4. [HARDER] Suppose that z = f (x, y) is a production function which determines output z as a function of the pair (x, y) of nonnegative factor inputs Assume that f(0, 0) = 0. Also, for each fixed (x, y) with x _ 0, and y _ 0, for all > > 0, define g(); x, y) = f(xx, ly) /2. Show that: (a) If f is twice continuously differentiable and concave, then for all x, y one has fl, (x, y)