Is a quasilinear function always quasiconcave?

A quasilinear function is both quasiconvex and quasiconcave. The graph of a function that is both concave and quasi-convex on the nonnegative real numbers. is a convex set. is strictly quasiconvex.

Can a concave function be quasiconvex?

A concave function can be quasiconvex. For example, is both concave and quasiconvex. Any monotonic function is both quasiconvex and quasiconcave. More generally, a function which decreases up to a point and increases from that point on is quasiconvex (compare unimodality ).

What is a quasiconcave utility function in economics?

In microeconomics, quasiconcave utility functions imply that consumers have convex preferences. Quasiconvex functions are important also in game theory, industrial organization, and general equilibrium theory, particularly for applications of Sion’s minimax theorem.

Is the utility function quasi-linear?

The curves are still shifted, but along the other axis. Taking the logarithm of the utility function you get $$ x + \\ln y $$which is more clearly quasi linear. Share Improve this answer

What is the difference between convex and quasiconvex functions?

The function f is said to be quasiconvex if for each x 1, x 2 ∈ S, we have f ( λ x 1 + ( 1 − λ) x 2) ≥ m i n { f ( x 1), f ( x 2) }, λ ∈ ( 0, 1) Every convex function is quasiconvex but the converse is not true. A function which is both quasiconvex and quasiconcave is called quasimonotone.

What is the difference between convex and quasimonotone?

Every convex function is quasiconvex but the converse is not true. A function which is both quasiconvex and quasiconcave is called quasimonotone. Let f: S → R and S is a non empty convex set in R n.

What is the difference between strictly quasiconcave and strictly quasiconvex?

is strictly quasiconvex. That is, strict quasiconvexity requires that a point directly between two other points must give a lower value of the function than one of the other points does. A quasiconcave function is a function whose negative is quasiconvex, and a strictly quasiconcave function is a function whose negative is strictly quasiconvex.