“Kinked" demand curves are similar to traditional demand curves, as they are downwardsloping. They are distinguished by a hypothesized convex bend with a discontinuity at the bend– "kink". Thus 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. This is because competitors will generally ignore price increases, with the hope of gaining a larger market share as a result of now having comparatively lower prices. 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. Firms will often enter the industry in the long run.