Deck 10: Production and Cost Estimation

Question 1

A short-run production function was estimated as $Q = - 0.002 L ^ { 3 } + 0.16 L ^ { 2 }$ At 20 units of labor,what is average product?

A)6.0
B)1.9
C)6.3
D)4.0
E)2.4

Answer 1

2.4

Question 2

A short-run production function was estimated as $Q = - 0.002 L ^ { 3 } + 0.16 L ^ { 2 }$ At 60 units of labor,what is marginal product?

A)4.1
B)1.2
C)6.3
D)2.4
E)-2.4

Answer 2

-2.4

Question 3

Straker Industries estimated its short-run costs using a U-shaped average variable cost function of the form $A V C = a + b Q + c Q ^ { 2 }$ and obtained the following results.Total fixed cost (TFC)at Straker Industries is $1,000. At what level of output is average variable cost (AVC)at its minimum point for Straker Industries?

A)0.14
B)4.7
C)7
D)14
E)28

Answer 3

7

Question 4

Which of the following specifications could NOT be employed for estimating a short run production function?

A)Q = aK + bL
B) $Q = a K ^ { 3 } L ^ { 3 } + b K ^ {2 } L ^ { 2 }$
C)Q = AL³ + BL²
D)both a and b
E)all of the above

Question 5

A short-run production function was estimated as $Q = - 0.002 L ^ { 3 } + 0.16 L ^ { 2 }$ At 20 units of labor,what is marginal product?

A)6.0
B)1.9
C)6.3
D)4.0
E)2.4

Question 6

An average variable cost function is estimated as $A V C = 96 - 2 Q + 0.05 Q ^ { 2 }$ Which of the following cost functions is associated with this estimate?

A)SMC = 96 - 4Q + 0.1Q²
B)TVC = 96Q - 2Q² + 0.05Q³
C)TVC = 96Q + 4Q² + 0.15Q³
D)SMC = 96 - 4Q + 0.15Q²
E)both b and d

Question 7

A short-run production function was estimated as $Q = - 0.002 L ^ { 3 } + 0.16 L ^ { 2 }$ At what level of labor usage does the maximum average product occur?

A)20
B)30
C)40
D)50
E)60

Question 8

With a cubic production function of the form $Q = a K ^ { 3 } L ^ { 3 } + b K ^ { - 2 } L ^ { 2 }$ ,in order for the average and marginal product functions to have their usual theoretical properties,it must be the case that

A)a < 0,b > 0
B)a > 0,b < 0
C)a < 0,b < 0
D)a > 0,b > 0

Question 9

A short-run production function was estimated as $Q = - 0.002 L ^ { 3 } + 0.16 L ^ { 2 }$ At 60 units of labor,what is average product?

A)9.4
B)8.6
C)3.7
D)2.4
E)6.4

Question 10

An estimated short-run cost function

A)can be used to make price and output decisions.
B)holds the capital stock constant.
C)can be estimated using time-series data.
D)both a and c
E)all of the above

Question 11

Straker Industries estimated its short-run costs using a U-shaped average variable cost function of the form $A V C = a + b Q + c Q ^ { 2 }$ and obtained the following results.Total fixed cost (TFC)at Straker Industries is $1,000. The estimated short-run marginal cost function (SMC)at Straker Industries is:

A) $S M C = 43.4 Q - 1.4 Q ^ { 2 } + 0.07 Q ^ { 3 }$
B) $S M C = 43.4 - 1.4 Q + 0.07 Q ^ { 2 }$
C) $S M C = 43.4 Q - 5.6 Q ^ { 2 } + 0.6 Q ^ { 3 }$
D) $S M C = 43.4 - 5.6 Q + 0.6 Q ^ { 2 }$

Question 12

When estimating a short-run average variable cost function,

A)the intercept must be forced to equal zero.
B)the cost data must be inflation-adjusted.
C)at least one input must have been constant during the period in which the data were collected.
D)both b and c
E)all of the above

Question 13

A short-run production function was estimated as $Q = - 0.002 L ^ { 3 } + 0.16 L ^ { 2 }$ What is average product when it is at its maximum level?

A)3.20
B)8.75
C)6.92
D)6.00
E)9.40

Question 14

Which of the following is an estimable form of a production function?

A)Q = f(L,K)
B)Q = f(L, $\bar { K }$ )
C) $Q = a K ^ { 3 } L ^ { 3 } + b K ^ { - 2 } L ^ { 2 }$
D)all of the above

Question 15

A short-run production function was estimated as $Q = - 0.002 L ^ { 3 } + 0.16 L ^ { 2 }$ What is total product when average product is at its maximum level?

A)94
B)86
C)100
D)128
E)150

Question 16

A short-run production function was estimated as $Q = - 0.002 L ^ { 3 } + 0.16 L ^ { 2 }$ At 20 units of labor,what is total product?

