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In typography, line length is the width of a block of typeset text, usually measured in units of length like inches or points or in characters per line (in which case it is a measure). A block of text or paragraph has a maximum line length that fits a determined design. If the lines are too short then the text becomes disjointed; if they are ...
The continuity of in the maximum theorem is the result of combining two independent theorems together. Theorem 1 . [ 9 ] [ 10 ] [ 11 ] If f {\displaystyle f} is upper semicontinuous and C {\displaystyle C} is upper hemicontinuous, nonempty and compact-valued, then f ∗ {\displaystyle f^{*}} is upper semicontinuous.
However, there is no hard and fast definition as to what is classified as "long" or "short" and mostly relies on the economic perspective being taken. Marshall's original introduction of long-run and short-run economics reflected the 'long-period method' that was a common analysis used by classical political economists.
For example, a solid cube is convex; however, anything that is hollow or dented, for example, a crescent shape, is non‑convex. Trivially , the empty set is convex. More formally, a set Q is convex if, for all points v 0 and v 1 in Q and for every real number λ in the unit interval [0,1] , the point
The identification conditions require that the system of linear equations be solvable for the unknown parameters.. More specifically, the order condition, a necessary condition for identification, is that for each equation k i + n i ≤ k, which can be phrased as “the number of excluded exogenous variables is greater or equal to the number of included endogenous variables”.
For example, in economics the optimal profit to a player is calculated subject to a constrained space of actions, where a Lagrange multiplier is the change in the optimal value of the objective function (profit) due to the relaxation of a given constraint (e.g. through a change in income); in such a context is the marginal cost of the ...
Examples of alternatives to utility maximisation due to bounded rationality are; satisficing, elimination by aspects and the mental accounting heuristic. The satisficing heuristic is when a consumer defines an aspiration level and looks until they find an option that satisfies this, they will deem this option good enough and stop looking.
Budget constraints give a straight line on the indifference map showing all the possible distributions between the two goods; the point of maximum utility is then the point at which an indifference curve is tangent to the budget line (illustrated). This follows from common sense: if the market values a good more than the household, the ...