Economics.

Definition. A function g : R" -> R is concave if for all x1, x2 E R" and 0 Ag(x]) + [1 - Ng(2-2). Consider a piecewise linear concave function g : R - R. Prove that g can be expressed as the minimum of a set of affine functions, i.e. there exists affine functions fi : R -> R for i = 1, . . ., k with the property that for every x E R, g(x) = min { f1(x), f2 (x), . . . , fk (2) }. HINT: Use the definition of a concave function to prove the following Proposition. Proposition. Consider a concave function g : R - R and an affine function f : R - R. Let a, b, c E R where a b. If g(a) = f(a) and g(b) = f(b) then g(c)