Deck 6: The Theory and Estimation of Production Appendices 6A,6B,and 6C

Question 1

The difference between the short-run and the long-run is

A)three months,or one business quarter.
B)the time it takes for firms to change all inputs in the production process.
C)the time it takes for firms to change only their variable inputs.
D)More information is required to answer this question.

Answer 1

B

Question 2

When the law of diminishing returns takes effect

A)firms must add increasingly more input if they are to maintain the same extra amount of output.
B)firms must add decreasingly more input if they are to maintain the same extra amount of output.
C)more input must be added in order to increase its output.
D)a firm must always try to add the same amount of input to the production process.

Answer 2

A

Question 3

Assume a firm employs 10 workers and pays each $15 per hour.Further assume that the MP of the 10th worker is 5 units of output and that the price of the output is $4.According to economic theory,in the short run

A)the firm should hire additional workers.
B)the firm should reduce the number of workers employed.
C)the firm should continue to employ 10 workers.
D)More information is required to answer this question.

Answer 3

A

Question 4

Decreasing returns to scale

A)indicate that an increase in all inputs by some proportion will result in a decrease in output.
B)must always occur at some point in the production process.
C)are directly related to the law of diminishing returns.
D)All of the above are true.
E)None of the above is true.

Question 5

The marginal product of the variable input

A)is always positive.
B)typically falls then rises.
C)is equal to the total product divided by the total amount of the variable input employed.
D)None of the above

Question 6

The term Production Function refers to the

A)use of machinery and equipment in production.
B)relationship between costs and output.
C)relationship between inputs and output.
D)role of labor unions.

Question 7

A firm that operates in Stage III of the short-run production function

A)has too much fixed capacity relative to its variable inputs.
B)has too little fixed capacity relative to its variable inputs.
C)has greatly overestimated the demand for its output.
D)should try to increase the amount of variable input used.

Question 8

Stage III of the short-run Production Function is

A)the most efficient mix of inputs.
B)the least costly level of output.
C)where additional units of variable inputs will lead to less output.
D)where additional units of variable inputs will lead to more output.

Question 9

Which of the following indicates when Stage II ends and Stage III begins in the short-run production function?

A)when AP = 0
B)when MP = 0
C)when MP = AP
D)when MP starts to diminish

Question 10

Which of the following statements about the short-run production function is true?

A)MP always equals AP at the maximum point of MP.
B)MP always equals zero when TP is at its maximum point.
C)TP starts to decline at the point of diminishing returns.
D)When MP diminishes,AP is at its minimum point.
E)None of the above is true.

Question 11

Which of the following indicates when Stage I ends and Stage II begins in the short-run production?

A)when AP = 0
B)when MP = 0
C)when MP = AP
D)when MP starts to diminish

Question 12

The "Law of Diminishing Returns" states that

A)additional inputs will reduce output.
B)additional inputs will decrease average productivity.
C)the supply of inputs is becoming scarce.
D)additional inputs will lead to less additional output.

Question 13

The production period in which at least one input is fixed in quantity is the

A)production run.
B)long run.
C)short run.
D)planning horizon.

Question 14

Output (Total Product)is maximized when

A)average productivity is at its maximum.
B)the "law of diminishing returns" sets in.
C)marginal productivity is zero.
D)marginal productivity is at its maximum.

Question 15

In a call center,which of the following situations can be considered as a variable input in the short run?

A)the level of computer software being utilized
B)the number of call center representatives on duty at the center
C)the number of call center managers or supervisors
D)the size (e.g.,square footage)of the call center

Question 16

A firm using two inputs,X and Y,is using them in the most efficient manner when

A)MPx = MPy.
B)Px = Py and MPx = MPy.
C)MPx/Py = MPy/Px.
D)MPx/MPy = Px/Py.

Question 17

If a firm finds itself operating in Stage I,it implies that

A)variable inputs are extremely expensive.
B)it overinvested in fixed capacity.
C)it underinvested in fixed capacity.
D)fixed inputs are extremely expensive.

Question 18

In the long run,a firm is said to be experiencing decreasing returns to scale if a 10 percent increase in inputs results in

A)an increase in output from 100 to 110.
B)a decrease in output from 100 to 90.
C)an increase in output from 100 to 105.
D)a decrease in output from 100 to 85.

Question 19

Which of the following holds true?

A)When the Marginal Product (MP)is rising,Marginal cost (MC)is rising; and when MP is falling,MC is falling.
B)When MP is rising,MC is falling,and when MP is falling,MC is rising.
C)When MP is rising,MC is constant,and when MP is falling,MC is negative.
D)There is no relationship between MP and MC.

Question 20

Which of the following is not true about the law of diminishing returns?

A)It is a short-run phenomenon.
B)It refers to diminishing marginal product.
C)It will have an impact on the firm's marginal cost.
D)It divides Stage I and II of the production process.
E)All of the above are true.

Question 21

Which of the following is the best example of two inputs that would exhibit a constant marginal rate of technical substitution?

A)trucks and truck drivers
B)natural gas and oil
C)personal computers and clerical workers
D)company-employed computer programmers and temporary supplemental computer programmers

Question 22

Based on the table above,if the wage rate is $500 and the price of output is $5,how many workers should the firm hire?

Question 23

If a firm used a combination of inputs that was to the left of its isocost line,it would indicate that

A)it is exceeding its budget.
B)it is not spending all of its budget.
C)it is operating at its optimal point because it is saving money.
D)None of the above

Question 24

When is it not in the best interest of a company to hire additional workers in the short run?

A)when the average product of labor is decreasing
B)when the firm is in Stage II of the production process
C)when the marginal revenue product equals zero
D)when the wage rate is equal to or greater than labor's marginal revenue product

Question 25

Which of the following is not one of the strengths of the Cobb-Douglas production function?