A)48
B)96
C)20
D)62
E)41

Question 17

The opportunity cost of capital owned by the firm should reflect

A)acquisition cost.
B)the return foregone by using the capital rather than renting it to another firm.
C)wage rate differences.
D)both a and b

Question 18

A theoretical restriction on the short-run cubic cost equation,TVC = aQ + bQ + cQ²,is

A)a > 0,b > 0,c > 0
B)a > 0,b < 0,c > 0
C)a > 0,b > 0,c < 0
D)a > 0,b < 0,c < 0

Question 19

When estimating a short-run production function of the form $Q = A L ^ { 3 } + B L ^ { 2 }$ ,it is necessary to specify in the computer routine that

A)A < 0.
B)B > 0.
C)the intercept term is forced to equal zero.
D)a and b
E)all of the above

Question 20

Which of the following represents a short-run cubic production function?

A) $Q = a K ^ { 3 } L ^ { 3 } + b K ^ { - 2 } L ^ { 2 }$
B) $Q = 3 A L ^ { 2 } + 2 B L \left( \text { where } A = a \bar { K } ^ { 3 } , B = b \bar { K } ^ { 2 } \right)$
C) $Q = A L ^ { 3 } + B L ^ { 2 } \left( \text { where } A = a \bar { K } ^ { 3 } , B = b \bar { K } ^ { 2 } \right)$
D) $Q = A L ^ { 2 } + B L \left( \text { where } A = a \overline { K ^ { - 3 } } , B = b \bar { K } ^ { 2 } \right)$

Question 21

Straker Industries estimated its short-run costs using a U-shaped average variable cost function of the form $A V C = a + b Q + c Q ^ { 2 }$ and obtained the following results.Total fixed cost (TFC)at Straker Industries is $1,000. If Straker Industries produces 12 units of output,what is estimated average total cost (ATC)?

A)$121.93
B)$171.40
C)$463.20
D)$1,348

Question 22

A firm estimates its long-run production function to be $Q = - 0.0075 K ^ { 3 } L ^ { 3 } + 12 K ^ { 2 } L ^ { 2 }$ Suppose the firm employs 12 units of capital.Marginal product when 10 units of labor are employed is

A)12,248
B)13,142
C)14,287
D)15,984
E)30,672

Question 23

Straker Industries estimated its short-run costs using a U-shaped average variable cost function of the form $A V C = a + b Q + c Q ^ { 2 }$ and obtained the following results.Total fixed cost (TFC)at Straker Industries is $1,000. If Straker Industries produces 20 units of output,what is estimated average total cost (ATC)?

A)$19.40
B)$67.40
C)$117.40
D)$1,348

Question 24

Straker Industries estimated its short-run costs using a U-shaped average variable cost function of the form $A V C = a + b Q + c Q ^ { 2 }$ and obtained the following results.Total fixed cost (TFC)at Straker Industries is $1,000. If Straker Industries produces 12 units of output,what is estimated short-run marginal cost (SMC)?

A)$28.04
B)$32.40
C)$33.33
D)$62.60

Question 25

Straker Industries estimated its short-run costs using a U-shaped average variable cost function of the form $A V C = a + b Q + c Q ^ { 2 }$ and obtained the following results.Total fixed cost (TFC)at Straker Industries is $1,000. If Straker Industries produces 20 units of output,what is estimated average variable cost (AVC)?

A)$19.40
B)$67.40
C)$171.40
D)$179.40

Question 26

The empirical specification $Q = A L ^ { 3 } + B L ^ { 2 }$ can be used to estimate

A)a short-run cubic production function.
B)short-run cubic cost function.
C)a family of U-shaped product curves.
D)both a and c
E)none of the above

Question 27

Straker Industries estimated its short-run costs using a U-shaped average variable cost function of the form $A V C = a + b Q + c Q ^ { 2 }$ and obtained the following results.Total fixed cost (TFC)at Straker Industries is $1,000. If Straker Industries produces 20 units of output,what is estimated total cost (TC)?

A)$1,348
B)$1,498
C)$2,348
D)$4,428

Question 28

A firm estimates its long-run production function to be $Q = - 0.0075 K ^ { 3 } L ^ { 3 } + 12 K ^ {2 } L ^ { 2 }$ Suppose the firm employs 12 units of capital.At ________ units of labor,average product of labor begins to diminish.

