Can a convex function be quasi concave?
Note that f is quasiconvex if and only if −f is quasiconcave. The notion of quasiconcavity is weaker than the notion of concavity, in the sense that every concave function is quasiconcave. Similarly, every convex function is quasiconvex.
Can a function be both quasi concave and quasi convex?
Definition and properties A quasilinear function is both quasiconvex and quasiconcave. The graph of a function that is both concave and quasiconcave on the nonnegative real numbers.
How do you determine if 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).
Are quasi linear functions convex?
* A function that is both concave and convex, is linear (well, affine: it could have a constant term). Therefore, we call a function quasilinear if it is both quasiconcave and quasiconvex. Example: any strictly monotone transformation of a linear aTx.
Is e x quasi convex?
If f : Rn → R is convex, then f is quasiconvex. ex is quasiconcave but not concave. In fact it is also convex and quasiconvex.
What is quasi concave utility function?
Definition: A function f is strictly quasi-concave if for any two points x and y, x = y, in the domain of f, whenever f(x) ≤ f(y), then f assigns a value strictly higher than f(x) to every point on the line segment joining x and y except the points x and y themselves.
Are quasi-linear preferences convex?
A characteristic feature of quasi-linear preferences is that they are not strictly convex. Under such preferences, the existence and uniqueness of an interior optimal allocation is not, in general, guaranteed.
Is quasi concavity ordinal?
The next theorem states that any monotonic transformation of a quasiconcave function is quasiconcave. This means that quasiconcavity is in fact an ordinal property!
What are quasi concave preferences?
Right: Preferences are strictly quasiconcave. Quasiconcavity implies that an individual’s indifference curves are convex; see Figure 3 for two examples.
How do you prove a function is convex?
A function f : Rn → R is convex if and only if the function g : R → R given by g(t) = f(x + ty) is convex (as a univariate function) for all x in domain of f and all y ∈ Rn.
What is quasi-linear equation?
What are Quasi-linear Partial Differential Equations? A partial differential equation is called a quasi-linear if all the terms with highest order derivatives of dependent variables appear linearly; that is, the coefficients of such terms are functions of merely lower-order derivatives of the dependent variables.
How do you know if preferences are convex?
Preferences are convex if and only if the corresponding utility function is quasi-concave. Assume preferences satisfy completeness, transitivity, continuity and monotonicity.
How do you determine if a function is concave or convex?
To find out if it is concave or convex, look at the second derivative. If the result is positive, it is convex. If it is negative, then it is concave.
What is convex and concave function?
A convex function has an increasing first derivative, making it appear to bend upwards. Contrarily, a concave function has a decreasing first derivative making it bend downwards.
How do you find quasi linear?
Definition 3: A partial differential equation is said to be quasilinear if it is linear with respect to all the highest order derivatives of the unknown function.
What is a quasi-concave function?
Further, the book also said: “Quasi-concave functions: these functions have the property that the set of all points for which such a function takes on a value greater than any specific constant is a convex set (i.e., any two points in the set can be joined by a line contained completely within the set”
How do you know if a function is quasi concave?
Quasi-concave functions and concave functions. IIf f is concave, then it is quasi-concave, so you might start by checking for concavity. IIf f is a monotonic transformation of a concave function, it is quasi-concave.
What is the concave function of a set?
Proposition 1.D.1(Concave Function). A differentiable function f: S → R, defined on a convex setS ⊂ RN, is concave if and only if f x(xa)(xb−xa) ≥f(xb)−f(xa),(7.1)
What is a geometric test of convexity?
A geometric test of convexity is that given any two points of the set, the whole line segment joining them should lie in the set. Figure 1 and 2 are examples ofconvexsets.