Deck 5: Production

Question 1

The following table shows the total output per hour produced in a factory at various levels of employment of labor. The firm sells each unit of output at $2 and each worker is paid a wage of $12.
Table 5-1
$\begin{array} { | c | c | } \hline \begin{array} { c } \text { Nurnber of } \\\text { workers }\end{array} & \text { Total output } \\\hline 1 & 8 \\\hline 2 & 18 \\\hline 3 & 30 \\\hline 4 & 41 \\\hline 5 & 50 \\\hline 6 & 55 \\\hline 7 & 59 \\\hline 8 & 61 \\\hline 9 & 62 \\\hline\end{array}$

-Refer to Table 5-1. What is the marginal revenue product of the 4th worker?

A) $82
B) $20.50
C) $22
D) $18
E) None of these answers is correct.

Answer 1

$18

Question 2

Firm X sells output at a price of $8 per unit and pays labor a wage of $20 per hour. The marginal product of labor is given by: MPL = 12 - .1L. To maximize profit, the firm should utilize _____ hours of labor.

A) 75
B) 80
C) 85
D) 90
E) 95

Answer 2

E

Question 3

What does the law of diminishing marginal returns state?

A) When all inputs to production are increased in equal proportions, output will eventually decrease.
B) When one input is increased, with all other inputs unchanged, the marginal product of the input will eventually decline.
C) When one input is held constant, and all other inputs are increased, output will eventually decrease.
D) When one input is increased, and all other inputs are held constant, output will increase at an increasing rate.
E) When all inputs to production are increased in equal proportions, the addition to output will increase at an increasing rate.

Answer 3

B

Question 4

A firm's production function shows:

A) the maximum level of output the firm can produce for any combination of inputs.
B) the least-cost combination of inputs that can be used to produce a given level of output.
C) the average cost associated with the production of various levels of output.
D) the profit-maximizing level of output that can be produced with a given level of inputs.
E) the marginal cost of producing an extra unit of output by employing an extra unit of an input.

Question 5

The following table shows the total output per hour produced in a factory at various levels of employment of labor. The firm sells each unit of output at $2 and each worker is paid a wage of $12.
Table 5-1
$\begin{array} { | c | c | } \hline \begin{array} { c } \text { Nurnber of } \\\text { workers }\end{array} & \text { Total output } \\\hline 1 & 8 \\\hline 2 & 18 \\\hline 3 & 30 \\\hline 4 & 41 \\\hline 5 & 50 \\\hline 6 & 55 \\\hline 7 & 59 \\\hline 8 & 61 \\\hline 9 & 62 \\\hline\end{array}$

-Refer to Table 5-1. What is the total revenue that accrues to the firm when it employs 4 workers?

A) $36
B) $112
C) $100
D) $60
E) $82

Question 6

The marginal product of labor initially rises as more labor is employed because of:

A) division and specialization of labor.
B) constant returns to scale.
C) total factor productivity.
D) an increase in profits from the additional output produced.
E) a fall in the cost of hiring additional labor.

Question 7

The following table shows the total output per hour produced in a factory at various levels of employment of labor. The firm sells each unit of output at $2 and each worker is paid a wage of $12.
Table 5-1
$\begin{array} { | c | c | } \hline \begin{array} { c } \text { Nurnber of } \\\text { workers }\end{array} & \text { Total output } \\\hline 1 & 8 \\\hline 2 & 18 \\\hline 3 & 30 \\\hline 4 & 41 \\\hline 5 & 50 \\\hline 6 & 55 \\\hline 7 & 59 \\\hline 8 & 61 \\\hline 9 & 62 \\\hline\end{array}$

-Refer to Table 5-1. What is the marginal profit of the 2nd worker?

A) $24
B) $20
C) $12
D) $8
E) $0

Question 8

Which of the following is true in the long-run?

A) A firm can vary all the inputs used in production.
B) A firm can vary only one of the inputs used in production.
C) All inputs used in production are fixed in the long-run.
D) The level of output produced can be varied only over a limited range.
E) The marginal cost is at a minimum.

Question 9

When a firm faces constant returns to scale, a proportionate increase in all inputs:

A) will keep output constant.
B) will increase output by the same proportion as the increase in inputs.
C) will lead to a decline in the cost of production.
C) will result in a higher-than-proportionate increase in output.
E) will not change the total costs of production.

Question 10

The short-run is best defined as the time period in which:

A) all inputs to production can be varied
B) the amount of output cannot be varied
C) one or more inputs to production are fixed
D) the marginal cost of production is low
E) all inputs to production remain fixed

Question 11

A profit-maximizing firm will hire the variable input, labor, until the point where:

A) marginal product of labor is equal to the marginal revenue product of capital.
B) marginal revenue from each unit of output is equal to the wage rate.
C) marginal revenue product of labor is equal to the marginal cost of labor.
D) marginal revenue product of labor is equal to zero.
E) marginal product of labor equals the marginal revenue from each unit of output.

Question 12

The marginal revenue product of labor is equal to the product of:

A) the marginal product of labor and the quantity of labor employed.
B) the wage rate and the marginal product of labor.
C) the wage rate and marginal revenue per unit of output
D) marginal product of labor and total revenue of the firm.
E) the marginal revenue per unit of output and the marginal product of labor

Question 13

Which of the following is true of a firm that faces increasing returns to scale?

A) An increase in the quantity of one input will increase output by a greater proportion.
B) As the quantity of all inputs are increased, the average cost of production will increase.
C) A given increase in the quantity of all inputs will increase output by a greater proportion.
D) As the quantity of one input is increased, its marginal product will increase at an increasing rate.
E) As the quantity of one input is increased, the marginal cost of production will decline.

Question 14

Which of the following correctly defines the marginal product of labor?

A) It is the additional output produced by an additional unit of labor, all other factors held constant.
B) It is the additional output produced by a proportionate increase in capital and labor, the demand for the product held constant.
C) It is the additional labor required to produce one additional unit of output, other inputs held constant.
D) It is calculated as the total output divided by the total units of labor employed in production.
E) It is the addition to total cost from employing an additional unit of labor.

Question 15

The following table shows the total output per hour produced in a factory at various levels of employment of labor. The firm sells each unit of output at $2 and each worker is paid a wage of $12.
Table 5-1
$\begin{array} { | c | c | } \hline \begin{array} { c } \text { Nurnber of } \\\text { workers }\end{array} & \text { Total output } \\\hline 1 & 8 \\\hline 2 & 18 \\\hline 3 & 30 \\\hline 4 & 41 \\\hline 5 & 50 \\\hline 6 & 55 \\\hline 7 & 59 \\\hline 8 & 61 \\\hline 9 & 62 \\\hline\end{array}$

-Refer to Table 5-1. Diminishing returns occurs beyond:

A) 2 workers.
B) 3 workers.
C) 4 workers.
D) 5 workers.
E) 6 workers.

Question 16

When the marginal product of a variable input is zero, it implies that the firm is at the point where the total product is:

A) increasing at an increasing rate.
B) also equal to zero.
C) at its maximum.
D) decreasing at an increasing rate.
E) increasing at a decreasing rate.

Question 17

The following table shows the total output per hour produced in a factory at various levels of employment of labor. The firm sells each unit of output at $2 and each worker is paid a wage of $12.
Table 5-1
$\begin{array} { | c | c | } \hline \begin{array} { c } \text { Nurnber of } \\\text { workers }\end{array} & \text { Total output } \\\hline 1 & 8 \\\hline 2 & 18 \\\hline 3 & 30 \\\hline 4 & 41 \\\hline 5 & 50 \\\hline 6 & 55 \\\hline 7 & 59 \\\hline 8 & 61 \\\hline 9 & 62 \\\hline\end{array}$

-Refer to Table 5-1. How many workers should the firm employ in order to maximize profit?

A) 7
B) 6
C) 5
D) 4
E) 3

Question 18

The following table shows the total output produced in a factory at various levels of employment of labor. The firm sells each unit of output at $2 and each worker is paid a wage of $32.
Table 5-1
$\begin{array} { | c | c | } \hline \begin{array} { c } \text { Number of } \\\text { workers }\end{array} & \text { Total output } \\\hline 1 & 8 \\\hline 2 & 18 \\\hline 3 & 30 \\\hline 4 & 41 \\\hline 5 & 50 \\\hline 6 & 56 \\\hline 7 & 60 \\\hline 8 & 61 \\\hline 9 & 62 \\\hline\end{array}$

-Refer to Table 5-1. Diminishing returns to labor occurs beyond:

A) 4 workers.
B) 3 workers.
C) 5 workers.
D) 9 workers.
E) 8 workers.

Question 19

The following table shows the total output per hour produced in a factory at various levels of employment of labor. The firm sells each unit of output at $2 and each worker is paid a wage of $12.
Table 5-1
$\begin{array} { | c | c | } \hline \begin{array} { c } \text { Nurnber of } \\\text { workers }\end{array} & \text { Total output } \\\hline 1 & 8 \\\hline 2 & 18 \\\hline 3 & 30 \\\hline 4 & 41 \\\hline 5 & 50 \\\hline 6 & 55 \\\hline 7 & 59 \\\hline 8 & 61 \\\hline 9 & 62 \\\hline\end{array}$

-Refer to Table 5-1. What is the marginal revenue product of the 2nd worker?

A) $36
B) $24
C) $22
D) $20
E) 0

Question 20

The following table shows the total output produced in a factory at various levels of employment of labor. The firm sells each unit of output at $2 and each worker is paid a wage of $32.
Table 5-1
$\begin{array} { | c | c | } \hline \begin{array} { c } \text { Number of } \\\text { workers }\end{array} & \text { Total output } \\\hline 1 & 8 \\\hline 2 & 18 \\\hline 3 & 30 \\\hline 4 & 41 \\\hline 5 & 50 \\\hline 6 & 56 \\\hline 7 & 60 \\\hline 8 & 61 \\\hline 9 & 62 \\\hline\end{array}$

-Refer to Table 5-1. What is the marginal product of the 5th worker?

A) 9 units
B) 2 units
C) 8 units
D) 6 units
E) 11 units

Question 21

Carefully define the term production function, and explain its importance.

Question 22

Which of the following identifies the optimal usage of inputs by a profit-maximizing firm?

A) Marginal product of labor = marginal product of capital = 0
B) Marginal product of labor/price of labor = marginal product of capital/price of capital
C) Marginal revenue product of labor = marginal revenue product of capital
D) Marginal cost of labor = marginal cost of capital
E) Marginal product of labor/marginal product of capital = price of capital/price of labor

Question 23

Dirt Diggers (DD) is a firm that excavates roadside ditches to lay drainpipe. Its output follows the production function: Q = 10L - .1L2, where Q denotes the length of the ditch in meters. The firm hires labor at a wage of $12 per hour. DD has received an offer to excavate 250 meters for a price of $500. Should it accept the offer? Suppose DD is offered as much or as little excavation work as it desires at a price of $2.00 per meter, what is the optimal quantity that it should choose to excavate?

Question 24

If a production function is expressed in a linear form, the inputs used in the production process:

A) are perfect complements.
B) are perfect substitutes.
C) have to be increased in the same proportion.
D) have fixed marginal costs.
E) have equal marginal productivity.

Question 25

Output elasticity is the percentage change in output that results from a 1 percent increase _____.

A) in all the inputs
B) in the price of an input
C) in the price of the final product
D) in the marginal revenue product of a variable input
E) in the marginal product of an input

Question 26

Carefully define returns to scale, and explain how this differs from marginal returns.

Question 27

When a profit-maximizing firm undertakes production in more than one plant, it will allocate a fixed level of inputs such that _____ is equal across plants.

A) the total product
B) the marginal cost of production
C) the marginal product
D) the average product
E) Answers the marginal product and the average product are both correct.

Question 28

If there is a change in input prices, what is the most likely impact on production isoquants?

A) They will shift leftward toward the origin.
B) The curvature of the isoquant will change.
C) They will remain unchanged.
D) They will shift outward away from the origin.
E) Uncertain, depends on which input prices change.

Question 29

Carefully define marginal rate of technical substitution. What are the assumptions on the basis of which it is calculated?

Question 30

Carefully explain why the marginal product of labor first rises and then falls as the use of labor increases. In which portion of the marginal product of labor curve will the firm typically produce?

Question 31

Which of the following is true of fixed-proportions production?

A) The inputs used in production have constant marginal products.
B) An increase in the price of an input will lead the firm to substitute away from it.
C) The inputs used in production display diminishing marginal returns.
D) The inputs used in production are perfect complements.
E) The marginal cost of the inputs used in production is fixed.

Question 32

Suppose that management increases the size of its plant. What is the most likely impact on total and marginal products of the other inputs? How will this affect usage of the variable inputs?

Question 33

If the sum of the exponents of a Cobb-Douglas production function is equal to 1.2, the production function exhibits:

A) increasing returns to scale.
B) constant returns to scale.
C) diminishing marginal returns.
D) declining productivity.
E) increasing average costs.

Question 34

Which of the following correctly describes a production isoquant?

A) An isoquant is a curve that shows all possible combinations of inputs that can produce a given level of output.
B) An isoquant is a curve that shows the least-cost combinations of inputs that can produce a given level of output.
C) An isoquant is a curve that shows all possible combinations of inputs that are used to produce various levels of output.
D) An isoquant is a curve that shows all possible levels of output that can be produced in the short-run using one variable input.
E) An isoquant is a curve that shows all possible levels of output that can be produced at various input price levels.

Question 35

The slope of an isocost line shows:

A) the ratio of the marginal revenue product of the inputs.
B) the ratio of marginal product of the inputs.
C) the marginal rate of technical substitution.
D) the ratio of the input prices.
E) the output elasticity of production.

Question 36

For the Cobb-Douglass production function: Q = cLαKβ derive the marginal rate of technical substitution?

Question 37

Which of the following production functions displays decreasing returns to scale?

A) Q = aL + bK²
B) Q = aL + bK
C) Q = bLK
D) Q = cL^.2K^.5
E) Q = cL²K⁵

Question 38

A factory produces product A according to the production function QA = 100XA, where XA denotes the amount of input and QA is the quantity produced. It also produces product B according to the production function QB = 200XB - XB2, where XB denotes the amount of input and QB is the quantity produced. The total available amount of input X is 100 units. The firm's profit-maximizing allocation of input X is:

A) X_A = 60 and X_B = 40.
B) X_A = 50 and X_B = 50.
C) X_A = 0 and X_B = 100.
D) X_A = 100 and X_B = 0.
E) X_A = 30 and X_B = 70.

Question 39

Explain how the optimal usage of the variable input, labor, will change in response to the following changes in the short-run:
(a) A drop in the price of the good or service that the firm sells

Question 40

Will a profit-maximizing firm seek to maximize output from a variable input? Explain.

Question 41

$\lambda$

-Ranger Construction is preparing to repair potholes, under contract to the local county road repair agency. Based on past experience, Ranger has found that output can be described by: Q = K^.5L^.5, where Q = pot holes filled, K = units of capital, and L = units of labor. Ranger can hire labor at $12 per hour, and the cost of capital is $8 per unit. Capacity limitations require that Ranger accepts no more than $96,000 worth of filling this season. What is the optimal mix of inputs for Ranger? How many potholes should Ranger agree to fill? Use the method of Lagrange multipliers to find the solution.

Question 42

Assume that a firm employs labor and capital by paying $40 per unit of labor employed and $200 per hour to rent a unit of capital. Given that the production function is given by: Q = 10L - L2 + 60K -1.5K2, where Q is total output, L is labor, and K is capital, what is the firm's optimal combination of capital and labor?

Question 43

Sleak Teak builds yard furniture, using domestic hardwoods and (in a smaller shop) handcrafted knick-knacks from the same sort of wood. Although hardwoods were readily available in the past, recently they have been much more difficult to obtain. Consultation with the plant managers of the two lines has resulted in the following production functions for hardwood usage in the two products. For yard furniture: Y = 2T_Y - .001T_Y², while for Knick-knack: K = 20T_K - .01T_K². Here Y and K denote units of the two types of products and T_Y and T_K denote teak used in yard furniture and knick-knacks respectively. Yard furniture can be sold at a profit of $100 per unit, and knick-knacks can be sold at a profit of $25 each. Sleak Teak has 1,300 units of teak available. How should it be allocated across the two products? Explain.

Question 44

Enpar manufactures engine parts for an automotive manufacturer. It operates two plants, A and B, which have the following production functions: QA = 30SA - .25SA2 and QB = 40SB - .5SB2, where QA and QB denote the outputs of engine parts from each plant and SA and SB denote the amounts of steel used in each plant. Suppose that total steel availability is 40 units. What is the optimal allocation of steel between the two plants?

Question 45

Standale Plastics produces plastic dustpans, using a semi-automated system of five machines to produce pans. The amount of labor to tend the machines, repair, adjust input flows, and remove completed pans, is variable, and output tends to follow the formula: Q = 300L.6, where Q = units of output produced per day and L = number of daily workers.
(a) Compute the total product per day and the marginal product of labor for the first five workers.

Question 46

Specialty Steel has carefully measured production in its new plant to determine whether it is technically efficient in production. It has found that, for its two inputs K and L, it has the following marginal products: MPK = 15 units and MPL = 22 units. The inputs are hired in perfectly competitive markets, and the firm faces input costs of PK = $7.50 and PL = $10 per unit. You have been hired as a consultant to assist Specialty in increasing profitability. What do you recommend about production planning? Explain.

Question 47

A firm produces according to the following production function: Q = K.25L.75. The price of K is $4 per unit, and the price of L is $6 per unit. What is the optimal capital/labor ratio?

Question 48

Crew Brew produces a popular brand of beer in its mini-brewery located on a small river in Wisconsin. It uses a special formula, combined with the fresh water from the local stream, to produce a drink popular with local folks and tourists who visit during the summer fishing season, and autumn deer hunting season. Crew's production function is: Q = 50K + 50L, where Q = barrels of beer, K = units of capital, and L = units of labor.
(a) Suppose that capital can be purchased for $8 per unit, and labor costs $6 per unit. What is the optimal combination of inputs for the firm to employ?

Question 49

Carefully explain the condition that the firm should follow if it wishes to produce at least cost in the long run.

Question 50

A firm has carefully estimated its production function to be: Q = K.55L.45. What is output elasticity in this case? What sort of returns to scale does the firm face? Explain.

Question 51

A firm produces a good in two factories: one in Tucson and one in Phoenix. Historically, the plants' long-run average costs have been comparable. Engineers have found that output elasticity at the Tucson plant is 1.1, while at Phoenix it is .93. A senior production manager has recommended expanding the scale of production in Tucson over the next few years and cutting production in Phoenix. Examine the validity of this proposal.