Assume that a firm's output is 1,000 units, Price = $1,000, total revenue is $1,000,000, total fixed cost = $300,000, total variable cost = $800,000. In the short run, should the firm shutdown or should it continue to operate? Please give an explanation.

(Even if a firm shuts down in the short run, it will still have to pay its fixed costs).

Suppose that production for good X is characterized by the following production function, Q = 4K^0.5L^0.5, where K is the fixed input in the short run. The per-unit rental rate of capital (cost of capital per unit of capital), "r", is $86 and the per-unit wage (cost of labor per unit of labor), "w", is $20, price of output is $16, the firm is using 25 units of capital and 64 units of labor.

(a) What is the output of this firm? Please show your calculations.

(b) What is the total cost of the firm? Please show your calculations.

(c) What is the average total cost of the firm? Please show your calculations.

(d) What is the total fixed cost of the firm? Please show your calculations.

(e) What is the average fixed cost of the firm? Please show your calculations