach, so consumers to its left would go to stand A while consumers to its right would go to stand B.

Two conditions are necessary for profits to be positive and maximized in both stands:

-Selling prices must be higher than marginal costs

–

This second condition implies that both stands can’t be located at the same point exactly in the middle of the beach. If this were the case it would be indifferent for the customers to go to either one. Each stand would decrease its prices in order to attract customers, and thus they would enter into what is referred to as a price war. If they had different marginal costs, the stand with the highest marginal cost would be in a clear disadvantage and would end up exiting the market, as the other stand would be able to push the prices further down, and so attract all customers. Depending on how prices are set it could lead to a Bertrand’s solution, in which the prices of both stands are equal to their marginal costs, thus achieving zero profits.

We can conclude by saying that in this model the key factor for product differentiation is location. Each stand will therefore set prices that will be higher than their marginal costs, and will choose a location other than the middle of the beach.

Dynamic model

In this case, the model has two stages. During the first stage, the stands chose their location and on the second stage prices are set. With regards to the previous model there are two additional assumptions:

Both stands have equal marginal production cost.

Total cost for consumers depends both on the price of the goods and the distance to its location (t).

The point of division between the areas served by these two stands is determined by the condition that at a certain point it is indifferent for consumers between consuming in one stand or the other. Equating and equalising we get

By solving, the demand function for each stand will be:

By using backwards induction we can find the subgame perfect Nash equilibrium where both firms maximize their profits.

Stage 2: having already determined a location the stands will now have to set the price that will report the highest possible profits. This will lead us once again to the static model result, in which each stand sets its own price.

Stage 1: the stands anticipate and choose their location. Profits will be higher the less distance there is to the extremes, therefore maximum differentiation between stands will be given when A locates at 0 and the B at 1.

The conclusions that can be drawn from this model are two opposite effects. On one hand, there is an incentive for both stands to locate at the centre of the beach in order to increase their market share by reaching out to the greatest amount of customers, in what is known as the demand effect. And, on the other hand, there is an incentive for both stands to locate at opposite extremes in what is considered to be the strategic effect. While the first effect will reduce differentiation between the stands, the second one will increase it.

In politics we can observe how candidates follows this demand effect, as they tend to come from a specific ideology but tend to convey towards a moderate ideology with the objective of attracting as many voters as possible.

Nov 6

Lope Gallego

Public goods

Public goods are those that are non-rival and non-excludable in consumption. Being non-rival implies that even if someone consumes it does not prevent someone else from doing it as well. Being non-excludable implies that no one will be prevented from consuming the good due to impossibility or because of a high price.

We can find an example of a non-excludable but rival good in a crowded street: it can be used by anyone but its use can be sometimes limited. On the other hand we use a coded television broadcast as a non-rival but excludable good: someone consuming it does not prevent someone else from doing so.

Finally to define a public good we may use the classical example of fireworks or street lights, once they are set they become non-rival and non-excludable and hence public goods. Nevertheless it is important to bear in mind that there can be different degrees of public goods. We can distinguish between pure public goods which are perfectly non-rival and non-excludable and between impure public goods which are rival and/or excludable to some extent. While pure public goods perfectly follow the non-rival and non-excludable condition, impure public goods are rival and/or excludable to some extent.

Normally these goods have to be provided by the public sector as the private sector is not interested in them due to the lack of profits. National defence, justice and public transportation, are just some examples.

Paul Samuelson’s work, specially his article “The Pure Theory of Public Expenditure”, 1954, is considered as the starting point of the development of the theory of public goods, as he formulated the efficiency condition for these goods.

The gratuity problem arises since once a public good has been produced and due to its characteristics (non-rival and non-excludable), anyone can enjoy it independently of who financed its production. In essence this problem is reduced to asymmetric information as people can hide their true preferences and this way they can still enjoy the good even if they don’t pay for them or pay much less

Nov 2

Lope Gallego

Chamberlin’s monopolistic competition

The Chamberlin´s model analyses and explains the short and long run equilibriums that occur under monopolistic competition, a market structure consisting of multiple producers acting as monopolists even though the market as a whole resembles a perfectly competitive one. The economist Edward H. Chamberlin gives name to this model, which he developed in his book “Theory of Monopolistic Competition”, 1933.

Assumptions

Chamberlin made a set of assumptions that were necessary for this market to perform properly. These assumptions include:

The existence of a set of products that the consumers perceive to be close substitutes. The crossed elasticity of these products is high but never infinite.

Each firm monopolises a product, although it shares the market with the rest of the industry.

There are a great number of firms in the market.

No entry or exit barriers to the market.

Full mobility of factors.

There is some degree of agent myopia in the sense that they do not learn from past errors.

Perceived vs actual demand

Chamberlin introduced in his model a distinction between perceived and effective demand curves. On the one hand, perceived demand, d in the adjacent figure, is the demand the firm is planning to supply or, in other words, how the firm believes customers will act to respect of its product. On the other hand, effective demand, D, is the way in which the market will act, in other words, how customers will act based on their perceptions on the market. However, consumers will always choose the best price and the greatest possible quantity, hence choosing always to be on what is called actual demand (green).

