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Semester Two Final Examinations, 2018 ECON3340 Productivity and Efficiency Analysis
Semester One Final Examinations, 2013 ECON7002 Economics for Commerce
Page 1 of 1
This exam paper must not be removed from the venue
School of Economics
EXAMINATION
Semester Deferred Examinations, 2013
ECON7002 Economics for Commerce
This paper is for St Lucia Campus students.
Examination Duration: 120 minutes
Reading Time: 10 minutes
Exam Conditions:
This is a Central Examination
This is a Closed Book Examination - specified materials permitted
During perusal - write only on the rough paper provided
This examination paper will be released to the Library
Materials Permitted In The Exam Venue:
(No electronic aids are permitted e.g. laptops, phones)
An unmarked Bilingual dictionary is permitted
Calculators - Casio FX82 series or UQ approved (labelled)
Materials To Be Supplied To Students:
1 x Multiple Choice Answer Sheet
Instructions To Students:
Venue ____________________
Seat Number ________
Student Number |__|__|__|__|__|__|__|__|
Family Name _____________________
First Name _____________________
For$Examiner$Use$Only$
Question)) Mark)
) )
) )
) )
) )
) )
) )
) )
) )
) )
) )
) )
) )
) )
) )
) )
) )
) )
) )
) )
) )
)
Total) ________)
School of Economics
EXAMINATION
Semester Two Final Examinations, 2018
ECON3340 Productivity and Efficiency Analysis
This paper is for St Lucia Campus students
Examination Duration: 120 minutes
Reading Time: 10 minutes
Exam Conditions
This is Central Examination
This is a Closed Book Examination — specified materials permitted
During reading time — write only on the rough paper provided
This Examination paper will be released to the Library
Materials Permitted In The Exam Venue:
(No electronic aids are permitted e.g. laptops, phones)
An unmarked bilingual dictionary is permitted
Calculators — Casio FX82 series or UQ approved (labelled)
Materials To Be Supplied To Students:
1 × Multiple Choice Answer Sheet
Instructions To Students:
Additional exam materials (e.g., answer booklets, rough paper) will be provided
upon request.
Answer ALL questions.
Each question is worth 4 marks.
All questions are multiple choice.
Consider all options before choosing the “most correct” answer
Total Questions: 25
Total Marks: 100
Se ester One Final Exa inations, 2013 ECON7150 Mathematical Techniques for Economics
Semester One Midsemester Examinations, 2013 ECON7002 Economics for Commerce
Page 1 of 8
This exam paper must not be removed from the venue
School of Economics
EXAMINATION
Semester One Midsemester Examinations, 2013
ECON7002 Economics for Commerce
This paper is for St Lucia Campus students.
Examination Duration: 90 minutes
Reading Time: 10 minutes
Exam Conditions:
This is a Central Examination
This is a Closed Book Examination - specified materials permitted
During perusal - write only on the rough paper provided
This examination paper will be released to the Library
Materials Permitted In The Exam Venue:
(No electronic aids are permitted e.g. laptops, phones)
An unmarked Bilingual dictionary is permitted
Calculators - Casio FX82 series or UQ approved (labelled)
Materials To Be Supplied To Students:
1 x 14 Page An w r Booklet
1 x Multiple Choice Answer Sheet
Rough Paper
Instructions To Students:
Venue ____________________
Seat Number ________
Student Number |__|__|__|__|__|__|__|__|
Family Name _____________________
First Name _____________________
For Examiner Use Only
Question Mark
Total ________
l f i s
I I
Se ester One Final Exa inations, 2013
ECON7150 Mathematical Techniques for Economics
his paper is for St Lucia a pus students
Examination Duration: inutes
Reading Time: minutes
Exam Conditions:
This is a Central Examination
This is a Closed Book Exa ination — specified materials permitted
During perus l — write nly on the r ugh aper provided
This Examination paper will be released to the Library
Materials Permit ed In The Exam Venue:
(No electronic aids ar permitted e.g. laptops, phones)
An unmarked bili gu l dictionary is p rmitted
Calculators — Casio FX82 series or UQ approv (labelled)
Materi s To Be Supplied To Students:
1 × 14 Page Answer Booklet
1 × ultiple Choice Answer Sh et
Instructions o Students:
Total Questions:
Total Marks:
For Examiner Use Only
Question Mark
Total
Page 1 of 2age 1 of 15
Semester Two Final Examinations, 2018 ECON3340 Productivity and Efficiency Analysis
THIS PAGE LEFT BLANK INTENTIONALLY
Page 2 of 15
Semester Two Final Examinations, 2018 ECON3340 Productivity and Efficiency Analysis
Answer ALL questions on the Multiple Choice Answer Sheet
Each question is worth 4 marks (Total marks: 100)
Consider all options before choosing the “most correct” answer.
