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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.
As used in biology, the indifference curve is a model for how animals 'decide' whether to perform a particular behavior, based on changes in two variables which can increase in intensity, one along the x-axis and the other along the y-axis. For example, the x-axis may measure the quantity of food available while the y-axis measures the risk ...
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.
The left plot, titled 'Concave Line with Log-Normal Noise', displays a scatter plot of the observed data (y) against the independent variable (x). The red line represents the 'Median line', while the blue line is the 'Mean line'. This plot illustrates a dataset with a power-law relationship between the variables, represented by a concave line.
A sigmoid function is convex for values less than a particular point, and it is concave for values greater than that point: in many of the examples here, that point is 0. Examples [ edit ]
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 ...
Concave preferences are the opposite of convex, where when , the average of A and B is worse than A. This is because concave curves slope outwards, meaning an average between two points on the same indifference curve would result in a point closer to the origin, thus giving a lower utility. [25]