1. Suppose Valcorp Enterprises is currently employing 600 laborers and 285 units of capital to produce its product. The wage rate is $100, and capital rents are $120. The last laborer adds 50 units to total output, while the last unit of capital adds 100 units to total output. Is the manager of this firm making the optimal input choice? Why or why not? If not, what should the manager do? (4 pts)

2. Recall that total cost for a firm is calculated as C = wL + rK. Suppose the firm has total costs of $1000, with wage rates of $25 and capital rents equal to $50. (5 pts)

a. If the firm employs 24 units of labor, how many capital units are they employing?

b. If the number of units of labor is reduced to 14, how many capital units are they employing?

c. Assuming the firms operations are technically efficient, what must the marginal rate of technical substitution of capital for labor (MRTSKL) be given the information above?

3. Suppose the empirical production function given is: Q = aKfixed3L2 + bKfixed2L3,

then Q = AL2 + BL3, where A = aKfixed3, and B = bKfixed2 for simplicity. (5 pts)

a. Derive the average product of labor, APL.

b. Derive the marginal product of labor, MPL.

c. Derive the slope of the MPL.

d. Find the amount of labor (LM) that maximizes MPL (the point where the curve goes from being positive to negative. Hint: the slope of the MPL at that point must be zero. Therefore, set the slope of MPL = 0 and solve for L).

4. Assume the quadratic form of a firms average variable cost curve is given as:

AVC = a + bQ + cQ2. Furthermore, suppose the parameter estimates tell us that a = 360, b = -20 and c = 5. (6 pts)

a. What is the estimated AVC function given the information provided above?

b. What is the estimated TVC function given the information provided above?

c. What is the estimated SMC function given the information provided above?

d. Find the AVC minimizing level of output (QM).

e. Using the QM from part (d), calculate AVC, TVC, and SMC.