(1) If outputs are strongly disposable, then:
(a) they are also weakly disposable.
(b) there is ’no free lunch’.
(c) output sets are bounded.
(d) All of the above.
(e) None of the above.
(2) Suppose the output distance function takes the form DtO(x, q, z) = Q(q)/[A(t, z)F (x)]
where t is a time index, x is a vector of inputs, q is a vector of outputs, and z is a vector of
environmental variables. The associated shadow revenue shares:
(a) do not depend on inputs.
(b) do not depend on environmental variables.
(c) do not change over time.
(d) All of the above.
(e) None of the above.
(3) If firms are price takers in input markets, then cost functions are linearly homogeneous in:
(a) output quantities.
(b) output prices.
(c) environmental variables.
(d) All of the above.
(e) None of the above.
(4) Computing measures of output quantity change involves assigning numbers to baskets of
outputs. Measurement theory says that so-called output index numbers must be
(a) computed using output prices as measures of relative value.
(b) assigned in such a way that the relationships between the numbers mirror the relationships
between the baskets.
(c) superlative.
(d) All of the above.
(e) None of the above.
EXAMINATION CONTINUES ON NEXT PAGE
Page 3 of 15
Semester Two Final Examinations, 2018 ECON3340 Productivity and Efficiency Analysis
(5) An analyst has obtained data on the quantities of two outputs for five firms over five time
periods. She has then used R to obtain the results presented in Figure 1. The geometric
Young index number that compares the outputs of firm 5 in period 5 with the outputs of
firm 1 in period 1 is:
(a) 24.751.
(b) 27.304.
(c) 28.285.
(d) 28.979.
(e) None of the above.
Figure 1. R Script and Output
(6) An analyst has used five indices to measure changes in the input quantities reported in the
first two columns of Table 1. The only proper index numbers are those reported in:
(a) columns A and B.
(b) column C.
(c) column D.
(d) column E.
(e) None of the above.
EXAMINATION CONTINUES ON NEXT PAGE
Page 4 of 15
Semester Two Final Examinations, 2018 ECON3340 Productivity and Efficiency Analysis
Table 1. Input Quantity Index Numbers
Input 1 Input 2 A B C D E
0.11 0.46 13.722 12.481 14.449 11.436 12.182
0.06 0.23 7.004 6.469 7.322 5.966 6.311
0.23 1.27 34.158 30.791 36.893 27.566 29.649
0.04 0.03 1.784 3.449 1.779 1.726 2.498
0.02 0.02 1.000 1.000 1.000 1.000 1.000
0.61 0.42 23.556 23.556 23.579 25.198 25.764
0.04 0.03 1.642 1.629 1.644 1.726 1.779
0.15 0.34 12.944 11.984 13.130 11.400 12.042
0.04 0.13 4.148 3.933 4.284 3.655 3.839
0.11 0.46 13.722 12.481 14.449 11.436 12.182
(7) Consider an industry in which firms use two inputs to produce three outputs. The set of
inputs that can produce a given output vector is depicted in Figure 2. The Lowe index
number that compares TFP at point A with TFP at point B using point B as the reference
point is:
(a) 0.5.
(b) 1.
(c) 2.
(d) something that cannot be determined using the information given.
(e) None of the above.
F7
0
x2
x1
A
B
1
1
0.50
0.50
Figure 2. An Input Set
EXAMINATION CONTINUES ON NEXT PAGE
Page 5 of 15
Semester Two Final Examinations, 2018 ECON3340 Productivity and Efficiency Analysis
(8) If a firm maximises profit, then:
(a) it must also maximise return to the dollar.
(b) it must be operating on the boundary of the production possibilities set.
(c) the manager must value outputs and inputs at market prices.
(d) All of the above.
(e) None of the above.
