Sylos Labini’s Model Of Limit Pricing

Introduction

J. S. Bain in his pioneering work ‘A Note on Pricing in Oligopoly and Monopoly‘ (1949) followed by his book ‘Barriers to New Competition’ developed the theory of limit pricing. The theory of limit pricing is also known as Entry-preventing Pricing.

The theory of Bain’s limit pricing has been further developed by Sylos-Labini, Modigliani and Jagdish Bhagwati. Sylos Labini further modified the limit pricing theory, whose basis was laid by J.S. Bain.

According to him, limit pricing laid special emphasis on the economies of scale barriers to entry of potential firms. His analysis of the economies of scale barriers to entry is more thorough than that of Bain. He also propounded a postulate about the behaviour pattern of established firms as well as the potential firms and it is known as Sylos postulate.

Sylos-Labini’s Theory of Limit Pricing

Sylos-Labini laid special emphasis on the economies of scale barriers to entry of potential firms. He assumed a given market demand curve with unitary price elasticity of demand. The products produced by the firms are homogeneous and are being sold by a few firms with a price leader firm.

He also assumed that three different sizes of plant size are available with which various firms are producing products. The different types of plant sizes that are available are small, medium and large size. A small plant is available with a capacity of 100 units of output, a medium-sized plant with a capacity of 1000 units of output, and a large-size plant with a capacity of 8000 units of output.

Each firm can expand by multiples of its initial plant size only. The small firm can expand by installing another small-size plant; a medium firm may expand by setting up a second medium-size plant, and so on. The economies of scale accrue as the size of the plant increases.

It is assumed that the nature of technology is rigid, and the continuous long-run average cost curve cannot be drawn. The long-run average cost curve would be straight line curves. We have three cost lines corresponding to the three plant sizes and the larger the plant size, the lower the long-run average cost.

The most important feature of the Sylos Labini model is the existence of a price leader firm. The price leader firm is the most efficient firm with the lowest average cost of production. The price is set by the price leader, who is the largest firm. Except for price leader firms, all other firms are so small that they cannot affect the price, i.e. they are price takers and not price makers.

However, collectively small firms may put pressure on the leader by regulating their output. The price leader firm sets a price that is acceptable to all the small firms in the industry, but the price that is set by the leader firm must be low enough to prevent the entry of new firms. The leader is fully aware of the cost structures of all plant sizes and the market demand for the product. Sylos Labini also assumed that the entrant is assumed to come into the industry with the smallest plant size.

The established firms and the potential firms behave according to what Modigliani called the ‘Sylos Postulate’. He made an important behavioural assumption concerning the expectations of the established firms and the potential entrants.

Firstly, the existing firms expect that the potential entrant will not come into the market if he thinks that the post-entry price will fall below his average cost of production.

Secondly, the new entrant expects that the established firms will continue in the post-entry period to produce the same level of output as in the period before entry so that as entry takes place, the market price falls and the whole of the resulting increase in the quantity demanded accrues to the new entrant.

Clearly, this is the same as Bain’s Model. Sylos has not given any reason for his behavioural pattern. The rationalization of Sylos’s postulate has been discussed by subsequent writers.

Limit Price Fixation

In this section, we will see how the limit price is determined under the Sylos model. Sylos assumed that there is a normal rate of profit which must be earned by the firms in order to remain in business in the industry. The minimum acceptable price must be enough to cover the average total cost and the normal rate of profits. The minimum acceptable price is set according to the full-cost pricing rule. Thus, the minimum acceptable price can be written as:

𝑃_𝑖 = 𝐴𝑇𝐶 (1 + 𝑟)

Where 𝑃_𝑖 is the minimum acceptable price to the firm with ith plant size

ATC is the average total cost of ith plant size

r is the normal rate of profits of the firm.

Let us explain it with the help of a diagram. In the figure, quantity is measured on X-axis and price on the Y-axis. DD is the market demand curve. AC1 is the average cost curve of the large-size plant, AC2 is the average cost curve of the medium size plant, and AC3 is the average cost curve of the small-size plant. The output OQs are the level of output with the minimum average cost of the small-size plant.

We have seen above that if a new firm has to enter the industry then it should set up the smallest size plant. So, a new firm enters the industry with this small size plant with an average cost equal to AC3. The price leader firm is the most efficient firm with the lowest average cost of production. The price leader firm sets a price that is acceptable to all the small firms in the industry, but the price that is set by the leader firm must be low enough to prevent the entry of new firms.

Here the most efficient firm has the lowest average cost AC1. Sylos assumed that the price leader firm does not think it profitable to compete with the smaller firms, and when setting prices, he ensures that the least efficient firm with the smaller plant size continues to make normal profits.

So, accordingly, the price leader firm will set a price above the average cost AC3 which is the average cost of the least efficient firm. The price that is set by the price leader firm must be such that it prevents the entry of new firms into the industry.

The quantity demanded at price OP3 (which is the average cost of the least efficient firm) is OQ2. Given that the new firm can enter the industry with a plant size with a production capacity equal to OQs, then QL=OQ2-OQs provides us with the quantity of output corresponding to which price will be set. The quantity of output OQL can be sold at the price OPL.

According to Sylos, This OPL price is the limit price that prevents the entry of new firms into the industry. This is so because at the price PL a new firm with an economically viable output OQs enters the industry, the total supply of output QL+QS will just exceed OQ2.

