Nov 28

Shaked-Sutton model

The Shaked-Sutton model derives from a series of papers written by Avner Shaked and John Sutton. This model is centred in studying vertical differentiation and its role when discriminating the market, in order for firms to absorb as many consumers’ surplus as they can and the consequences this has for the market.

Vertical differentiation between products means discriminating goods as a result of their different qualities. Quality is a characteristic that all consumers want. Given the same price, higher quality products will always be chosen. However due to different income levels that vary from a to b, consumers will have different willingness to pay. This way, individuals with higher incomes will buy goods of higher quality paying a higher price, while lower income individuals purchase lower quality goods at a lower price. Given a higher spread of income between consumers, there will be a higher number of firms in the market each producing a different quality, and thus, making the number of firms in the market subject to the dispersion of incomes.

Firms will have to go through two key decision stages. In the first stage firms will have to choose the quality of their products, taking into consideration that higher quality goods have associated a higher production cost but are also preferred by consumers. Due to this firms are encouraged to produce higher quality goods as it will increase the competitiveness of their product. On the second stage firms will set their prices. Once the quality of the product is determined, firms will want to maintain the greatest differentiation for their product in order to raise their market power.

In markets with a great number of firms, competition between firms will be translated into a lower price for higher quality goods and will end up driving lower quality goods out of the market. A finite number of firms will exist in equilibrium depending on the size of the market and of the cost function associated to the firm. If the market is in equilibrium it will only allow as many firms as different demands of quality are.

Nov 22

Lope Gallego

Samuelson’s criterion

The Samuelson criterion, sometimes referred to as the Samuelson condition, was raised by the economist Paul A. Samuelson in his paper “Evaluation of Real National Income”, 1950, and belongs to the theory of welfare economics and used as a condition for the efficient provision of public goods. This critique provides a way to avoid intransitivity problems: state X will be preferred to Y if the alternative of X, X’, is preferred to the alternative of Y, Y’.

This criterion however, brings some limitations, since it is very similar to Pareto optimality. Samuelson explains that previous compensation criteria, such as Kaldor’s, Hicks’ or Little’s, hold just because they consider partial redistribution.

Nov 21

Lope Gallego

Little’s criterion

The Little criterion was developed by Ian M.D. Little in his paper “A Critique of Welfare Economics”, 1949, and it constitutes a further step for compensation principle theory. Little criticises the separation between efficiency and distribution and he demands as in Scitovsky’s criterion, for the Kaldor’s and Hicks’ criteria to hold. Furthermore, this criterion also requires that the income distribution is not worsened by the change of states.

This criterion however, brings some limitations, as a result of its implicit value judgement. The criterion will be met, if by a change of states the positively affected individual (winner) is poorer than the negatively affected individual (loser). As an example, let’s analyse the following graph, where we consider the utility of two individuals (A on the x-axis and B on the y-axis), which we will compare using the utility possibility frontier of two different moments.

Kaldor’s criterion is met when going from X to Y, Y to X or Y to Z, but not when going from Z to Y. However, Hicks’ criterion is only met when going from Y to Z. Therefore, when comparing state Y to Z, winners can compensate the loss of the losers, but losers cannot compensate the other part in order to avoid the change. This is the only case in our example where the Scitovsky criterion is met, making Z preferred to Y. However, Little’s criterion is only met if individual B is poorer than individual A.

Nov 20

Lope Gallego

Scitovsky’s criterion

The Scitovsky criterion was developed by Tibor Scitosky in his paper “A Note on Welfare Propositions in Economics”, 1941, in order to solve the inconsistencies, -known as the Scitovsky paradox-, that Nicholas Kaldor’s and John Richard Hicks’ criteria presented. In order to solve these inconsistencies, he required the fulfilment of both criteria simultaneously. As an example, let’s analyse the following graph, where we consider the utility of two individuals (A on the x-axis and B on the y-axis), which we will compare using the utility possibility frontier of two different moments.

Kaldor’s criterion is met when going from X to Y, Y to X or Y to Z, but not when going from Z to Y. However, Hicks’ criterion is only met when going from Y to Z. Therefore, when comparing state Y to Z, winners can compensate the loss of the losers, but losers cannot compensate the other part in order to avoid the change. This is the only case in our example where the Scitovsky criterion is met, making Z preferred to Y.

Scitovsky considered the possibility of changes in Pareto terms caused by state changes. This justified the dual requirements. Analytically,

Although this criterion brings some positive contributions, there are still only minor changes that furthermore need to meet conditions. The estimation of a potential Pareto improvement is yet to be answered. Nevertheless, the Scitovsky criterion contributes to an intransitive organisation of different states

Nov 19

Lope Gallego

Hicks’ criterion

The Hicks criterion is a compensation criterion developed by John Richard Hicks in his paper “The Valuation of the Social Income”, 1940. It is similar to that of Kaldor’s, with different implications although with the same limitations. In this criterion, state Y is preferred to X, if there is not a potential reassignment that turns X into Xˈ, that is at least as good as Y in Pareto terms. In the following graph we consider the utility of two individuals (A on the x-axis and B on the y-axis), which we will compare using the utility possibility frontier of two different moments.

When moving from state X to Y, individual A’s utility decreases while it increases for individual B. Due to this, individual A should compensate individual B so the change of states does not happen, going from X to X’, which will increase B’s utility as much as going from X to Y, while the drop in A’s utility would not be as large. The same would happen if moving from Y to X. Since this ex-ante compensation is possible, neither X is preferred to Y nor Y will be preferred to X.

