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Non‑convex sets have been incorporated in the theories of general economic equilibria, [2] of market failures, [3] and of public economics. [4] These results are described in graduate-level textbooks in microeconomics , [ 5 ] general equilibrium theory, [ 6 ] game theory , [ 7 ] mathematical economics , [ 8 ] and applied mathematics (for ...
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.
Demand curve are, however, considered to be generally convex in accordance with diminishing marginal utility. [9] Theoretically, the Demand curve is equivalent to the Price-offer curve and can be derived by charting the points of tangency between Budget Lines and indifference curves for all possible prices of the good in question.
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 ...
In economics, Knightian uncertainty or ambiguity may occur. Thus, one must make assumptions about the probabilities, but the expected values of various decisions can be very sensitive to the assumptions. This is particularly problematic when the expectation is dominated by rare extreme events, as in a long-tailed distribution.
A community indifference curve is an illustration of different combinations of commodity quantities that would bring a whole community the same level of utility. The model can be used to describe any community, such as a town or an entire nation.
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 following are among the properties of log-concave distributions: If a density is log-concave, so is its cumulative distribution function (CDF). If a multivariate density is log-concave, so is the marginal density over any subset of variables. The sum of two independent log-concave random variables is log-concave. This follows from the fact ...