Consider a firm with production function f (z1, z2) = z1 + z2 (1) What are the return to scale for this production function? (2) Find the firm's conditional input demand functions and its cost function. (3) Find the input demand, output supply and profit functions. (4) Find, from the profit function that you found in part (3) and Hotelling's Lemma, the output supply and the input demands and verify that they are the same as the functions you found in part (3).