Consider a firm that has a Cobb-Douglas technology. The firm wishes to minimize the cost of producing y units of output and has access to perfectly competitive factor markets. The firm's cost minimization problem is given by: min wl + rk {k.1} st kP =y Let p denote the Lagrange multiplier on the output constraint. 1. What are the parameters of the problem? [1 point| 2. Find the conditional factor demand functions. Label them [*(w,r,y) and k*(w,r,y). (Hint: You can check your algebra with Varian pp 54-55.) |15 points| 3. Find the cost function: e(w,r, y). What is its interpretation? |8 points| 4. Find p*. What is its interpretation? |7 points| 5. Find g; and show that it is equal to p*. |4 points| 6. How does %3} depend on (o + 3)7 |graded for completion]| 7. Show that the cost function is homogeneous of degree in output. [graded for completion| 8. How do the returns to scale (degree of homogeneity of the production function) relate to the properties of the cost function? Does this make sense to you? Explain clearly why. |graded for completion|