Exercise 5.b.3 from microeconomics theory by Andreu Mas-Colell: show that for a single-output technology. Y is convex if and only if the production function f(z) is concave.

Exercise 5.3.3: Show that for a single-output technology. 1' is convex if and only if the production function Hz) is concave. I: xii) Y is a convex cone. This is the conjunction of the convexity (xi) and constant returns to scale (ix) properties. Formally. Y is a convex cone if for any production vector y. y' e Y and constants a: 12 0 and 2 D. we have any + y' E Y. The production set depicted in Figure 5.3.? is a convex cone