Complete the table showing labor average variable cost and

Question

1. Suppose a firm employs labor as its only variable input. All workers are paid $20 per day. Output per day and variable cost are shown in the following table. Complete the table, showing labor, average variable cost, and marginal cost for the first eight units of output. Draw a graph showing average and marginal cost.

q    VC    L    AVC    MC

1    20

2    40

3    60

4    80

5   120

6   160

7   240

8   320

2. Consider the following short-run production function: q = 4L² - (2/3) L³.

a. At what level of L do diminishing marginal returns begin? Show your derivation.

b. At what level of L do diminishing returns begin? Show your derivation.

3. Find the Marginal Rate of Technical Substitution for the following production functions. Show how you derived these results.

a. q = 10L^1/3K^2/3

b. q = 4L^0.5 + 2K^0.5

c. q = min{2K, 4L}

d. q = 3L + 8K

4. A company has the following cost function: C(q) = 4q3 - 200q2 + 500q + 50,000.

a. What level of output will minimize the average variable cost?

b. Does the production process indicate diminishing marginal product? How can you tell?

5. Assume that a firm produces its output subject to the following production function: q = 5K^0.4L^0.6. Market input prices are r and w. The firm minimizes the cost of whatever output it produces. Use the Lagrangian method to determine the equation of the output expansion path.