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In microeconomics, a production–possibility frontier (PPF), production possibility curve (PPC), or production possibility boundary (PPB) is a graphical representation showing all the possible options of output for two that can be produced using all factors of production, where the given resources are fully and efficiently utilized per unit time.
A plane curve is the image of any continuous function from an interval to the Euclidean plane.Intuitively, it is a set of points that could be traced out by a moving point. More specifically, smooth curves generally at least require that the function from the interval to the plane be continuously differentiable, and in some contexts are defined to require higher derivative
The knee of a curve can be defined as a vertex of the graph. This corresponds with the graphical intuition (it is where the curvature has a maximum), but depends on the choice of scale. The term "knee" as applied to curves dates at least to the 1910s, [1] and is found more commonly by the 1940s, [2] being common enough to draw criticism.
Intuitively, the graph of a bounded function stays within a horizontal band, while the graph of an unbounded function does not. In mathematics , a function f {\displaystyle f} defined on some set X {\displaystyle X} with real or complex values is called bounded if the set of its values is bounded .
In economics, an indifference curve connects points on a graph representing different quantities of two goods, points between which a consumer is indifferent. That is, any combinations of two products indicated by the curve will provide the consumer with equal levels of utility, and the consumer has no preference for one combination or bundle ...
A universal graph is a graph that contains as subgraphs all graphs in a given family of graphs, or all graphs of a given size or order within a given family of graphs. 2. A universal vertex (also called an apex or dominating vertex) is a vertex that is adjacent to every other vertex in the graph.
Note however that a Lorenz curve for net worth would start out by going negative due to the fact that some people have a negative net worth because of debt. The Lorenz curve is invariant under positive scaling. If X is a random variable, for any positive number c the random variable c X has the same Lorenz curve as X.
Definition and notation: If F : X → 2 Y is a set-valued function in a set Y then the graph of F is the set Gr F := { ( x , y ) ∈ X × Y : y ∈ F ( x ) } . Definition : A function f : X → Y can be canonically identified with the set-valued function F : X → 2 Y defined by F ( x ) := { f ( x ) } for every x ∈ X , where F is called the ...