Producer's Problem (10 pts) Consider a rm that produces using capital (K) and labor (Nd). The rm's production technology is: zF(K, Nd) = zKN1 d for some (0, 1). The Firm has a xed amount of capital and can hire labor at exogenous wage w. Problems: (a) Set up the rm's prot maximization problem. (b) Prove the rm's technology is constant returns to scale in (K, Nd). (c) Find the rst order condition of the rm and interpret it. (d) Solve for the optimal labor demand of the rm. (e) Find the rm's maximum possible prot. (f) Is the labor demand increasing in K? Why?