(9) Consider the output set depicted in Figure 3. If (a) firms are price takers in output markets,
(b) output prices are strictly positive, and (c) the price of output 1 is greater than the price
of output 2, then the revenue maximising point:
(a) is point A.
(b) is point B.
(c) is point C.
(d) cannot be determined from the information given.
(e) None of the above.F9
0
q2
q1
A
C
B
1
1
Figure 3. An Output Set
(10) If firms are price setters in input markets and inverse demand functions are nondecreasing
in inputs, then cost-minimising input combinations:
(a) may lie above the boundary of the input set.
(b) always lie on the boundary of the input set.
(c) may lie below the boundary of the input set.
(d) are also productivity-maximising input combinations.
(e) None of the above.
EXAMINATION CONTINUES ON NEXT PAGE
Page 6 of 15
Semester Two Final Examinations, 2018 ECON3340 Productivity and Efficiency Analysis
(11) The input-oriented technical efficiency of a manager can be viewed as:
(a) a proper input index.
(b) a proper TFP index.
(c) the cost efficiency of the manager divided by his/her input-oriented allocative inefficiency.
(d) All of the above.
(e) None of the above.
(12) The output-oriented mix efficiency of a manager can be viewed as:
(a) an output-oriented measure of how well he/she has captured economies of input substitution.
(b) the component of revenue efficiency that remains after accounting for output-oriented
allocative efficiency.
(c) the component output-oriented technical and mix efficiency that remains after accounting
for output-oriented technical efficiency.
(d) All of the above.
(e) None of the above.
(13) Measures of technical, scale and mix efficiency (TSME) and output-oriented technical efficiency
(OTE) for six firms are reported in Table 2. The output-oriented mix efficiency of firm E is:
(a) 0.078.
(b) 0.512
(c) 1.000.
(d) something that cannot be determined from the information given.
(e) None of the above.
Table 2. Input Quantity Index Numbers
Firm TSME OTE
A 0.334 0.652
B 0.337 1.000
C 1.000 1.000
D 1.000 1.000
E 0.078 1.000
F 0.388 0.500
EXAMINATION CONTINUES ON NEXT PAGE
Page 7 of 15
Semester Two Final Examinations, 2018 ECON3340 Productivity and Efficiency Analysis
(14) Consider the following linear program:
min
µ,λ11,...,λIt
{
µ :
I∑
h=1
t∑
r=1
λhrqhr ≥ qit,
I∑
h=1
t∑
r=1
λhrzhr ≤ zit,
µxit ≥
I∑
h=1
t∑
r=1
λhrxhr,
I∑
h=1
t∑
r=1
λhr = 1, λhr ≥ 0 for all h and r
}
,
where qit is a vector of outputs, xit is a vector of inputs, and zit is a vector of environmental
variables. The value of µ at the optimum is an estimate of input-oriented:
(a) allocative efficiency.
(b) mix efficiency.
(c) technical efficiency.
(d) scale efficiency
(e) None of the above.
(15) Which of the following statements is true?
(a) Estimates of scale efficiency can be obtained by dividing estimates of technical efficiency
obtained under a VRS assumption by corresponding estimates of technical efficiency
obtained under a CRS assumption.
(b) If inputs are not strongly disposable, then the coefficients of the input variables in
locally-linear output and input distance functions are nonnegative.
(c) If production possibilities sets are not convex, then there is no linear programming
duality theory to link the primal and dual forms of piecewise frontier models.
(d) All of the above.
(e) None of the above.
(16) An analyst has used data on two outputs, two inputs and one environmental variable to
analyse the performance of a group of firms. Relevant R script and output is presented in
Figure 4. The variable Z is a measure of:
(a) technical efficiency.
(b) revenue efficiency.
(c) technical, scale and mix efficiency.
(d) environmental change.
(e) None of the above.
EXAMINATION CONTINUES ON NEXT PAGE
Page 8 of 15
Semester Two Final Examinations, 2018 ECON3340 Productivity and Efficiency Analysis
Figure 4. R Script and Output
EXAMINATION CONTINUES ON NEXT PAGE
Page 9 of 15
Semester Two Final Examinations, 2018 ECON3340 Productivity and Efficiency Analysis
(17) An analyst has used data on two-input-two-output firms to test the null hypothesis that the
average efficiency of firms operating in a relatively poor production environment (defined as
an environment where the value of an environmental variable, z, is less than the mean) is no
greater than the average efficiency of firms operating in a relatively favourable environment.
