Bain’s Model of Limit Pricing

2 years ago

Atiqur Rahman

15 minutes

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.

According to him, the limit theory implies that firms do not maximize profit in the short run because of the fear of excessive profit, which induces the entry of new firms and thus reduces the profits in the long run.

According to him, the oligopolistic firms do not charge a price that is equal to the short-run profit-maximizing price but charges a lower price so as to prevent the entry of new firms into the industry. 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.

Bain’s Theory of Limit Pricing

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 explains as to why firms do not set the price following the marginal principle rule.

According to Bain, the price is not set at the minimum point of the long-run average cost curve. He explained that the firms deliberately set a price above the minimum of the long-run average cost in order to restrict the potential entry of new firms.

Thus, the ‘limit price’ was the highest price, which the established firms believed they could charge without inducing further entry. This price may be lower than the price set by the profit-maximizing firm. This theory is basically related to the case of a collusive oligopoly firm.

According to Bain, The limit price is determined by the following:

The cost of the potential entrants,
Market size where firms are operating
The number of established firms in the industry
Price elasticity of demand for the industry product and
The shape of the long-run average cost Curve.

Assumptions of Bain’s Model of Limit Pricing:

i. There are some established firms in the industry.

ii. The market demand curve for the product is not affected by price adjustment by the existing firms or by the entry of new firms in the industry.

iii. There is effective collusion among the firm which is based upon the dominant leader firm.

iv. There are long-run price and output adjustments.

v. The leader firm fixes the limit price below which entry will not take place.

vi. The other firms in the group follow a unified price policy.

vii. The established firms seek the maximization of their own long-run growth.

Under Bain’s Model, he defined the limit price model as the condition for entry. The condition for entry is defined as a percentage by which an established firm can increase the price above the competitive price without attracting the entry of new firms into the industry. The conditions for entry can be expressed mathematically as follows:

𝐶 = 𝑃_L − 𝑃_c / 𝑃_c

Or 𝑃_𝐿 = 𝑃_𝐶 (1 + 𝐶)

Where

𝑃_𝐿 is the limit price

𝑃_𝐶 is the perfectly competitive price

C is the percentage which the established firms may get.

Suppose the firm sets the limit price 𝑃_𝐿 above the competitive price 𝑃_𝐶, then each firm would earn supernormal profit as the price is more than the average cost. If the price is equal to the average cost then firms are earning only normal profits. Thus, C is the percentage or a premium above the competitive price which the existing firms earn by fixing the higher limit price 𝑃_𝐿.

Bain assumed that the condition of entry of a new firm involved which time period which is long enough. This time period depends upon the changing conditions of demand and input prices. The more time a firm takes to establish itself, the lesser the degree of threat posed by its entry.

So, there exists a wide gap between the limited price and the competitive price. This gap between a competitive price and the limited price is known as the entry barrier or entry gap.

Entry Barriers:

The condition of entry by which the established firm can charge a higher price as compared to the competitive price depends on the presence of various barriers to entry. The major sources of entry barriers are:

i. Product Differentiation
ii. Economies of Scale
iii. Absolute Cost Advantage of Established Firms
iv. Large Initial Capital Requirements
v. The Minimum Scale for Efficient or Optimum Production.

i. Product Differentiation:

Product differentiation gives an individual firm an advantage in terms of the degree of control over the price of its product. The new entrant cannot produce the same identical product as produced by the established firms. An entrant is at a disadvantage because she has to make her product known and attract some customary buyers from established firms. As a result, the new firm has to sell at a lower price or spend more on advertising or undertake both. Hence, the cost of the new entrant goes up.

ii. Economies of Scale:

There are three reasons for internal economies of scale, and one of them was given by Adam Smith.

a. Division of Labor and Specialization:

In short, run when we have some fixed factors with variable factors, then expanding variable factors alone (say, number of workers) reduces the opportunities for specialization and division of labour. In this situation, marginal product rises, quickly reaching its maximum and declines thereafter.

But when fixed and variable factors are expanded together, then certain economies of scale are reaped by specialization and division of labour. If the capacity of the plant is small, then it employs a small number of workers, and each worker has to perform several tasks in the process of production.

So, he would not be able to specialize in one task as he will be engaged in several tasks together. But the scenario would be different if the size of the plant is a bit large. As the plant size is large, it can employ a large number of workers, and this will allow each worker to specialize in one task and reduce the unit cost of production.

b. Technological Factors:

When a firm increases its scale of operations, then it is possible to have more technically efficient forms of all factors. The cost of purchasing larger machines is usually proportionately less in comparison to smaller machines.

For example, a printer that can print 100000 papers per day does not cost 10 times much as one that prints 10000 per day and nor does it require 10 times more workers and so on. Expanding usage of technological factors reduces the unit cost of production.

c. One-Time Cost:

This is the third source of increasing returns to scale where even in the long run, inputs do not have to be increased as the output of a product increases. For example, the Research and Development cost to design a new product is incurred only once for each product. So the average total cost falls as the output increases. The effect of one-time costs is that they cause average costs to fall over an entire range of output.

iii. Absolute Cost Advantage of Established Firms:

The established firms enjoy an absolute cost advantage over the potential entrants. The established firms enjoy an absolute cost advantage due to:

(a) the skills of expert management personnel who experienced various expertise during work
(b) patents and superior techniques
(c) control of the supply of raw materials and
(d) lower cost of capital markets.

If any type of absolute cost advantage exists, then the long-run average cost of the new firm would be higher at every scale of production than that of the established firms. Thus, due to this cost advantage of the established firms, the new firms cannot compete with the already existing firms.

iv. Large Initial Capital Requirements:

In order to set up a new firm, the firm needs a large amount of initial capital, which may be difficult for the new firms to mobilize. Banks may be reluctant to finance a new business, and the capital market could be almost inaccessible to new entrants. This acts as a barrier to the entry of firms into an industry.

v. The Minimum Scale for Efficient or Optimum Production:

In order to produce optimally, the new firm should set a minimum size of the plant where the average cost is minimum.