When moving from state Y to Z, again individual A´s utility decreases while it increases for individual B. When going from Y to Z, there is no possible compensation from individual A to individual B, since to the left of Y the utility possibility frontier is always higher. Individual A therefore can not compensate individual B, so Z is preferred to Y in Hicks’ terms. However, when comparing movement from Z to Y, the opposite logically occurs. Individual A’s utility increases while individuals B’s decreases. Individual B would compensate individual A going from Z to Z’ , and hence Y is not preferred to Z.

If we compare this with Kaldor’s criterion we see some significant changes but still both criteria fall under the Scitovsky paradox. This paradox is centred in the phenomenon that while Y can be preferred to X the opposite can also be true. This does not give a truly asymmetric result as it could just mean that going back to the initial situation is preferred. The economy would therefore oscillate between both points.

Nov 18

Lope Gallego

Kaldor’s criterion

The Kaldor criterion is a compensation criterion developed by Nicholas Kaldor in his paper “Welfare Propositions of Economics and Interpersonal Comparisons of Utility”, 1939. This criterion is satisfied if state Y is preferred to state X and there is such a compensation and reassignment that Y turns to Yˈ that is at least as good as X in a Pareto sense. In the following graph we consider the utility of two individuals (A on the x-axis and B on the y-axis), which we will compare using the utility possibility frontier of two different moments.

When moving from state X to Y, individual A’s utility decreases, while individual B’s increases. Individual B is willing to compensate individual A and move to Yˈ where both increase their initial utility. The opposite, moving from Y to X, can also occur if the winner, this time individual A, compensates the looser, individual B, and is willing to relocate to Xˈ.

When moving from state Y to Z, the utility of individual A decreases, while individual B’s increases. Individual B is willing to compensate individual A and go to Zˈ where both increase their initial utility. On this case the opposite, moving from Z to Y, would not be feasible.

Tibor Scitovsky pointed out some inconsistencies and the consequent limitations of this criterion which are known as the Scitovsky paradox. This paradox is centred in the phenomenon that while Y can be preferred to X the opposite can also be true, as it was previously explained. This does not give a truly asymmetric result as it could just mean that going back to the initial situation is preferred. Economy would therefore oscillate between both points.

Nov 14

Lope Gallego

Compensation criteria

In welfare economics, compensation criteria or the compensation principle is known as a rule of decision for selecting between two alternative states. Two states will be compared; if one state provides an improvement for one part but causes deterioration in the state of the other, it will be chosen if the winner can compensate the loser’ losses until they situation is at least as good as in the initial situation. However, this compensation may not necessarily occur.

This neo-Paretian concept was developed in order to solve the dead end in which the Pareto criterion was at the moment due to its limitations. Although, in essence, the compensation principle reduces to the Pareto criterion, it values positively a wider set that allows a positive ordering without transgressing the Pareto optimal.

To this day there has not been yet a unique and definitive compensation criterion due to its limits and some of its paradoxical implication; on the contrary, a great number of similar criterions have been formulated. From them we must highlight:

Kaldor’s criterion, Hicks’ criterion, Scitovsky’s criterion, Little’s criterion and Samuelson’s criterion.

Nov 9

Lope Gallego

Salop’s circular city

Salop’s circular city model is a variant of the Hotelling’s linear city model. Developed by Steven C. Salop in his article “Monopolistic Competition with Outside Goods”, 1979, this locational model is similar to its predecessor´s, but introduces two main differences: firms are located in a circle instead of a line and consumers are allowed to choose a second commodity. Consumers will have to choose between buying one or none of the differentiated goods, and spending the rest of their income in the second, non-differentiated good.

In this circular model all firms that offer the differentiated goods are located on a circle of perimeter 1, equidistant from each other, and it is an outside firm that offers the undifferentiated good. Consumers purchase goods taking into consideration several aspects such as their preferred brand specification, the distance and transportation cost and their price, and so will act accordingly in order to maximize their utility.

We will designate x’ as the consumer’s preferred good, and x will be the least valued good. Consumers enjoy a surplus S when x’ is consumed instead of x. Knowing that consumers can buy x at location x_i for a price of p_i, we can equate a decision formula:

Taking into consideration transportation cost,

where x_i-x’ is the shortest arc length between x_i and x’. If we reformulate the first equation,

This way the effective reservation price v is given by,

Changing now our attention towards the firm’s perspective, there is a total of n firms, and we know that they are at an equidistant distance of 1/n from each other, spread around in a circle. Suppose firm A charged p while the rest of firms charged p*. In the absence of competition the maximum distance consumers are willing to travel T, which is equal to:

If L is the total number of customers in the market, the catchment area of a given firm in the absence of competition is defined by,

However competition is a condition that is given in this market and consumers will consume from the firm that reports the highest surplus. The quantity sold by firm A will be equal to,

It is a logical outcome that firms that have their price set above v will not sell their goods. Only when they lower prices below v will they start attracting consumers.

There will be a point where the price is low enough to overlap with neighbouring firms. If a firm keeps lowering its price it will even capture its competition’s customers.

The choice amongst firms is indifferent to client when the price is equal to,

To sum up, the number of firms in this market will depend on the degree of differentiation between goods, as well as price. We have here similar conclusions to those seen in the linear city model: there 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.

This model constitutes an important development from its predecessor, since it can be used to understand contestable markets and entry and exit barriers. It is considered, along with Harold Hotelling’s model, an important part of monopolistic competition theory.

Nov 7

Lope Gallego

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