Relevant R script and output is presented in Figure 5. Assume the inefficiency effects are
independent exponential random variables. The value of the test statistic is:
(a) 0.522.
(b) 1.250.
(c) 1.916.
(d) 2.105.
(e) None of the above.
Figure 5. R Script and Output
(18) Growth accountants typically assume that:
(a) input sets are homothetic.
(b) inputs are strongly disposable.
(c) technical change is implicit Hicks input neutral.
(d) All of the above.
(e) None of the above.
EXAMINATION CONTINUES ON NEXT PAGE
Page 10 of 15
Semester Two Final Examinations, 2018 ECON3340 Productivity and Efficiency Analysis
(19) Consider the deterministic frontier model yit = β0 + β1xit − uit where xit is not random
and uit is an independent G(P, σu) random variable with P > 2. Which of the following
statements is true?
(a) The ordinary least squares estimator for β0 is unbiased.
(b) The corrected ordinary least squares estimator for β1 is asymptotically efficient.
(c) The maximum likelihood estimator for β1 is asymptotically normal.
(d) All of the above.
(e) None of the above.
(20) Consider the following regression relationship:
yi = 5 + 0.6 lnx1i + 0.3 lnx2i − ui
where yi denotes the logarithm of the output of firm i, x1i and x2i denote inputs of capital
and labour, and ui ≥ 0 is an output oriented technical inefficiency effect. Consider a firm
that uses one unit of capital and two units of labour to produce fifty units of output. The
output-oriented technical efficiency of the manager is:
(a) 0.237.
(b) 0.274.
(c) 0.772.
(d) 1.
(e) None of the above.
(21) Consider the following output-oriented deterministic frontier model:
yit = α +
M∑
m=1
βm lnxmit − uit
where yit is the logarithm of the aggregate output of firm i in period t, xmit is an input, and
uit ≥ 0 is a random variable with the following properties:
LS1 E(uit) = µ ≥ 0 for all i and t.
LS2 var(uit) ∝ σ2u for all i and t.
LS3 cov(uit, uks) = 0 if i 6= k or t 6= s.
LS4 uit is uncorrelated with the explanatory variables.
EXAMINATION CONTINUES ON NEXT PAGE
Page 11 of 15
Semester Two Final Examinations, 2018 ECON3340 Productivity and Efficiency Analysis
A researcher has used R to generate the results in Figure 6. The corrected ordinary least
squares (COLS) estimate of α is:
(a) -0.485.
(b) 0.372.
(c) 1.230.
(d) something that cannot be determined from the information given.
(e) None of the above.
Figure 6. R Script and Output
EXAMINATION CONTINUES ON NEXT PAGE
Page 12 of 15
Semester Two Final Examinations, 2018 ECON3340 Productivity and Efficiency Analysis
(22) Which of the following statements is true?
(a) Stochastic frontier models are underpinned by the assumption that the functional forms
of relevant distance, revenue and cost functions are known.
(b) Except in restrictive special cases, stochastic frontier models cannot be used to compute
primal TFP index numbers.
(c) The presence of statistical noise does not affect our ability to give an economic interpretation
to the parameters in stochastic frontier models.
(d) All of the above.
(e) None of the above.
(23) The statistical noise component in a stochastic frontier model:
(a) can generally be interpreted as a productivity index.
(b) is a normally distributed random variable.
(c) is generally included to account for functional form errors, measurement errors, and
omitted variable errors.
(d) All of the above.
(e) None of the above.
(24) Consider the following stochastic frontier model:
ln q1it = α + δ ln zit +
M∑
m=1
βm lnxmit − φ ln(q2it/q1it) + vit − uit
where qnit is the n-th output of firm i in period t, xmit is the m-th input, vit represents
statistical noise, and uit ≥ 0 is a random variable representing technical inefficiency. A
researcher has used observations on five firms in five time periods to estimate the parameters
of this model. The results are reported in Figure 7. She subsequently uses these results to
estimate the statistical noise component. Her estimate of v11 is:
(a) -1.223
(b) -0.950.
(c) 0.305.
(d) 0.578.
(e) None of the above.
