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This famous model was developed almost simultaneously by Sweezy (1939) and Hall and Hitch (1939). The model seeks to explain an observed tendency for price to be rather inflexible or ‘rigid’ in many oligopolistic markets. The idea behind the kinked demand curve model is that each firm in an oligopoly may be reluctant to initiate either a price increase or price cut, for the following reasons:

n The firm believes if it increases its price, its rivals will not follow suit, but will instead seek to take advantage by encouraging the firm’s customers to switch to them. Consequently the firm stands to lose a sizable portion of its market share if it increases its price.

n The firm also believes if it cuts its price, its rivals will follow suit, in order to protect their own market shares. Consequently the firm does not stand to gain market share if it cuts its price.

In other words, the firm tends to take a rather cautious or pessimistic view of its rivals’

likely reaction to any decision to either increase or reduce its own price. If all firms think in this way, prices throughout the industry tend to be inflexible or rigid, because no firm wishes to be the first to implement a price change in either direction.

Sweezy’s model is shown in Figure 4.12. P1is the firm’s current price. dd is the firm’s demand function, drawn on the assumption that if it raises or lowers its price from P₁, its rivals do not follow suit. dd is relatively price elastic, because if the firm is the only one raising its price, it loses most of its customers; and if it is the only one cutting its price, it gains customers rapidly from its rivals. DD is the firm’s demand function, drawn on the assumption that if it raises or lowers its price from P1, its rivals do follow suit. DD is less price elastic, because if all firms simultaneously raise or lower their prices, they only gain or lose sales to the extent that total industry sales rise or fall; the firms do not tend to gain or lose customers from one another.

In Figure 4.12, the firm faces two possible demand functions, drawn on differing assumptions about rivals’ reactions to any price change. What is the firm’s perceived demand function? On the pessimistic assumptions described above, we should consider dd to be the demand function applicable for a price rise above P1(or for quantities less than q1). DD is the demand function applicable for a price cut below 138 Chapter 4 n Oligopoly: non-collusive models

P1(or for quantities greater than q1). Therefore dAD is the firm’s perceived demand function. There is a kink at point A, which identifies the current price and quantity, P₁and q₁.

What is the shape of the firm’s perceived marginal revenue (MR) function?

Applying similar logic, mm is the MR function associated with the demand function dd, applicable for quantities less than q1. MM is the MR function associated with the demand function DD, applicable for quantities greater than q₁. Therefore mBCM is the firm’s perceived MR function. There is a discontinuity between points B and C located at the current quantity q1, at which point a switch between the two MR functions takes place.

Profit is maximized where MR = MC. MR > MC to the left of q1, and MR < MC to the right of q1. Therefore profit is maximized at P1and q1, because MC intersects the discontinuous section of the perceived MR function at q1. Even if MC rises or falls slightly, as long as the point of intersection remains within the discontinuity BC, the profit-maximizing price and quantity are unchanged. This provides a more formal demonstration of the property of price rigidity or ‘sticky prices’.

The degree of price rigidity depends on the length of the discontinuity in the MR function, BC. This in turn depends on the angle of the kink (λ), which has been called the barometer of price rigidity. Stigler (1947) identifies several factors that might affect the angle of the kink.

n If there are very few rivals, both price increases and price cuts are more likely to be followed, since the firms are highly conscious of their interdependence.

The perceived demand function may approach DD. If there are many rivals, price increases and price cuts are less likely to be followed, as competition approaches the atomistic case in which each firm’s actions have a negligible effect on its rivals. Stigler thought an intermediate number of firms would generate the most acute λ, and the longest discontinuity in the MR function.

4.5 The kinked demand curve and models of price leadership 139

Figure 4.12 Sweezy’s kinked demand curve model

n The size of the rivals may also affect the size of the kink. If there is one large firm, or a clique of firms, it may act as a price leader, with others following its price decisions. In this extreme case there may be no kink. The same applies if there is collusion.

n Product homogeneity (or a large and positive cross-elasticity of demand) pro-duces an acute λ and a long discontinuity, as customers are more likely to shift when facing a price differential.

