1. A price-taking firm has the following cost function: C (v, w, q) = 297 02 Wz Where v is the price of capital, w is the price of labor, and q is output. a. Use Shephard's Lemma to help you recover this firm's underlying production function. Does this firm have increasing, decreasing, or constant returns to scale? Why do returns to scale matter for profit maximization? (1 point) b. Derive the profit function, and verify that its properties hold. (1 point) c. Derive the supply function, and verify that its properties hold. (1 point) d. Derive the unconditional demand for labor, and verify that its properties hold. (1point)