This excess supply of output will cause the price to fall below the average cost AC3 of the least efficient firm, which is also the average cost of the new potential entrant firm. This requirement of the average cost of the least efficient firm acts as a scale barrier.

At limit price PL, all firms are making supernormal profits irrespective of plant sizes. The limit price PL corresponding to output OQL is the equilibrium price because this price is acceptable to all firms, and it also prevents the entry of new firms into the industry.

Thus, PL acts as an upper limit of the limit price, and OP3 acts as the lower limit. The equilibrium price cannot be higher than OPL or lower than OP3. In other words, any output smaller than OQL will not prevent the entry of new firms, whereas output larger than OQL will deter entry into the industry.

According to Sylos, the new potential entrant knows that if it enters the market then the resultant increase in the supply of output would drive the post-entry price to fall below its own average cost of production. As the price is less than the average cost, the firm would incur losses.

Thus, PL is the limit price that is fixed so as to restrict the entry of new firms. To quote Sylos, “The price tends to settle at a level immediately above the entry preventing the price of the least efficient firms, which it is to the advantage of the largest and most efficient firms to let life”.

The Determinants of the Entry-preventing Price or Limit Pricing

The major determinants of the entry-preventing price under Sylos’s model are:

The absolute size of the market.
The elasticity of market demand.
The technology of the industry defines the available sizes of plants.
The prices of the factors of production, together with the technology, determine the total average cost of the firms.

(i) The Absolute Size of the Market

The relationship between limited price and the absolute size of the market is negative. The greater the market size, the lower the entry prevention price or, the lesser the market size, the higher the entry prevention price.

If there is an increase in demand, then the demand curve would shift to the right. The effect of this increased demand on the price and the structure of the industry depends on the size and the rate of increase. If the increase in demand occurs rapidly and considerably and if at this stage firms wish to prevent the entry of potential entrant, then they must lower the price (or set a lower price initially, in anticipation of the developments on the demand side) and build up additional capacity to meet the demand (or have adequate foresight so as to keep a continuous reserve capacity).

Suppose the already established firms cannot build up the required capacity, which is fast enough to keep up with the rate of increase in demand, then entry from new firms as well as from already established firms in other industries would take place. This occurs because of abnormal profits earned by existing firms as the price is more than the average cost.

If we suppose to relax the restrictive assumption that the potential entrant will enter with the smallest optimal plant size and accept that large firms from other industries somehow manage to enter at a lower average cost, then some or all of the small firms will be eliminated, and prices would fall down. As a result, the entire profit drives down to zero because now the price is no longer more than the average cost of production.

Thus, an increase in the absolute market size will tend to reduce the price and increase the average plant size in the industry unless the existing firms can keep their shares constant by keeping continuously adequate reserve capacity. This policy may be very costly. Thus in fast-expanding industries, entry is almost certain to occur, and prices will be reduced.

On the other hand, if the growth of increase in demand is slow, then the established firms would be able to meet the increased demand by appropriate reserve capacity and gradual new investment, and the price will not be reduced unless new techniques with lower costs can be adopted for the larger scales of output to which the established firms are gradually led.

(ii) The Elasticity of Market Demand

The relationship between the elasticity of market demand and the limit price is negative. The more elastic the market demand, the lower the price that established firms can charge without attracting entry and vice versa.

Suppose there is a considerable increase in the elasticity of demand due to any price reductions and if the firms are able to identify this change in the elasticity of demand, then the effects of this change in elasticity on price and on market structure are the same as in the case of a shift in the market demand curve.

Practically it is very difficult to detect the changes in the elasticity of market demand, and established firms would not plan ahead for such uncertain changes in the elasticity of market demand.

Thus, if the elasticity of market demand change substantially, then established firms in other industries would enter the market since the existing firms will not be able to cope with such change, and the price would ultimately fall.

(iii) Technology and Technical Change:

The technology determines the minimum viable plant size. The larger the minimum viable plant size, the higher will be the limit price. Thus there is a positive relationship between the minimum viable plant and the premium included in the limit price.

Technical progress is defined as improvement in technology. Technical progress benefits all plant sizes- small, medium or large. It results in a fall in average cost, and the price would decrease. If technical progress is such that only large firms have access to it, then the limit price would not change. The large firms would have larger profits, but under the assumptions of Sylos’s model, the price need not change.

If technical progress is associated with product innovation rather than process innovation, then the price in the market would not be affected. One should expect an intensification of non-price competition as all firms in the industry will attempt to imitate the innovation.

(iv) The Prices of Factors of Production:

The prices of factors of production play an important role in determining the limit price. Any change in the factor prices affects all the firms in the industry in the same way. Thus, an increase in factor prices will lead to an increase in the costs and the limit price in the industry.

Similarly, a reduction in factor prices will lead to a decrease in the limit price. Thus, a positive relationship exists between the price of factors of production and the limit price.

Sylos Labini’s Model of Limit Pricing

Introduction

Sylos-Labini’s Theory of Limit Pricing

Limit Price Fixation

The Determinants of the Entry-preventing Price or Limit Pricing

(i) The Absolute Size of the Market

(ii) The Elasticity of Market Demand

(iii) Technology and Technical Change:

(iv) The Prices of Factors of Production:

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Introduction

Sylos-Labini’s Theory of Limit Pricing

Limit Price Fixation

The Determinants of the Entry-preventing Price or Limit Pricing

(i) The Absolute Size of the Market

(ii) The Elasticity of Market Demand

(iii) Technology and Technical Change:

(iv) The Prices of Factors of Production:

Read More- Microeconomics

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