EXAMINATION CONTINUES ON NEXT PAGE
Page 13 of 15
Semester Two Final Examinations, 2018 ECON3340 Productivity and Efficiency Analysis
Figure 7. R Script and Output
EXAMINATION CONTINUES ON NEXT PAGE
Page 14 of 15
Semester Two Final Examinations, 2018 ECON3340 Productivity and Efficiency Analysis
(25) Stochastic production frontier models are often estimated using maximum likelihood methods
because:
(a) least squares estimators are biased in finite samples.
(b) maximum likelihood methods can be used to make valid finite sample inferences concerning
levels of efficiency.
(c) maximum likelihood methods involve fewer assumptions than least squares methods.
(d) least squares methods cannot be used to impose equality restrictions on the unknown
model parameters.
(e) None of the above.
END OF EXAMINATION
Page 15 of 15
Semester One Final Examinations, 2013 ECON7002 Economics for Commerce
Page 1 of 1
This exam paper must not be removed from the venue
School of Economics
EXAMINATION
Semester Deferred Examinations, 2013
ECON7002 Economics for Commerce
This paper is for St Lucia Campus students.
Examination Duration: 120 minutes
Reading Time: 10 minutes
Exam Conditions:
This is a Central Examination
This is a Closed Book Examination - specified materials permitted
During perusal - write only on the rough paper provided
This examination paper will be released to the Library
Materials Permitted In The Exam Venue:
(No electronic aids are permitted e.g. laptops, phones)
An unmarked Bilingual dictionary is permitted
Calculators - Casio FX82 series or UQ approved (labelled)
Materials To Be Supplied To Students:
1 x Multiple Choice Answer Sheet
Instructions To Students:
Venue ____________________
Seat Number ________
Student Number |__|__|__|__|__|__|__|__|
Family Name _____________________
First Name _____________________
For$Examiner$Use$Only$
Question)) Mark)
) )
) )
) )
) )
) )
) )
) )
) )
) )
) )
) )
) )
) )
) )
) )
) )
) )
) )
) )
) )
)
Total) ________)
School of Economics
EXAMINATION
Semester Two Final Examinations, 2018
ECON3340 Productivity and Efficiency Analysis
This paper is for St Lucia Campus students
Examination Duration: 120 minutes
Reading Time: 10 minutes
Exam Conditions
This is Central Examination
This is a Closed Book Examination — specified materials permitted
During reading time — write only on the rough paper provided
This Examination paper will be released to the Library
Materials Permitted In The Exam Venue:
(No electronic aids are permitted e.g. laptops, phones)
An unmarked bilingual dictionary is permitted
Calculators — Casio FX82 series or UQ approved (labelled)
Materials To Be Supplied To Students:
1 × Multiple Choice Answer Sheet
Instructions To Students:
Additional exam materials (e.g., answer booklets, rough paper) will be provided
upon request.
Answer ALL questions.
Each question is worth 4 marks.
All questions are multiple choice.
Consider all options before choosing the “most correct” answer
Total Questions: 25
Total Marks: 100
Se ester One Final Exa inations, 2013 ECON7150 Mathematical Techniques for Economics
Semester One Midsemester Examinations, 2013 ECON7002 Economics for Commerce
Page 1 of 8
This exam paper must not be removed from the venue
School of Economics
EXAMINATION
Semester One Midsemester Examinations, 2013
ECON7002 Economics for Commerce
This paper is for St Lucia Campus students.
