A competitive firm produces computer chips. Its production function is ???? = X1^1/4 X2^1/2, where X1 denotes the units of labor and X2 denotes the number of machines. The price of each unit of labor is W1= and the price of each machine is W2. The price of a unit of computer chip is P.

(a)Does this production exhibit increasing, decreasing, or constant returns to scale? Justify your answer.

(b)Compute the marginal product of labor. Is marginal product of labor diminishing in X1?

(c)Write down the firm's profit-maximizing problem and solve the following questions (c.i) and (c.ii).

(c.i) Now suppose there are 4 machines in the short run. Solve for the short-run demand and short-run output level.

(c.ii) Now consider the long-run production. Does this firm have a long-run profit maximization plan? If yes, solve for the long-run demands and long-run output level. Otherwise, explain why it doesn't have a profit maximization plan.

(d)Write down the firm's cost minimization problem and solve for questions (d.i) and (d.ii).

(d.i) Derive the conditional input demand functions.

(d.ii) Derive the total cost function.