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Q: Why is it that If production set is convex then production function is concave?
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If production set is convex then production function is concave?

correct.


Why do it possible to for a cave?

A real-valued function f on an interval (or, more generally, a convex set in vector space) is said to be concave if, for any x and y in the interval and for any t in [0,1],A function is called strictly concave iffor any t in (0,1) and x ≠ y.For a function f:R→R, this definition merely states that for every z between x and y, the point (z, f(z) ) on the graph of f is above the straight line joining the points (x, f(x) ) and (y, f(y) ).A function f(x) is quasiconcave if the upper contour sets of the function are convex sets.


Is the union of two convex sets a non-convex set?

the union of two convex sets need not be a convex set.


Why demand curve is convex?

Convex function on an open set has no more than one minimum. In demand it shows the elasticity is linear after some point and non linear on other points.


Is a circle a convex set?

no


Is A union B a convex set?

yes


Is an empty half plane still a convex set?

The answer depends on how it is halved. If the plane is divided in two by a step graph (a zig-zag line) then it will not be a convex set.


What are convex polygons?

A convex polygon is one with no reflex angles (angles that measure more than 180 degrees when viewed from inside the polygon). More generally a convex set is on where a straight line between any two points in the set lies completely within the set.


Region enclosed by a circle a convex set?

Yes.


Is a ray a convex set?

no, because it should be a segment .


Two lines with intersection is the empty set?

It can be if the set consists of convex shapes, for example.


How do you know if a figure can create a tessellation?

It is extremely difficult. In fact the 15 class of pentagon was only discovered in 2015.All triangles will tessellate. All quadrilaterals will tessellate 15 classes of irregular convex pentagons will tessellate. Regular hexagons will tessellate as will 3 classes of irregular convex hexagons which will tessellate. No convex polygon with 7 or more sides will tessellate.Then, there are concave polygons as well as non-polygonal shapes which will tessellate. One interesting collection of examples is MC Escher's set of symmetric artwork from 1942, mostly watercolours.