Consider a firm that produces using capital (K) and labor (Na). The firm's production technology is:...

  

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Consider a firm that produces using capital (K) and labor (Na). The firm's production technology is: 2F (K, Na)=2KN -a for some a (0, 1). The Firm has a fixed amount of capital and can hire labor at exogenous wage w. Problems: (a) Set up the firm's profit maximization problem. (b) Prove the firm's technology is constant returns to scale in (K, Na). (c) Find the first order condition of the firm and interpret it. (d) Solve for the optimal labor demand of the firm. (e) Find the firm's maximum possible profit. (f) Is the labor demand increasing in K? Why? Consider a firm that produces using capital (K) and labor (Na). The firm's production technology is: 2F (K, Na)=2KN -a for some a (0, 1). The Firm has a fixed amount of capital and can hire labor at exogenous wage w. Problems: (a) Set up the firm's profit maximization problem. (b) Prove the firm's technology is constant returns to scale in (K, Na). (c) Find the first order condition of the firm and interpret it. (d) Solve for the optimal labor demand of the firm. (e) Find the firm's maximum possible profit. (f) Is the labor demand increasing in K? Why?