This list is extended by Cohen and Cyert (1965, p. 251):

n If entrants are unsure about the market structure, or incumbent firms are unsure about the intentions of entrants, firms may adopt a wait-and-see attitude and be reluctant to initiate price rises.

n The same may also be true in a new industry, where firms are attempting to size each other up.

n If there is substantial shareholder control, risk-averse managers may decide to play safe, by avoiding actions that could provoke damaging reactions from rivals.

The kinked demand curve model can be criticized for not explaining how price is formed at the kink. The model begins with the price as given; it does not explain how price is determined. It explains the existence of the kink but not its location.

Furthermore, price rigidity might be explained in other ways. Firms may be reluctant to raise price for fear of alienating their customers. Firms may wait for a convenient time to introduce one large price rise, rather than revise prices continuously, the latter being a strategy that might annoy customers. Levy et al. (1997) suggest that changing price is itself a costly and complex operation. Accordingly, in businesses where menu costs are high, price changes are less frequent.

Stigler (1947) found little empirical evidence of price rigidity. Having examined the evidence in seven oligopolistic markets (cigarettes, automobiles, anthracite, steel, dynamite, refining and potash) he claimed price changes were quite frequent, although there was some evidence to suggest the smaller the number of firms, the less frequent were price changes.

But is this adverse conclusion really surprising? The kink is a barrier to changes in prices that will increase profits, and business is the collection of devices for circumventing barriers to profits. That this barrier should thwart businessmen – especially when it is wholly of their own fabrication – is unbelievable.

(Stigler, 1947, p. 435) In a later article, Stigler said he was amazed at the continuing popularity of the model. ‘The theory has received no systematic empirical support and virtually no theoretical elaboration in these decades, but these lacks have been no handicap in maintaining its currency’ (Stigler, 1978, p. 183). However, there is some evid-ence to support Sweezy’s reasoning. For example, Kashyap (1995) examined price changes for 12 retail goods over 35 years, and found prices were typically fixed 140 Chapter 4 n Oligopoly: non-collusive models

for more than a year. In a study based on 80 industries, Domberger and Fiebig (1993) found price cuts were more readily followed than price increases in tight oligopolies.

Sweezy’s basic assumption that price increases will not be followed and that price cuts will, has been challenged. A price cut need not send signals to rivals that a firm is aggressively seeking to capture a larger market share. Rivals may reason that the firm’s product is of lower quality, or the firm has financial problems. Rivals react according to how they interpret the price cut. Likewise, price increases may be followed if firms believe market conditions warrant such an increase, or if they face temporary capacity shortages and are unable to meet increases in demand. In times of increasing demand and possible price inflation, producing any additional output increases costs substantially for a firm approaching capacity (Brofenbrenner, 1940; Efroymson, 1955). Accordingly, a capacity-constrained firm may be eager to follow a rival’s price rise and reluctant to follow a price cut, which would only increase demand further.

This case is illustrated in Figure 4.13, where the perceived demand function is DAd, the marginal revenue function is MCBm, and the kink has become reflexive.

In this case, profit is not maximized at (P₁/q₁) the current price and quantity P₁q₁. By reducing output to q2, the firm could increase profit by X (the area between MC and MR over the range q2to q1). Alternatively, by increasing output to q3, the firm could increase profit by Y (the area between MR and MC over the range q1

to q₃). In Figure 4.13, since Y is larger than X, the firm should select output q₃. However, this outcome is not inevitable. During times of inflation in particular, both MC and the demand functions dd and DD tend to rise. If the increase in MC is greater than the increase in demand, perhaps (as suggested above) because the firm is approaching a production capacity constraint, Y tends to become smaller than X.

Therefore a profit-maximizing firm would eventually switch to the lower output level q2.

4.5 The kinked demand curve and models of price leadership 141

Figure 4.13 The reflexive kinked demand curve