Exam 7: Production Theory and Estimation

Given: Q = 100K0.5L0.5, C* = $1,000, w = $30, and r = $40. Determine the amount of labor and capital that the firm should use in order to maximize output. What is this level of output?

The firm hires 5 additional employees which produce 500 additional parts. If the revenue increases by 100,000, what is the marginal revenue product of labor?

The law of comparative advantage postulates that even if a nation is less efficient or has an absolute disadvantage with respect to another in production of all commodities, there is still a basis for mutually beneficial trade.

A line that connects all points where the marginal rate of technical substitution is equal to the ratio of input prices is called the

Having a Cobb-Douglas production function with parameters A = 2 and α = 0.5, set up an output table varying each of the inputs from 0 to 4.

Suppose that the production function of a firm is Q = 100L0.5K0.5 and K = 100, P = $1, w = $30, and r = $40. Determine the quantity of labor that the firm should hire in order to maximize profits. What is the maximum profit of this firm?

Use the following to answer questions below: -Refer to the isocost lines graph. Which of the following shifts represents an increase in total cost while the rental price of capital and the wage rate of labor are constant?

Use the following to answer questions below: -Refer to the equilibrium graph. What is the marginal rate of technical substitution at point A?

A firm wants to minimize the cost of producing 2,800 units of output per week. It has hired a production engineer to identify alternative production technologies that will accomplish this goal. The production technologies use the different combinations of capital (K) and labor (L) that are listed below. K 200 180 160 140 120 100 80 60 40 20 16 L 16 18 22 28 36 46 60 80 110 160 180 Assume that the rental price of capital is $10 and the wage rate of labor is $8. Determine the minimum cost of producing 2,800 units of output.

Product innovation is shown on an isoquant map by a shift in all isoquants toward the origin.

Toyota Corporation was one of the first firms to pioneer just-in-time production, which is an example of

Suppose that the production function for a commodity is given by $Q = 20 \sqrt { L K }$ where Q is the quantity of output, L is the quantity of labor, and K is the quantity of capital. (a) Indicate whether this production function exhibits constant, increasing, or decreasing returns to scale. (b) Does the production function exhibit diminishing returns? If so, when does the law of diminishing returns begin to operate? Could we ever get negative returns?

Short-run is a time of period during which

Use the following to answer questions below: -Refer to the isocost lines graph. Which of the following shifts represents an increase in the rental price of capital?

If the sum of the output elasticities for a production function is greater than one, then the production function exhibits decreasing returns to scale.

The firm hires 10 new employees and the total costs increase by 25,000 per time period. What is the marginal resource cost of labor?

The production function is an equation, table, or graph that shows the maximum output that can be produced from different combinations of inputs.

The marginal product of labor is equal to

Use the following to answer questions below: -Refer to the isoquant maps graph. Assume that the four isoquants in each graph represent output levels of 100, 200, 300, and 400. Which of the four graphs shows an isoquant map in which returns to scale are continuously decreasing?

A firm currently employs 45 production workers and 6 supervisors. The marginal product of the last production worker employed is 50 units of output per hour and production workers are paid $10 per hour. The marginal product of the last supervisor employed is 150 units of output per hour and supervisors are paid $30 per hour. Every employee works 40 hours per week. (i)What is the firm's total labor cost per week? (ii)Assume that hours of labor by supervisors (L_s) is plotted on the vertical axis and hours of labor by production workers (L_p) is plotted on the horizontal axis. What is the equation for the firm's isocost line? What are the two intercepts of the isocost line? (iii)Assume that the firm's isoquants are smooth curves and that labor hours can be varied continuously. Is the firm producing the maximum level of output given its current level of cost? If it is, explain how you can tell. If it isn't, explain what it should do to increase output.