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Convexity is a geometric property with a variety of applications in economics. [1] Informally, an economic phenomenon is convex when "intermediates (or combinations) are better than extremes". For example, an economic agent with convex preferences prefers combinations of goods over having a lot of any one sort of good; this represents a kind of ...
A set of convex-shaped indifference curves displays convex preferences: Given a convex indifference curve containing the set of all bundles (of two or more goods) that are all viewed as equally desired, the set of all goods bundles that are viewed as being at least as desired as those on the indifference curve is a convex set.
In mathematical finance, convexity refers to non-linearities in a financial model.In other words, if the price of an underlying variable changes, the price of an output does not change linearly, but depends on the second derivative (or, loosely speaking, higher-order terms) of the modeling function.
The issue with this approach, as outlined by Baumol, is that only one point on a demand curve can ever be observed at a specific time. Demand curves exist for a certain period of time and within a certain location, and so, rather than charting a single demand curve, this method charts a series of positions within a series of demand curves. [5]
In economics, non-convexity refers to violations of the convexity assumptions of elementary economics.Basic economics textbooks concentrate on consumers with convex preferences (that do not prefer extremes to in-between values) and convex budget sets and on producers with convex production sets; for convex models, the predicted economic behavior is well understood.
In finance, bond convexity is a measure of the non-linear relationship of bond prices to changes in interest rates, and is defined as the second derivative of the price of the bond with respect to interest rates (duration is the first derivative). In general, the higher the duration, the more sensitive the bond price is to the change in ...
The new definition required a change of mathematical technique from the differential calculus to convex set theory. Their definition in effect was this: an equilibrium attainable from an endowment ω consists of an allocation x and a budget line through x and ω such that there is no point along the line which either consumer (strictly) prefers ...
Right graph: With fixed probabilities of two alternative states 1 and 2, risk averse indifference curves over pairs of state-contingent outcomes are convex. In economics and finance, risk aversion is the tendency of people to prefer outcomes with low uncertainty to those outcomes with high uncertainty, even if the average outcome of the latter ...