Suppose that f() is the production function associated with a single-output technology, and let Y be the production set of this technology. Show that Y satisfies contact returns to scale if and only if f() is homogeneous of degree one.

For single-output technologies. properties of the production set translate readily into properties of the production function f( - ). Consider Exercise 5.3.2 and Example 5.3.3. Exercise 5.3.2: Suppose that f(-) is the production function associated with a single-output technology, and let Y be the production set of this technology. Show that Y satises constant returns to scale if and only if f( -) is homogeneous of degree one