A)32.21
B)44.44
C)66.67
D)76.66
E)82.27

Question 29

For the short-run cost function AVC = a + bQ + cQ²,

A)the AVC curve is $U$ -shaped when a < 0,b > 0,and c < 0.
B)the AVC curve is $U$ -shaped when a > 0,b < 0,and c > 0.
C)the corresponding SMC function is $S M C = a Q + 2 b Q ^ { 2 } + 3 c Q ^ { 3 }$ .
D)both a and c
E)all of the above

Question 30

The empirical specification $T V C = a Q + b Q ^ { 2 } + c Q ^ { 3 }$ can be used to estimate

A)a short-run cubic production function.
B)short-run cubic cost function.
C)a $\text { U }$ -shaped TVC curve.
D)both b and c
E)none of the above

Question 31

Straker Industries estimated its short-run costs using a U-shaped average variable cost function of the form $A V C = a + b Q + c Q ^ { 2 }$ and obtained the following results.Total fixed cost (TFC)at Straker Industries is $1,000. If Straker Industries produces 12 units of output,what is estimated average variable cost (AVC)?

A)$28.04
B)$32.40
C)$33.33
D)$38.60

Question 32

Straker Industries estimated its short-run costs using a U-shaped average variable cost function of the form $A V C = a + b Q + c Q ^ { 2 }$ and obtained the following results.Total fixed cost (TFC)at Straker Industries is $1,000. At Straker Industries,average variable cost (AVC)reaches its minimum value at $________.

A)$24.50
B)$33.60
C)$72.80
D)$121.80

Question 33

Straker Industries estimated its short-run costs using a U-shaped average variable cost function of the form $A V C = a + b Q + c Q ^ { 2 }$ and obtained the following results.Total fixed cost (TFC)at Straker Industries is $1,000. If Straker Industries produces 20 units of output,what is estimated total variable cost (TVC)?

A)$1,348
B)$1,498
C)$2,348
D)$4,428

Question 34

A cubic specification for a short-run production function is appropriate when the scatter diagram indicates

A)an S-shaped total product curve.
B)marginal product of labor falls throughout the range of labor usage.
C)total product is decreasing throughout the range of labor usage.
D)an S-shaped marginal product of labor curve.
E)a $\text { U }$ -shaped marginal product of labor curve (MP first falls and then rises as labor usage increases.

Question 35

Straker Industries estimated its short-run costs using a U-shaped average variable cost function of the form $A V C = a + b Q + c Q ^ { 2 }$ and obtained the following results.Total fixed cost (TFC)at Straker Industries is $1,000. If Straker Industries produces 12 units of output,what is estimated total cost (TC)?

A)$1,000
B)$1,463
C)$2,348
D)$4,428

Question 36

A firm estimates its long-run production function to be $Q = - 0.0075 K ^ { 3 } L ^ { 3 } + 12 K ^ { 2 } L ^ { 2 }$ Suppose the firm employs 12 units of capital.The product curve(s)in the short-run are

A)TP = -12.96 L³ + 1,728L².
B)AP = -12.96 L³ + 1,728L².
C)MP = -38.88 L² + 3,456L.
D)both a and b
E)both a and c

Question 37

A firm estimates its long-run production function to be $Q = - 0.0075 K ^ { 3 } L ^ { 3 } + 12 K ^ { 2 } L ^ { 2 }$ Suppose the firm employs 12 units of capital.At _______ units of labor,marginal product of labor begins to diminish.

A)32.21
B)44.44
C)66.67
D)76.66
E)82.27

Question 38

Straker Industries estimated its short-run costs using a U-shaped average variable cost function of the form $A V C = a + b Q + c Q ^ { 2 }$ and obtained the following results.Total fixed cost (TFC)at Straker Industries is $1,000. If Straker Industries produces 20 units of output,what is estimated short-run marginal cost (SMC)?

A)$171.40
B)$463.20
C)$1,348
D)$2,348

Question 39

When estimating a cubic short-run production function $Q = A L ^ { 3 } + B L ^ { 2 }$ using linear regression analysis,you must

A)transform the equation into linear form by defining L3 and L2 as L³ and L²,respectively.
B)suppress the intercept term (regress through the origin).
C)convert the right-hand-side variables to logarithms.
D)both a and b
E)both b and c

Question 40

Straker Industries estimated its short-run costs using a U-shaped average variable cost function of the form $A V C = a + b Q + c Q ^ { 2 }$ and obtained the following results.Total fixed cost (TFC)at Straker Industries is $1,000. If Straker Industries produces 12 units of output,what is estimated total variable cost (TVC)?

A)$171.40
B)$463.20
C)$1,348
D)$2,348

Question 41

The manager of Greene Enterprises,Inc.,recently estimated its average variable cost (AVC)function to be $A V C = 88 - 0.026 Q + 0.000003 Q ^ { 2 }$ Greene Enterprises faces total fixed costs (TFC)of $300,000.When Greene's output is 2,000 units,what is short-run marginal cost (SMC)?

A)$20
B)$42
C)$72
D)$90
E)$100

Question 42

The manager of Greene Enterprises,Inc.,recently estimated its average variable cost (AVC)function to be $A V C = 88 - 0.026 Q + 0.000003 Q ^ { 2 }$ Greene Enterprises faces total fixed costs (TFC)of $300,000.What is total variable cost (TVC)at Greene Enterprises when average variable cost (AVC)is at its minimum?