Equilibrium in the short-run

In the short-run, as shown in the second figure, each firm will act as a monopolist in its market. Given their demand and cost curves they will maximize profits by producing the level of output at which marginal cost equals marginal revenue. Whether they make profits or not will depend on the cost structure. In our example, there are no profits.

Equilibrium in the long-run

In the long run, the cost structure of the firm varies, allowing it to lower its prices in order to attract more customers. Lets start analysing the equilibrium in the long run considering the firm is in this situation of equilibrium (A), and because of its profits, it has no incentives for changing its price. However, the extraordinary profits that the firm is making will attract new competitors to the market. Although aggregate demand in the market is maintained, the entrance of new firms will translate into a fall of the effective demand of the firm. This drop in the demand of the firm is illustrated by the shift of the demand curve to the left, from D to Dˈ and a new equilibrium point will be reached at B.

However the firm will want to recover its previous profits levels and will therefore lower its price seeking to attract customers. The rest of firms will follow the same strategy so no customers are lost, and therefore the changes in its competitors and own strategies will change the perceived demand of the firm, from d to d’. A new equilibrium will be reached at C but this time firms will be incurring in losses, as price will be below average cost. This loss of profits will cause the exit of firms from the market, displacing effective demand rightwards and perceived demand downwards, as each firm that remains in the market will increase their individual demand. This process will be repeated until the equilibrium point is reached, from D to D*. At this equilibrium point, E*, the demand curve will be tangent to average cost in the long-run and price set at this level. Profits will be equal to zero and hence no entry or exit of firms will occur.

Main conclusions

Chamberlin’s monopolistic competition model analyses a whole new market structure, apart from the classic monopoly and perfect competition. It demonstrates that in a market the number of firms can be irrelevant, and perfectly competitive results can be reached. In fact, in terms of welfare and product differentiation, monopolistic competition is desirable.

It’s worth mentioning that these results are similar to those of William Baumol’s contestable markets, since the number of firms in the market does not necessarily determine how competitive it is. Also, the results are contrary to the results found in Bertrand’s duopoly model.

Nov 2

Lope Gallego

Product differentiation

Product differentiation is a marketing process that has the objective of making customers perceive the product of a specific firm as unique or superior to any other product belonging to the same group, and so creating a sense of value. Differentiation does not always imply changing the product, sometimes it is enough just by simply creating a new advertising campaign or by changing its packaging. This term was introduced in economics by Edward H. Chamberlin in his book “Theory of Monopolistic Competition”, 1933.

What a firm achieves by differentiating its product from competitors is to create a market in which it can act as a monopoly, enabling them to have price-making power. However, since products are also similar enough and there are plenty of customers, this type of market structure is also considered as perfect competition. This market is therefore characterized by a group of related products that can be considered to be close substitutes amongst each other which is reflected by their high crossed elasticity. Nevertheless, product differentiation can also be a way to avoid or to create entry barriers and thus become a source of competitive advantage. As a product becomes more differentiated and unique for consumers, it will become more difficult to compare it to other products and it will move competition with other products to non-pricing factors.

There is an important distinction to be made between different differentiation strategies. Product differentiation can be subject to subjective or objective preferences. Two categories are distinguished from this division, horizontal and vertical differentiation. The former is given when consumers base their purchasing decision on subjective preferences when comparing products, e.g. colours or flavours. The latter occurs when a product can be evaluated against the other ones in terms of measurable and qualitative factors, e.g. technological differences or technical properties in engines. Several models have been developed to analyse these two strategies, the most famous being Hotelling’s linear city model and its extension, the Salop’s circular city model, for horizontal differentiation and the Shaked-Sutton’s model for vertical differentiation.

Oct 9

Lope Gallego

Microeconomics

Microeconomics is a branch of economic theory that is centred in modelling the interactions amongst market agents, specially between consumers, which are trying to maximise their utility, and firms, which try to maximise their profits. It analyses the underlying logic of the individual behaviour of economic agents such as the employer, the consumer, etc., and the notions that derive from them, such as, profit, utility, market structures, etc. In its purest form it answers the philosophical question regarding the resources allocation process.

The line that separates microeconomics from macroeconomics has become increasingly narrow throughout time. Nevertheless, it has always existed, and most probably will always exist, as some barriers are insurmountable. The goal of macroeconomics is to understand and predict the behaviour of economic variables in its aggregate terms. Therefore we make the distinction of microeconomics as relating to individual, micro, terms (consumers, firms, etc.), while macroeconomics relate to aggregate, macro, variables (consumption, unemployment, investment, etc.). A way to view both terms is from a disaggregated vs. aggregated perspective.

The methods and tools used in microeconomics are mainly the construction of models that simplify the reality so that the interdependence between variables can be analysed and represented. Many techniques may be used for the construction of these models; however, the great majority of them fall into the categories of optimisation analysis and equilibrium analysis. Furthermore, models of optimising behaviour represent nearly all of the models of individual behaviour in microeconomics.

