Exam 6: Producer Behavior

A donut shop has a production function given by Q = 50K^1/3L^1/2, where Q is the number of donuts produced per hour, K is the number of donut fryers (which is fixed at eight in the short run), and L is the number of employed workers. How many donuts can be produced per hour with four workers in the short run?

Which of the following statements is (are) TRUE, assuming the firm is choosing the optimal bundle of inputs that minimizes the cost of producing a given quantity of output? ​ I. The marginal product per dollar spent on labor equals the marginal product per dollar spent on capital. II. AP_L = APK III. IV. MP_L × W = MP_K × R ​

For the production function Q(K,L) = K^0.5L^0.5, the marginal rate of technical substitution MRTS_LK is:

Answer the following questions. a. Suppose that a firm spends $6,000 producing 80 units of output. The rental rate of capital is $600 per hour and the wage rate is $50 per hour. Graph the firm's isocost line and show the values of the horizontal intercept and vertical intercept. b. The cost function for a firm is given by C = 25K + 50L. What is the slope of the isocost line for C = $10,000 and C = $18,000? c. Graphically illustrate the effect of a rise in the price of labor on a firm's isocost line. d. Why do isocost lines have a constant slope?

Suppose the production function for a car manufacturer is: Q = 2K²L² Where Q is the number of cars produced, K is the number of machine hours used, and L is the number of worker hours used. The function for the marginal product of labor is ____.

(Table: Short-run Production I) The short-run production situation for a firm is listed on this table. The average product of labor with one unit of labor is ____.

Assume that Chia Pets International has the production function Q = K + 2L. If the price of capital is $50 and the price of labor is $50, graphically determine this company's expansion path.

(Table: Capital and Labor XIV) Consider the production function that this table shows. a. Does this production function exhibit a constant return to scale? Explain your answer. b. How many units of output are produced with 4 units of labor and 2 units of capital? c. Suppose the firm is using 3 units of capital and 2 units of labor and then decides to employ a third worker. What is the marginal product of the third worker? d. Suppose the firm is using 1 unit of labor and 1 unit of capital. What is the marginal product of capital for K = 2, K = 3, and K = 4? Does return on capital diminish?

(Figure: Capital and Labor VIII) The movement in the isocost line is caused by a(n):

The short-run production function for a firm is given by Q = 10L^0.5. What is the marginal product?

If a firm is using a lot of capital and just a little labor, the marginal product of labor is_____ relative to the marginal product of capital making it _____ to substitute labor for capital.

MRTS_LK decreases as the firm substitutes labor for capital along the isoquant for all production functions below EXCEPT:

Why are the slopes of isocost lines constant?

(Table: Short-run Production I) The short-run production situation for a firm is listed on this table. The marginal product of labor for the third unit of labor is ____.

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

Suppose the production function for a coffee shop is: Q = 2K + 5L Where Q is the number of cups of coffee produced, K is the number of coffee makers, and L is the number of workers. The function for the marginal product of labor is ____.

Consider the production function Q = Af(K, L). Which of the following statements is (are) TRUE? I. An increase in total factor productivity growth is represented by an increase in K or L. II. An increase in total factor productivity growth means that the same amount of output can be produced using fewer inputs. III. If A increases by 10%, the amount of output produced will increase by 10%, holding the quantity of inputs fixed.

Production is an extremely complicated task, so economists make a number of simplifying assumptions. Which of the following assumptions do economists make in their basic model of producer behavior? ​ I. Multiproduct firms: All firms produce at least two goods. II. Firms only use two inputs in the production process: capital and labor. III. Cost minimization: Firms attempt to produce a fixed quantity of output at the lowest possible total cost. IV. Firms can produce more output by using more inputs.

(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. The slope of the isoquant at Point B is ____.

Suppose that a furniture manufacturer produces tables. The manufacturer's production function is Q(K,L) = 2K^0.8L^0.2, where K is the number of wood saws and L is the number of labor hours used to produce tables. The prevailing wage rate is $10 per hour and the rental rate associated with wood saws is $50. The manufacturer has a goal to produce 1,000 units. What Lagrangian equation can be used to solve the manufacturer's cost minimization problem?