A)$48,000
B)$101,101
C)$137,222
D)$190,476
E)$437,212

Question 43

The manager of Greene Enterprises,Inc.,recently estimated its average variable cost (AVC)function to be $A V C = 88 - 0.026 Q + 0.000003 Q ^ { 2 }$ Greene Enterprises faces total fixed costs (TFC)of $300,000.If Greene Enterprises produces 6,000 units of output,what is estimated average total cost (ATC)?

A)$40
B)$75.25
C)$80
D)$90
E)$168.42

Question 44

A firm estimates its long-run production function to be $Q = - 0.0075 K ^ { 3 } L ^ { 3 } + 12 K ^ { 2 } L ^ { 2 }$ Suppose the firm employs 12 units of capital.Average product when 10 units of labor are employed is

A)12,248
B)13,142
C)14,287
D)15,984
E)30,672

Question 45

The manager of Greene Enterprises,Inc.,recently estimated its average variable cost (AVC)function to be $A V C = 88 - 0.026 Q + 0.000003 Q ^ { 2 }$ Greene Enterprises faces total fixed costs (TFC)of $300,000.At what level of output does average variable cost (AVC)reach its minimum value for Greene Enterprises?

A)800
B)3,144
C)3,800
D)4,333
E)51,672

Question 46

The manager of Greene Enterprises,Inc.,recently estimated its average variable cost (AVC)function to be $A V C = 88 - 0.026 Q + 0.000003 Q ^ { 2 }$ Greene Enterprises faces total fixed costs (TFC)of $300,000.When Greene's output is 2,000 units,average variable cost (AVC)is

A)rising
B)falling
C)greater than short-run marginal cost
D)less than short-run marginal cost
E)both b and c

Question 47

The manager of Greene Enterprises,Inc.,recently estimated its average variable cost (AVC)function to be $A V C = 88 - 0.026 Q + 0.000003 Q ^ { 2 }$ Greene Enterprises faces total fixed costs (TFC)of $300,000.If Greene Enterprises produces 6,000 units of output,what is estimated short-run marginal cost (SMC)?

A)$45.60
B)$62.40
C)$83
D)$92
E)$100

Question 48

The manager of Greene Enterprises,Inc.,recently estimated its average variable cost (AVC)function to be $A V C = 88 - 0.026 Q + 0.000003 Q ^ { 2 }$ Greene Enterprises faces total fixed costs (TFC)of $300,000.When Greene's output is 2,000 units,what is total cost (TC)?

A)$144,000
B)$396,000
C)$444,000
D)$642,000
E)$846,000

Question 49

The manager of Greene Enterprises,Inc.,recently estimated its average variable cost (AVC)function to be $A V C = 88 - 0.026 Q + 0.000003 Q ^ { 2 }$ Greene Enterprises faces total fixed costs (TFC)of $300,000.When Greene's output is 2,000 units,what is average variable cost (AVC)?

A)$20
B)$48
C)$62
D)$72
E)$85

Question 50

The manager of Greene Enterprises,Inc.,recently estimated its average variable cost (AVC)function to be $A V C = 88 - 0.026 Q + 0.000003 Q ^ { 2 }$ Greene Enterprises faces total fixed costs (TFC)of $300,000.When Greene Enterprises produces 6,000 units,average variable cost (AVC)is $_________.

A)$40
B)$49.62
C)$55
D)$60
E)$72.46

Question 51

The manager of Greene Enterprises,Inc.,recently estimated its average variable cost (AVC)function to be $A V C = 88 - 0.026 Q + 0.000003 Q ^ { 2 }$ Greene Enterprises faces total fixed costs (TFC)of $300,000.At Greene Enterprises,average variable cost (AVC)reaches its minimum value at $________.

A)$28.00
B)$31.67
C)$39.64
D)$43.33
E)$82.00

Question 52

The manager of Greene Enterprises,Inc.,recently estimated its average variable cost (AVC)function to be $A V C = 88 - 0.026 Q + 0.000003 Q ^ { 2 }$ Greene Enterprises faces total fixed costs (TFC)of $300,000.When Greene's output is 6,000 units,average variable cost (AVC)is

A)rising
B)falling
C)greater than short-run marginal cost
D)less than short-run marginal cost
E)both a and d

Question 53

A short-run marginal cost function is estimated as $S M C = 96 - 4 Q + 0.15 Q ^ { 2 }$ .Which of the following cost functions is associated with this estimated SMC equation?

A)TVC = 96Q - 2Q² + 0.05Q³
B)SMC = 96 - 4Q + 0.1Q²
C)TVC = 96Q + 4Q² + 0.15Q³
D)AVC = 96 - 2Q + 0.05Q²
E)a and d