Diagrammatic Representation of the Limit Pricing Model

We have seen that limit pricing is the entry-preventing price. Under this model, Bain assumed that products produced by established firms and potential firms are homogeneous. It is also assumed that a collusive oligopoly seeks to maximize profits over the long run rather than short-run profits.

There is a given determinate demand curve for the industry. The market demand curve for the product is not affected by price adjustment by the existing firms or by the entry of new firms in the industry. It remains unaltered and stable. Corresponding to this demand curve, there is a marginal revenue curve which shows the addition to revenue attributable to the sale of one more unit of product.

The next task is to decide what would be the level of limit price that has to be set by the collusive oligopolistic firms to prevent the entry of new firms.

In the figure, the price is measured on the x-axis and the output on the y-axis. DD is the market demand curve faced by the collusive oligopoly firms.MR is the marginal revenue curve. LACEF is the long-run average cost curve of the existing established collusive oligopolists. It is constant and parallel to a horizontal axis.

As the long-run average cost of the established firms is constant, the long-run marginal cost is equal to the long-run average cost of the established firm, i.e. LACEF= LMCEF. If the collusive oligopolistic firm wants to maximize short-run profits, it would produce a level of output where the marginal revenue is equal to the marginal cost.

It is shown as point E where the long-run marginal cost LMCEF is equal to marginal revenue. The short-run profit-maximizing price is Pm, and oligopolistic firms are selling OQm units of output. This OPm price is the monopoly price because this price is charged by collusive oligopolistic firms. This price (OPm) will induce the entry of new firms in the industry as this price is more than the long-run average cost of the potential entrants by PmPLAC.

With the entry of new firms into the industry, the established firm would lose a part of the market demand. This reduction in the market demand curve would cause a shift in the market demand curve to the left. This results in uncertainty among firms about the price level of demand for their product as a result of the new entry of firms.

Diagrammatic Representation of Bain's Limit Pricing Model — Diagrammatic Representation of Bain’s Limit Pricing Model

Suppose the firms set the price PL which is equal to the long-run average cost of the potential entrants’ firms, i.e. LACPF; then, firms are ready to sell OQL units of output. At this price, the established collusive oligopolistic firms are still earning profits as this price is still more than their long-run average cost, i.e. LAC_EF.

This price is beneficial for the already established collusive oligopolistic firms but not for the new rival firms. It is not beneficial for the new firms to enter the market as the price is equal to their long-run average cost, i.e. LAC_PF.

As the price is equal to the average cost, they are just earning normal profits. If these new firms would enter the market, then the supply of the product would increase and for a given price, this increase in supply results in a fall in the prices below their average cost of production.

Thus, the post-entry price would be less than the average cost of the potential entrants. So, if the potential firms enter at this price then they are incurring losses as the post-entry price is less than their long-run average cost. This price would act as entry preventing price or the limit price.

Therefore, the price PL is the limit price which the established firms can charge without inducing entry. At this price, the established collusive oligopolistic firms are still earning profits but this profit is less than the profit that they are incurring at the monopoly price, i.e. PmAEmB>PmACP_L.

Bain’s Limit Pricing and Price Elasticity of Demand

The important aspect of Bain’s limit pricing theory is that Bain tried to explain the phenomenon of oligopolistic firms in some industries keeping their price at a level of demand where the price elasticity of demand is less than unity. It can be seen from the figure that if the average cost of the potential entrants is OJ on the given market demand curve DD, the price elasticity of demand is less than unity.

This corresponds to a point below the mid-point of the linear demand curve DD, and at this price, the marginal revenue curve becomes negative. According to Bain, the established oligopoly could set price OJ as the limit price as this price is still more than their long-run average cost curve. At this price, established firms are earning profit as the price is more than the long-run average cost.

Another important feature of Bain’s limit pricing theory is that if the market demand and the cost conditions allow the monopoly price to be less than the limit price, then the oligopolistic firms would charge the monopoly price to maximize their short-run profits. This price not only maximizes the short-run profits but also serves to prevent potential entrants and maximizes the long-run profits.

We have seen that Bain was able to explain why collusive oligopolistic firms charge prices below the short-run profit-maximizing price. This is because of the threat of the potential entry of new firms. These firms want to prevent the new entry to ensure long-run maximum profits.

Bain’s Model of Limit Pricing

Introduction

Bain’s Theory of Limit Pricing

Assumptions of Bain’s Model of Limit Pricing:

Entry Barriers:

i. Product Differentiation:

ii. Economies of Scale:

a. Division of Labor and Specialization:

b. Technological Factors:

c. One-Time Cost:

iii. Absolute Cost Advantage of Established Firms:

iv. Large Initial Capital Requirements:

v. The Minimum Scale for Efficient or Optimum Production:

Diagrammatic Representation of the Limit Pricing Model

Bain’s Limit Pricing and Price Elasticity of Demand

Read More- Microeconomics

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Introduction

Bain’s Theory of Limit Pricing

Assumptions of Bain’s Model of Limit Pricing:

Entry Barriers:

i. Product Differentiation:

ii. Economies of Scale:

a. Division of Labor and Specialization:

b. Technological Factors:

c. One-Time Cost:

iii. Absolute Cost Advantage of Established Firms:

iv. Large Initial Capital Requirements:

v. The Minimum Scale for Efficient or Optimum Production:

Diagrammatic Representation of the Limit Pricing Model

Bain’s Limit Pricing and Price Elasticity of Demand

Read More- Microeconomics

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