A)Both marginal product and returns to scale can be estimated from it.
B)It can be converted into a linear function for ease of calculation.
C)It shows a production function passing through increasing returns to constant returns and then to decreasing returns.
D)The sum of the exponents indicates whether returns to scale are increasing,constant or decreasing.

Question 26

A major advantage of the ________ production function is that it can be easily transformed into a linear function,and thus can be analyzed with the linear regression method.

A)cubic
B)power
C)quadratic
D)None of the above

Question 27

Which of the following combination of inputs is most closely reflective of decreasing marginal rate of technical substitution (MRTS)?

A)oil and natural gas
B)sugar and high fructose corn syrup
C)computers and clerks
D)keyboards and computers

Question 28

The perfect substitution of two inputs implies that

A)two inputs can be substituted at a ratio of 1 to 1.
B)one input can be substituted for another up to some point.
C)two inputs can be substituted at some constant ratio.
D)one input can be substituted for another.

Question 29

Marginal rates of technical substitution (MRTS)represent

A)the optimum combinations of inputs.
B)cost-minimizing combinations of inputs.
C)the degree to which one input can replace another without output changing.
D)All of the above

Question 30

Increasing returns to scale result when

A)in the long-run,an increase in inputs will lead to an increase in the average products of inputs.
B)in the long run,an increase in inputs will lead to an equivalent increase in output.
C)labor becomes more skilled.
D)All of the above

Question 31

When the exponents of a Cobb-Douglas production function sum to more than 1,the function exhibits

A)constant returns.
B)increasing returns.
C)decreasing returns.
D)either increasing or decreasing returns.

Question 32

Isocost curves represent

A)least cost combinations of inputs.
B)combinations of inputs that can be purchased given their prices for the same total cost.
C)a producers cost function.
D)None of the above

Question 33

An advantage of using the cross-sectional regression method in estimating production is that

A)the problem of technological change over time is overcome.
B)there is no need to adjust data,which are in monetary terms for geographical differences.
C)we can assume that all plants operate at their most efficient input combinations.
D)All of the above

Question 34

If MRP > MLC,it means that a firm should

A)use less labor.
B)use more labor.
C)increase its fixed capacity.
D)decrease its fixed capacity.

Question 35

A firm has two plants,one in the United States and one in Mexico,and it cannot change the size of the plants or the amount of capital equipment.The wage in Mexico is $5.The wage in the U.S.is $20.Given current employment,the marginal product of the last worker in Mexico is 100,and the marginal product of the last worker in the U.S.is 500.
a.Is the firm maximizing output relative to its labor cost? Show how you know.
b.If it is not,what should the firm do?

Question 36

The following Cobb-Douglas production function,Q = 1.8L^0.74K^0.36,exhibits

A)increasing returns.
B)constant returns.
C)decreasing returns.
D)Both A and B

Question 37

In economic theory,if an additional worker adds less to the total output than previous workers hired,it is because

A)there may be less that this person can do,given the fixed capacity of the firm.
B)he/she is less skilled than the previously hired workers.
C)everyone is getting in each other's way.
D)the firm is experiencing diminishing returns to scale.

Question 38

________ functions are very useful in analyzing production functions,which exhibit both increasing and decreasing marginal products.

A)Cobb-Douglas
B)Straight-line
C)Quadratic
D)Cubic

Question 39

In the short run,finding the optimal amount of variable input involves which relationship?

A)MP = MC
B)AP = MP
C)MP = 0
D)MRP = MFC

Question 40

An isoquant indicates different combinations of

A)two inputs that can be purchased for the same amount of money.
B)two inputs that can produce the same amount of output.
C)output that can be produced with the same amount of input.
D)output that cost the same amount to produce.

Question 41

Q = K^1/2L^1/2
w = $2,r = $2
The firm would like to know the minimum cost of producing 2000 units of output.Find the combination of inputs that minimizes the cost of producing 2000 units,the total cost,and identify the expansion path.

Question 42

What does the expansion path represent?

Question 43

How would you choose to estimate a production function for a single plant? How would you choose to estimate a production function for a number of firms in an industry? Explain.

Question 44

If the price of capital is $24,the price of labor is $15,and the marginal product of capital is 16,the least costly combination of capital and labor requires that the marginal product of labor be ________.

Question 45

Given the Production Function Q = 72X + 15X² - X³,where Q = Output and X = Input
a.What is the Marginal Product (MP)when X = 8?
b.What is the Average Product (AP)when X = 6?
c.At what value of X will Q be at its maximum?
d.At what value of X will Diminishing Returns set in?

Question 46

What are the major issues that must be considered in measuring inputs for regression analysis of production functions?

Question 47

For each of the following functions,describe returns to scale.
a.Q = K + L
b.Q = K^1/2L^3/4
c.Q = K²L

Question 48

A firm is making a long-run planning decision.It wants to decide on the optimal size of plant and labor force.It is considering building a medium-sized plant and hiring 100 workers.Engineering estimates suggest that at those levels,the marginal product of capital will be 100 and the marginal product of labor will be 75.If the wage rate is $5 and the rental rate on capital is $10,is the firm making the right decision? Support your answer.

Question 49

Q = K^1/2L^1/2
w = $2,r = $2
The firm would like to know the maximum output that can be produced for $8,000.Find the combination of inputs that maximizes output for a cost of $8,000,the amount of output that can be produced,and identify the expansion path.

Question 50

If a production function is given by the equation Q = 12X + 10X² - X³,where Q = Output and X = Input,then calculate the equations for
a.average product
b.marginal product
c.point of diminishing average returns
d.point of diminishing marginal returns