Kinked" demand curves have in common with traditional demand curves that they are downward-sloping. They are distinguished by a hypothesized convex bend with a discontinuity at the bend - the "kink." Therefore, the first derivative at that point is undefined and leads to a jump discontinuity in the marginal revenue curve.
Classical economic theory assumes that a profit-maximizing producer with some market power (either due to oligopoly or monopolistic competition) will set marginal costs equal to marginal revenue. This idea can be envisioned graphically by the intersection of an upward-sloping marginal cost curve and a downward-sloping marginal revenue curve (because the more one sells, the lower the price must be, so the less a producer earns per unit). In classical theory, any change in the marginal cost structure (how much it costs to make each additional unit) or the marginal revenue structure (how much people will pay for each additional unit) will be immediately reflected in a new price and/or quantity sold of the item. This result does not occur if a "kink" exists. Because of this jump discontinuity in the marginal revenue curve, marginal costs could change without necessarily changing the price or quantity.
The motivation behind this kink is the idea that in an oligopolistic or monopolistically competitive market, firms will not raise their prices because even a small price increase will lose many customers. However, even a large price decrease will gain only a few customers because such an action will begin a price war with other firms. The curve is therefore more price-elastic for price increases and less so for price decreases.
Formulation
The two seminal papers on kinked demand were written nearly simultaneously in 1939 on both sides of the Atlantic. Paul Sweezy of Harvard College published "Demand Under Conditions of Oligopoly." Sweezy argued that an ordinary demand curve does apply to oligopoly markets and promotes a kinked demand curve.
From Queen's College in Oxford, Robert L. Hall and Charles J. Hitch wrote "Price Theory and Business Behavior," presenting similar ideas but including more rigorous empirical testing, including a business survey of 39 respondents in the manufacturing industry.
Hall and Hitch further present a hypothesis for the initial setting of prices; this explains why the "kink" in the curve is located where it is. They base this on a notion of "full cost" - marginal cost of each unit plus a percent of overhead costs or fixed costs with an additional percent added for profit. They emphasize the importance of industry tradition in history in determining this initial price, noting further, "An overwhelming majority of the entrepreneurs thought that a price based on full average cost…was the ‘right’ price, the one which ‘ought’ to be charged
Criticism
Others such as George Stigler have argued against kinked demand. His primary opposition is summarized in a Working Paper out of the Stanford University Economics Department by seminal authors Elmore, Kautz, Walls et al.
New classical economists, led by Chicago’s George Stigler, worked to discredit the kinked demand models. Stigler first argues that the kinked demand models are not useful, as Hall and Hitch’s model only explains observed phenomenon and is not predictive. He further explains that the kinked demand analysis only suggests why prices remain sticky and does not describe the mechanism that establishes the kink and how the kink can reform once prices change. Stigler also asserts that the model is unnecessary because Chicago theory already included allowances for short-run sticky prices due to collusion, menu costs, and regulatory or bureaucratic inefficiencies in markets
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