What is a quasi concave utility function explain?
A function with the property that for every value of a the set of points (x, y) such that f(x, y) ≥ a—the set of points inside every contour on a topographic map—is convex is said to be quasiconcave. Not every mountain has this property.
How do you show a function is quasi concave?
Reminder: A function f is quasiconcave if and only if for every x and y and every λ with 0 ≤ λ ≤ 1, if f(x) ≥ f(y) then f((1 − λ)x + λy) ≥ f(y). Suppose that the function U is quasiconcave and the function g is increasing. Show that the function f defined by f(x) = g(U(x)) is quasiconcave. Suppose that f(x) ≥ f(y).
What is concave optimization?
The twin notions of concavity and convexity are used widely in economic theory, and are also central to optimization theory. 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.
What is convex and concave in Optimization?
Algebraically, f is convex if, for any x and y, and any t between 0 and 1, f( tx + (1-t)y ) <= t f(x) + (1-t) f(y). A function is concave if -f is convex — i.e. if the chord from x to y lies on or below the graph of f.
What are quasi-concave preferences?
A utility function is quasi–concave if and only if the preferences represented by that utility function are convex. A utility function is strictly quasi–concave if and only if the preferences represented by that utility function are strictly convex.
Is a concave function convex?
In mathematics, a concave function is the negative of a convex function. A concave function is also synonymously called concave downwards, concave down, convex upwards, convex cap, or upper convex.
What is the MRS formula?
The Marginal Rate of Substitution of Good X for Good Y (MRSxy) = ∆Y/ ∆X (which is just the slope of the indifference curve).
Is a magnifying glass convex or concave?
convex lens
Magnifying glasses A magnifying glass is a convex lens used to make an object appear much larger than it actually is. This works when the object is placed at a distance less than the focal length from the lens.
Is Log strictly concave?
Logarithm is Strictly Concave – ProofWiki.