2.10 the CobbDouglas function The CobbDouglas function can be described: y = (x1)(x2), where and are positive constants that are each less than

2.10 the Cobb–Douglas function The Cobb–Douglas function can be described:

y = (x1)α(x2)β, where α and β are positive constants that are each less than 1.

a.

Show that this function is quasi-concave by applying Equation 2.114.

b.

c.

Show that the Cobb–Douglas function is quasi concave by showing that any contour line of the form y = c (where c is any positive constant) is convex and therefore that the set of points for which y > c is a convex set.

Show that if α + β > 1 then the Cobb–Douglas function is not concave (illustrating that not all quasi-concave functions are concave).