= za z 1. Suppose that a firm has a Cobb-Douglas production function, that is, f(21, 22) where a, b > 0. (a) Show that this production technology satisfies the no-free lunch property. (b) Show that this production technology satisfies the free disposal property. (c) Does this production technology have increasing, decreasing or constant returns to scale? (d) Suppose that a = b= 1. Illustrate this production technology's isoquants, and show that it has convex input sets Z(q). (e) Without doing any of the work, describe how you would verify that the production set Q is convex. (f) Find the marginal rate of technical substitution at inputs (2, 22) = (2,3) and (, ) = (4,4).