Sep 27

Lope Gallego

Transaction costs

Transaction costs are the associated costs that derive from the formalisation of complex relationships that necessarily exist for the production of goods and services. As an example, transactions cost can occur during the processes of negotiation, search, determination of prices, etc.

Ronald H. Coase developed a theory regarding industrial organisation, and specifically business formation, in which transaction costs play a main role. In his book “The Nature of the Firm”, 1937, he explained why productive individuals find it beneficial to form coordinating agencies (firms) as a reaction to transactions costs. Instead of individuals operating independently, and repeatedly incurring in numerous transaction costs, they could work in a global framework, and at the same time they could benefit, amongst other things, from learning and experience curves and from economies of scale.

Sep 25

Lope Gallego

Market failure

Market failures appear whenever a market is unable to work “successfully”, meaning it cannot achieve equilibrium with an efficient allocation of resources, which is known as Pareto efficiency. This imperfection in the price assignment system prevents an efficient resource allocation, and thus, government intervention is considered necessary and justified. Although the concept has been around since Adam Smith, it is unclear who coined the term, even though F. Bator was probably the first economist to use it, in his paper “The Anatomy of Market Failures”, 1958. The most common ways in which market failure appears are externalities, public goods and information asymmetry:

-Externalities are caused when the production or consumption of a good or service has a spill-over effect which is not fully reflected in its price and so no appropriate compensation is paid for it. If the price does not include the true cost of the good or service it will be incurring in market failure. It is important to point out that externalities can be either positive or negative. To prevent negative externalities, governments may add specific taxes to the goods or services to cover its social cost.

– Public goods are defined as non-excludable and non-rival goods, which are the main reasons why the private sector may find it impossible, or at least very difficult, to make an economic profit from producing the goods. Consumers can become as what is known as free riders as they can enjoy the good without paying for it. Due to the poor incentives of the private sector to produce these kinds of goods, it relies in the public sector to provide them.

-Information asymmetry is understood as the difference of information levels between different parties. If one of the parties has more information than the other, it can use it to its advantage and so causing the transactions to be unfair. This kind of information asymmetry may lead to adverse selection and moral hazard, which will lead to market failures. The government can use several measures in order to reduce this kind of market failure, such as, collection and provisions of information, product standards, warrants, etc.

Sep 22

Lope Gallego

Ceteris paribus

Ceteris paribus is a Latin phrase that translates as “other things the same” and is a frequently used expression in economics. It refers to a phenomenon in which two or more variables intervene and for which it is assumed that, with the exception of the variable that is under study, the rest remain constant and stable, e.g. if the price of rice decreases, ceteris paribus, the demand for it will increase.

It is widely used in marginalism and macroeconomics, its use becoming popular thanks to the English economist Alfred Marshall.

Jun 3

Lope Gallego

Exit barrier

Exit barriers (or barriers to exit) are obstacles that stop or prevent the exit of a firm from a specific market. It is associated with firms that are incurring in some form of losses, but cannot exit the market as a result of exit barriers that would further increase their level of loss. In Michael Porter’s model of competitive analysis, barriers are a fundamental element to gauge the level of competition in a sector, and defines the market structure in that industry. He identified the following exit barriers:

Non-transferable assets: when a firm invests on specialised assets, which cannot be used in other industries, exiting the market implies losing those assets.

Fixed exit costs: such as indemnities paid to employees, cancelation costs in contracts with suppliers, etc.;

Synergies: when producing one good allows for lower costs in the production of other goods, exiting an industry may imply higher costs when producing that good.

Although barriers may have negative consequences for some firms, for others they will be positive. Where some firms loose other win, it can be regarded as a zero-sum game. For abnormal profits to occur in a market, barriers have to exist. Using Joe Bain’s definition, “barriers give firms the power to maintain in the long-term prices higher than average cost”.

Jun 3

Lope Gallego

Entry barrier

Entry barriers (or barriers to entry) are obstacles that stop or prevent the entrance of a firm in a specific market. It is associated with the situation in which a firm wants to enter a market due to high profits or increasing demand but cannot do so because of these barriers. In Michael Porter’s model of competitive analysis, barriers are a fundamental element to gauge the level of competition in a sector, and relates to the market structure. Here are some of these entry barriers:

Economies of scale, economies of scope: any of these could be necessary to enter an industry, since fewer costs can mean the possibility to remain in that industry;

Product differentiation: if incumbent firms in the industry have from customers a certain degree of loyalty towards their products, differentiation may be its origin;

Minimum capital requirements: in some industries, high investments may be needed in order to be able to produce;

Complicated change of supplier: if our potential customers find it hard to change suppliers, they might not be willing to change;

Access to distribution channels: of special interest when considering consumer goods, it means that getting the distribution channels to distribute your product may prove hard;

Costa advantages other than economies of scale: such as technology, know-howor simply because of the learning curve;

Government regulation: requirement of permits or licenses such as construction permits or taxi licenses;

Expected reaction from incumbents: if price wars or predatory pricing is expected, this could act as a barrier to entry.

The figure below shows the relation between entry barriers and market structure: