Deck 5: Production Analysis

Question 1

The marginal rate of technical) substitution is equal to the inverse of the slope of an isoquant.

Answer 1

False

Question 2

A least-cost combination of inputs requires that the marginal product per dollar spent on each variable input be equal.

Answer 2

True

Question 3

The marginal product of a variable input is the rate of change of total product with respect to the input, all other things kept fixed.

Answer 3

True

Question 4

The short run is a period so brief that the amount of at least one input, or factor of production, is fixed.

Question 5

With output held constant, for a combination of inputs to be a least cost combination, the slopes of an isocost line and the isoquant curve must be equal at the point the where the two curves touch.

Question 6

For each possible combination of inputs, the production function indicates the minimum quantity of output that can be produced.

Question 7

A production function is a mathematical statement of the way that the quantity of output of a particular product depends on the use of specific inputs, or resources.

Question 8

The long run is a period of time long enough for at least one input, or factor of production, to vary as far as the individual firm is concerned.

Question 9

The long run is a period of time long enough for all inputs, or factors of production, to be variable as far as the individual firm is concerned.

Question 10

At the point where MP_L is equal to zero, TP_L is at its maximum.

Question 11

The marginal product of a variable input is the rate of change of average product with respect to the input, all other things kept fixed.

Question 12

An isoquant is a contour line that shows the various combinations of two inputs that will produce a given level of output.

Question 13

The reason that we can say that the production function indicates the maximum quantities that can be produced with each combination of inputs is because we are assuming that all of the inputs are being used efficiently.

Question 14

The short run is a period so brief that the amount of at least one input, or factor of production, is variable.

Question 15

Fat Cat Farms Inc. is a small catfish farm. Fat Cat estimates that output would increase by 1800 pounds per month with an additional 2,000 pounds of catfish food provided monthly by a new feeding system. Alternatively, output could be increased by 3,000 pounds per month with an additional 20,000 gallons of fresh water per month. Assuming the cost of water is $.06 per gallon and that fertilizer is $.25 per pound, Fat Cat is using an optimal combination of fish food and water.

Question 16

For each possible combination of inputs, the production function indicates the maximum quantity of output that can be produced.

Question 17

An isocost curve is a line that represents all combinations of inputs that can be employed for a given cost.

Question 18

The expansion path of a firm refers to the path that connects least cost combinations of input for different levels of output, assuming constant input prices.

Question 19

Hill Country Farms Inc. is a small grower of peaches. Hill Country estimates that peach output would increase by 600 bushels per season with an additional 6,000 gallons of water provided strategically throughout the season by an existing irrigation system. Alternatively, peach output could be increased by 500 bushels per season with an additional 2 tons of fertilizer applied at the beginning of the season. Given the cost of water is $.01 per gallon and that fertilizer is $25 per ton, Hill Country Farms is using an optimal combination of fertilizer and water.

Question 20

The marginal rate of technical) substitution is equal to the negative of the slope of the isoquant and shows how much of one input can be substituted for another, output constant.

Question 21

Which of the following statements is correct for a variable input "a" and short-run product curves?

A) When TP_a reaches a maximum, the MP_a is zero.
B) Then TP_a reaches a maximum, the MP_a is +1.
C) When AP_a reaches a maximum, MP_a is zero.
D) When MP_a reaches a maximum, AP_a is zero.
E) None of the above is correct.

Question 22

If two inputs can be substituted for each other at a fixed rate then:

A) the inputs are perfect substitutes.
B) the inputs are imperfect substitutes.
C) the inputs are not substitutable.
D) the amount of each input is the same along an isoquant.
E) none of the above.

Question 23

The given production function exhibits which of the following?

A) constant returns to scale - for every 100% increase in input, there is a 100% increase in output.
B) decreasing returns to scale - for every 100% increase in input, there is a .700% increase in output.
C) decreasing returns to scale - for every 100% increase in input, there is a .425% increase in output
D) increasing returns to scale - for every 100% increase in input, there is a 700% increase in output
E) increasing returns to scale - for every 100% increase in input, there is a 425% increase in output.

Question 24

If equal increments of one variable input are added while keeping the amounts of all other inputs fixed, and increasing additions to total product occur, then:

A) diminishing marginal returns have begun.
B) the output level where marginal product is maximized has not yet been reached.
C) average product has reached its maximum.
D) average product is at its minimum.
E) average product is declining.

Question 25

The given production function exhibits which of the following?

A) constant returns to scale - for every 100% increase in input, there is a 100% increase in output.
B) decreasing returns to scale - for every 100% increase in input, there is a .675% increase in output.
C) decreasing returns to scale - for every 100% increase in input, there is a .425% increase in output
D) increasing returns to scale - for every 100% increase in input, there is a 675% increase in output
E) increasing returns to scale - for every 100% increase in input, there is a 425% increase in output.

Question 26

If, after reaching a certain level of production, one additional unit an input variable would produce a decline in total product, then:

A) diminishing marginal returns to that input have begun.
B) the output level where marginal product of that input is maximized has not yet been reached.
C) the output level where marginal product of that input is equal to zero has been reached.
D) average product of that input is at its minimum.
E) average product of that input is increasing.

Question 27

To an economist, for a firm to be operating in the long run,

A) all inputs are variable.
B) some inputs are fixed
C) only one input can be variable.
D) no more than one input can be fixed.
E) at least one input must be variable.

Question 28

If the percentage increase in a firm's output is lower than the percentage increase in all of its inputs, then:

A) diminishing marginal returns have begun.
B) the firm is employing the least cost combination of inputs.
C) returns to scale are constant.
D) returns to scale are decreasing.
E) returns to scale are increasing.

Question 29

Van Farms Inc. is a small grower of watermelons. Van Farms estimates that watermelon output would increase by 1,200 per month with an additional 1,000 gallons of water per month provided by an irrigation system. Alternatively, watermelon output could be increased by 500 per month with an additional 2 tons of fertilizer per month. Assuming the cost of water is $.03 per gallon and that fertilizer is $25 per ton, is Van Farms using an optimal combination of fertilizer and water? Why or why not?

Question 30

If the percentage increase in a firm's output is the same as the percentage increase in all of its inputs, then:

A) diminishing marginal returns have begun.
B) the firm is employing the least cost combination of inputs.
C) returns to scale are constant.
D) returns to scale are decreasing.
E) returns to scale are increasing.

Question 31

To an economist, for a firm to be operating in the short run,

A) all inputs are variable.
B) no more than one input can be fixed.
C) all inputs are fixed.
D) it must operate with its existing plant and equipment.
E) at least one input is fixed.

Question 32

If two inputs can be substituted for each other at different rates while maintaining the same output level, then:

A) the inputs are perfect substitutes.
B) the inputs are imperfect substitutes.
C) the inputs are not substitutable.
D) the amount of each input is the same along an isoquant.
E) none of the above.

Question 33

A mathematical statement of the way that the quantity of output of a particular product depends on the use of specific inputs or resources is called:

A) a demand curve.
B) a total revenue curve.
C) a production function.
D) the marginal rate of technical) substitution.
E) an isoquant curve

Question 34

The marginal rate of technical) substitution is the:

A) negative of the slope of the isoquant.
B) slope of the isoquant.
C) always constant.
D) inverse of the slope of the isoquant.
E) none of the above.

Question 35

Hill Country Farms Inc. is a small grower of peaches. Hill Country estimates that peach output would increase by 600 bushels per season with an additional 6,000 gallons of water provided strategically throughout the season by an existing irrigation system. Alternatively, peach output could be increased by 500 bushels per season with an additional 2 tons of fertilizer applied at the beginning of the season. Assuming the cost of water is $.01 per gallon and that fertilizer is $25 per ton, is Hill Country Farms using an optimal combination of fertilizer and water? Why or why not?

Question 36

The given production function exhibits which of the following?

A) constant returns to scale - for every 100% increase in input, there is a 100% increase in output.
B) decreasing returns to scale - for every 100% increase in input, there is a less than 100% increase in output.
C) decreasing returns to scale - for every 100% increase in input, there is a .425% increase in output
D) increasing returns to scale - for every 100% increase in input, there is a 675% increase in output
E) increasing returns to scale - for every 100% increase in input, there is a 425% increase in output.

Question 37

If the percentage increase in a firm's output is higher than the percentage increase in all of its inputs, then:

A) diminishing marginal returns have begun.
B) the firm is employing the least cost combination of inputs.
C) returns to scale are constant.
D) returns to scale are increasing.
E) returns to scale are decreasing.

Question 38

If two inputs must be used in fixed proportions, then:

A) the inputs are perfect substitutes.
B) the inputs are imperfect substitutes.
C) the inputs are not substitutable.
D) the amount of each input is the same along an isoquant.
E) none of the above.

Question 39

If equal increments of one variable input are added while keeping the amounts of all other inputs fixed, and decreasing additions to total product begin, then:

A) diminishing marginal returns have begun.
B) the firm is employing the least cost combination of inputs.
C) returns to scale are constant.
D) returns to scale are decreasing.
E) returns to scale are increasing.

Question 40

If equal increments of one variable input are added while keeping the amounts of all other inputs fixed, and decreasing additions to total product begin, then:

A) diminishing marginal returns have begun.
B) marginal product has reached its maximum.
C) total product is rising.
D) average product is rising.
E) all of the above

Question 41

A manufacturing firm is trying to decide if it should purchase an automated assembly line. The firm currently has employees completing the assembly portion of its production line. The workers are very efficient; a single worker can produce 5 assembled products per hour. An average worker earns $42.50 per eight-hour day. The automated assembly line can produce 2000 assembled products in eight hours. The company estimates that the costs associated with the automated assemble line total $250 per hour.
a. Should the company use the automated assembly line? Why or why not?
b. The manufacturer of the assembly line is anticipating an increase in the price of its product. What would be the maximum hourly capital cost that you would be willing to incur?

Question 42

Suppose The Solis Company, Inc has the following total product function, where Q is output per time period and L is the number of units of labor hired:
Q = 1000L + 3L² -.02L³
a. What will be the maximum short-run output the firm can produce?
b. At what value of input L will the MP_L for this firm be at its maximum?
c. At what level of output will the firm reach the point of diminishing marginal returns to L?
d. What will be the numerical value of AP_L when it is at its maximum?

Question 43

Use the following table to complete the following problem.

a. Complete the table, given that L is labor units, Q is output per day, and that L is the only variable input.
b. Suppose the firm is producing between 260 and 290 units of output per day and that the price per unit of input L is $60.00. If at that level of production the marginal product of the only fixed input, capital, is 48 units per day, should the firm consider adding to its capital equipment if the price of a unit of capital is $360? Explain.

Question 44

Fast Film, Inc. has a production function as follows:
Q = .4K² + .2KL + .3L²
where Q is the output rolls of film processed per week), K is the capital number of film developing hours), and L is labor number of labor hours employed). Assume a weekly rate of use where K = 40 film developing hours and L = 150 labor hours.
a. What is the total product per week?
b. At this level of production, what is the marginal product of labor?
c. At this level of production, what is the marginal product of capital?

Question 45

The following table gives the quantities of output that can be produced with different amounts of capital and labor utilized by a firm.

a. What are the returns to scale for this firm over the range of capital and labor shown on the table? Why?
b. Compute the marginal product and average product of capital for L = 2 as K varies from 1 unit to 5 units.
c. Compute the marginal product and average product of labor for K = 3 as L varies from 1 unit to 5 units.
d. Suppose the firm is producing 230 units of output using 3 units of capital and 2 units of labor. The cost of one unit of capital is $100 and the cost of one unit of labor is $5. Is the firm using a least cost combination of inputs? Why or why not?

Question 46

The We Make Them Like They Used To Manufacturing Company, Inc produces Victorian wood molding for the booming home restoration market. As they have only recently entered the market, WMTLTUMC, Inc produces only one product - bullet molding. A production function for this single product firm can be expressed as follows:
Q = 60L + 30K + .75LK
where:
Q = number of pallets containing 1000 board feet of molding produced per day
L = units of labor input used per day
K = units of capital input used per day
They are currently utilizing 100 units of capital per day, and 60 units of labor per day. As this process requires highly skilled labor, the price of labor is currently $18.00 per unit and the price of a unit of capital is $6.00. These prices are expected to remain constant into the foreseeable future. Is WMTLTUMC, Inc operating its woodworking facility at a least-cost combination of inputs? Why or why not?

Question 47

Fat Cat Farms Inc. is a small catfish farm. Fat Cat estimates that output would increase by 1800 pounds per month with an additional 2,000 pounds of catfish food provided monthly by a new feeding system. Alternatively, output could be increased by 3,000 pounds per month with an additional 20,000 gallons of fresh water per month. Assuming the cost of water is $.06 per gallon and that fertilizer is $.25 per pound, is Fat Cat using an optimal combination of fish food and water? Why or why not?

Question 48

The We Make Them Like They Used To Manufacturing Company, Inc produces Victorian wood molding for the booming home restoration market. As they have only recently entered the market, WMTLTUMC, Inc produces only one product - bullet molding. A production function for this single product firm can be expressed as follows:
Q = 120L + 60K + 1.5LK
where:
Q = number of pallets containing 1000 board feet of molding produced per day
L = units of labor input used per day
K = units of capital input used per day
They are currently utilizing 200 units of capital per day , and 120 units of labor per day. As this process requires highly skilled labor, the price of labor is currently $18.00 per unit and the price of a unit of capital is $12.00. These prices are expected to remain constant into the foreseeable future. Is WMTLTUMC, Inc operating its woodworking facility at a least-cost combination of inputs? Why or why not?

Question 49

The following table gives the quantities of output that can be produced with different amounts of capital and labor utilized by a firm.

a. What are the returns to scale for this firm over the range of capital and labor shown on the table? Why?
b. Compute the marginal product and average product of capital for L = 4 as K varies from 1 unit to 5 units.
c. Compute the marginal product and average product of labor for K = 1 as L varies from 1 unit to 5 units.
d. Suppose the firm is producing 376 units of output using 1 units of capital and 4 units of labor. The cost of one unit of capital is $39.50 and the cost of one unit of labor is $11.00. Is the firm using a least cost combination of inputs? Why or why not?

Question 50

The following table gives the quantities of output that can be produced with different amounts of capital and labor utilized by a firm.

a. What are the returns to scale for this firm over the range of capital and labor shown on the table? Why?
b. Compute the marginal product and average product of capital for L = 3 as K varies from 1 unit to 6 units.
c. Compute the marginal product and average product of labor for K = 4 as L varies from 1 unit to 6 units.
d. Suppose the firm is producing 300 units of output using 4 units of capital and 3 units of labor. The cost of one unit of capital is $15.00 and the cost of one unit of labor is $75.00. Is the firm using a least cost combination of inputs? Why or why not?

Question 51

The Garbage Muncher Inc, a commercial garbage service, is considering the purchase of a newer combination truck and open top dumpster system which will allow them to collect 10 additional tons of garbage per day. The new system will require an additional capital investment of $96,000 per year based on a 240 workday year of 8 working hours per day. As an alternative Muncher could hire additional laborers at $7.50 per hour. These laborers, utilizing current equipment, can load one ton of garbage every four hours. Assume that demand for Muncher's services is great, and that they intend to expand to meet this demand. Also assume that with the utilization of either system, Muncher's price exceeds its average variable cost) If Muncher wishes to maximize profit, should they purchase a new system or hire more laborers? Why?