Exam 6: Producer Behavior

(Figure: Capital and Labor XVI) Consider the production function Q = L^0.5K^0.5, with MP_K = L^0.5/K^0.5 and MP_L = K^0.5/L^0.5. When K = 5 and L = 10, the marginal rate of technical substitution is ____.

Solving for the value of the Lagrange multiplier in the firm's cost minimization problem tells us:

(Table: Capital and Labor XIV) Consider the production function that this table shows. Suppose the firm is using 3 units of capital and 1 unit of labor. The marginal product of capital for K = 4 is ____.

(Table: Capital and Labor XIV) Consider the production function that this table shows. With 4 units of labor and 2 units of capital, the level of output is ____.

Which of the following is a Cobb-Douglas production function?

(Figure: Production Function V) Refer to the production function, which has a slope of 1/L^0.5. The marginal product of labor for L = 1, assuming that labor is infinitely divisible, is ____.

A firm spends $12,000 per day producing a good. The wage per worker is $200 per day and rental per unit of capital is $400 per day. The firm faces the production function Q = 3K^1/3L^2/3 with MP_K = L^2/3/K^2/3 and MP_L = 2K^1/3/L^1/3. The cost-minimizing level of capital will be_____ and the cost-minimizing level of labor will be _____.

(Figure: Production Function VI) The MP_L at point A is _____, and the AP_L is _____. What do your results imply about how AP_L will change with increased production?

For the production function Q(K,L) = 3K + 2L, the marginal product of labor is:

(Figure: Capital and Labor XII) Which of the following statements is (are) TRUE? I. Panel a illustrates constant returns to scale. II. Panel b illustrates decreasing returns to scale. III. Panel a illustrates increasing returns to scale IV. Panel b illustrates constant returns to scale.

Suppose that a farmer grows corn. The farmer's production function is Q(K,L) = 5K^0.4L^0.6, where K is the number of harvesters and L is the number of farmworker labor hours. The prevailing wage rate is $8 per hour and the rental rate associated with harvesters is $75. The farmer has a goal of delivering 100,000 bushels of corn to market. What Lagrangian equation can be used to solve the farmer's cost minimization problem?

Consider the following production functions along with their corresponding marginal product of labor function. I. Q = 15KL, where MP_L = 15K II. Q = 2K^0.4L^0.6, where MP_L = III. Q = 8K + L, where MP_L = 1 a. In each case, what happens to the marginal product of labor as the firm uses more labor? b. In each case, what happens to the marginal product of labor as the firm uses more capital?

Brenda's Pastry employs three workers who produce 6 dozen pastries per hour. After Brenda hires a fourth worker, the number of pastries produced increases to 7 dozen per hour. Because the marginal product of the fourth worker is _____ than the average product of three workers, the average product must _____.

Which of the following statements is (are) TRUE? I. If labor and capital are perfect substitutes in production, the isoquant is a downward-sloping line. II. If a company needs to use inputs in fixed proportion such that the capital to labor ratio is always 2, the firm's isoquants are L-shaped. III. If the production function is given by Q = min(14, 7), the firm can produce, at minimum, 21 units of output.

(Figure: Production Function I) The average product at L = 2 and L = 8, respectively, are:

Which of the following statements violates the basic assumptions of isoquants?

Answer the following questions. a. Complete the following table by filling in the missing output values. Assume the production function is given by Q = KL, where Q is units of output, K is units of capital, and L is units of labor. b. What is the equation for the new production function if total factor productivity increases by 50%? Complete the following table.

Here is a copy of your friend's class notes on the nine basic assumptions of producer behavior: 1. The firm produces two goods. 2. The firm has already decided which product to produce. 3. The firm's goal is to produce as much output as possible at minimum cost. 4. The firm uses only capital and labor inputs in making its product. 5. In the short run and long run, both labor and capital inputs are fixed. 6. In general, the more inputs a firm uses, the more output it produces. 7. There are constant marginal returns to labor and capital. 8. As the firm buys more labor and capital inputs, the increased demand raises input prices. 9. The firm's budget constraint is negatively sloped. Because your friend was half-asleep during class, they may have errors in their notes. Correct the errors in their notes where necessary.

(Table: Short-run Production I) The short-run production situation for a firm is listed on this table. The total output when there are four units of labor is ____.

The production function for laser eye surgery is given by Q = 20K^0.5L^0.5, where Q is the number of laser eye surgeries performed per day, K is the number of eye surgery machines (which is fixed at 2 in the short run), and L is the number of employees. a. Write the equation for the firm's short-run production function. b. Write the equation for the firm's short-run average product of labor function. c. Calculate the average product of labor for L = 9 and L = 16. d. Calculate the marginal product of labor for L = 1, L = 2, and L = 3.