2. A price-taking firm produces a single output, y, using capital (K) and labor (L). In the short-run, capital is fixed at K. The firm's short-run cost function is Cs(y) = yz + K (a) Give an expression for the firm's short-run average total cost and marginal cost func- tions. (8 points) (b) At what output level does the firm's short-run average total cost function reach a minimum? (7 points) (c) What is the value of short-run average total cost when it reaches its minimum value? That is, if y is the output level that minimizes short-run average total cost, calculate ATCs(y). (4 points) (d) Give an expression for the firm's long-run average total cost function, and the long-run total cost function. (Hint: your answer to part (c) will come in handy) (9 points) (e) What are the returns to scale of this firm's production function? Explain how you know. (7 points)