Convexity in economics - Wikipedia
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".
Concave and convex functions – The Economy 1.0 - CORE
When 𝛼> 1 α> 1, the slope of the graph of the production function increases as hours increase, so the marginal product of labour is increasing rather than diminishing, as in Figure 3 in which 𝛼 = 1.6 α = 1.6. We would then describe the production function as convex rather than concave.
Mathematical methods for economic theory: 3.1 Concave and convex …
A function of a single variable is concave if every line segment joining two points on its graph does not lie above the graph at any point. Symmetrically, a function of a single variable is convex if every line segment joining two points on its graph does not lie below the graph at any point.
Ec 181: Convex Analysis and Economic Theory - Ohio State …
Convex analysis is the study of the properties of convex sets and convex and concave functions. The fundamental results in the field are the separating hyperplane theorems. These results have interpretations as existence theorems for prices, so they are fundamental in many areas of economic theory.
Mathematical methods for economic theory: 3.3 Concave and convex …
We say that f is concave if the line segment joining any two points on the graph of f is never above the graph; f is convex if the line segment joining any two points on the graph is never below the graph. (That is, the definitions are the same as the definitions for functions of a single variable.)
Strictly convex vs. convex and well-behaved preferences in economics
The curve that is bowed in is strictly convex, and all three of them are convex. Lines A, B, and C all represent indifference curves, while points D and E represent points where the indifference curves touch or intersect (for discussions sake, point …
A function may be concave in some portions of its domain, and convex in other parts of it. The point where a function switches from concavity to convexity, or the other way around, is called an inflection point. The plot below is of a function fx x x ( ) 10= + 3, its first derivative is fx x ′( ) 3 10= + 2 and its second derivative is fx x ...
Preferences are said to be convex if, for any reference bundle x ∈ X, the at least as good as set (x) is a convex set. – Typeset by FoilTEX – 1
A set of points S in is said to be convex if the lineRN segment between any two points of the set is completely included in the set. S is convex if x, y ∈ S, implies {z z =αx+(1 −α)y,0≤α≤1} ⊆ S. S is said to be strictly convex if x, y ∈S, x ≠y,0<α<1, implies .αx+(1 −α)y ∈interior S
The economic interpretation of convex preference sets in consumer theory is diminishing marginal rates of substitution; the interpretation of convex production sets is constant or decreasing returns to scale.