Suppose that a firm has the production function f(z1,z2)=Az^1/2,z^1/3, where A>0 is

a parameter. You can assume that the firm's production set is convex.

1. (a)[2] Show that this production technology satisfies the no-free lunch property.
2. (b)[2] Show that this production technology satisfies the free disposal property.
3. (c)[2] Show that this production technology has decreasing returns to scale.
4. (d)[2] Illustrate this production technology's isoquant through the production level q = A.
5. (e)[2] Given input prices w1 > 0 and w2 > 0 and output price p > 0, write down the firm's profit maximisation problem.
6. (f)[2] Write down the Lagrangean of the firm's profit maximisation problem and derive its first-order necessary conditions for an interior solution.
7. (g)[2] Under what conditions is z2 = 0 optimal for the firm?
8. (h)[2] Derive the firm's supply functions z1(w1, w2, p), z2(w1, w2, p) and q(w1, w1, p).