Examination Duration: 90 minutes
Reading Time: 10 minutes
Exam Conditions:
This is a Central Examination
This is a Closed Book Examination - specified materials permitted
During perusal - write only on the rough paper provided
This examination paper will be released to the Library
Materials Permitted In The Exam Venue:
(No electronic aids are permitted e.g. laptops, phones)
An unmarked Bilingual dictionary is permitted
Calculators - Casio FX82 series or UQ approved (labelled)
Materials To Be Supplied To Students:
1 x 14 Page An w r Booklet
1 x Multiple Choice Answer Sheet
Rough Paper
Instructions To Students:
Venue ____________________
Seat Number ________
Student Number |__|__|__|__|__|__|__|__|
Family Name _____________________
First Name _____________________
For Examiner Use Only
Question Mark
Total ________
l f i s
I I
Se ester One Final Exa inations, 2013
ECON7150 Mathematical Techniques for Economics
his paper is for St Lucia a pus students
Examination Duration: inutes
Reading Time: minutes
Exam Conditions:
This is a Central Examination
This is a Closed Book Exa ination — specified materials permitted
During perus l — write nly on the r ugh aper provided
This Examination paper will be released to the Library
Materials Permit ed In The Exam Venue:
(No electronic aids ar permitted e.g. laptops, phones)
An unmarked bili gu l dictionary is p rmitted
Calculators — Casio FX82 series or UQ approv (labelled)
Materi s To Be Supplied To Students:
1 × 14 Page Answer Booklet
1 × ultiple Choice Answer Sh et
Instructions o Students:
Total Questions:
Total Marks:
For Examiner Use Only
Question Mark
Total
Page 1 of 2age 1 of 15
Semester Two Final Examinations, 2018 ECON3340 Productivity and Efficiency Analysis
THIS PAGE LEFT BLANK INTENTIONALLY
Page 2 of 15
Semester Two Final Examinations, 2018 ECON3340 Productivity and Efficiency Analysis
Answer ALL questions on the Multiple Choice Answer Sheet
Each question is worth 4 marks (Total marks: 100)
Consider all options before choosing the “most correct” answer.
(1) If outputs are strongly disposable, then:
(a) they are also weakly disposable.
(b) there is ’no free lunch’.
(c) output sets are bounded.
(d) All of the above.
(e) None of the above.
(2) Suppose the output distance function takes the form DtO(x, q, z) = Q(q)/[A(t, z)F (x)]
where t is a time index, x is a vector of inputs, q is a vector of outputs, and z is a vector of
environmental variables. The associated shadow revenue shares:
(a) do not depend on inputs.
(b) do not depend on environmental variables.
(c) do not change over time.
(d) All of the above.
(e) None of the above.
(3) If firms are price takers in input markets, then cost functions are linearly homogeneous in:
(a) output quantities.
(b) output prices.
(c) environmental variables.
(d) All of the above.
(e) None of the above.
(4) Computing measures of output quantity change involves assigning numbers to baskets of
outputs. Measurement theory says that so-called output index numbers must be
(a) computed using output prices as measures of relative value.
(b) assigned in such a way that the relationships between the numbers mirror the relationships
between the baskets.
(c) superlative.
(d) All of the above.
(e) None of the above.
EXAMINATION CONTINUES ON NEXT PAGE
Page 3 of 15
Semester Two Final Examinations, 2018 ECON3340 Productivity and Efficiency Analysis
(5) An analyst has obtained data on the quantities of two outputs for five firms over five time
periods. She has then used R to obtain the results presented in Figure 1. The geometric
Young index number that compares the outputs of firm 5 in period 5 with the outputs of
firm 1 in period 1 is:
(a) 24.751.
(b) 27.304.
(c) 28.285.
(d) 28.979.
(e) None of the above.
Figure 1. R Script and Output
(6) An analyst has used five indices to measure changes in the input quantities reported in the
first two columns of Table 1. The only proper index numbers are those reported in:
(a) columns A and B.
(b) column C.
(c) column D.
(d) column E.
(e) None of the above.
EXAMINATION CONTINUES ON NEXT PAGE
Page 4 of 15
Semester Two Final Examinations, 2018 ECON3340 Productivity and Efficiency Analysis
Table 1. Input Quantity Index Numbers
Input 1 Input 2 A B C D E
0.11 0.46 13.722 12.481 14.449 11.436 12.182
0.06 0.23 7.004 6.469 7.322 5.966 6.311
0.23 1.27 34.158 30.791 36.893 27.566 29.649
0.04 0.03 1.784 3.449 1.779 1.726 2.498
0.02 0.02 1.000 1.000 1.000 1.000 1.000
0.61 0.42 23.556 23.556 23.579 25.198 25.764
0.04 0.03 1.642 1.629 1.644 1.726 1.779
0.15 0.34 12.944 11.984 13.130 11.400 12.042
0.04 0.13 4.148 3.933 4.284 3.655 3.839
0.11 0.46 13.722 12.481 14.449 11.436 12.182
(7) Consider an industry in which firms use two inputs to produce three outputs. The set of
inputs that can produce a given output vector is depicted in Figure 2. The Lowe index
number that compares TFP at point A with TFP at point B using point B as the reference
point is:
(a) 0.5.
(b) 1.
(c) 2.
(d) something that cannot be determined using the information given.
(e) None of the above.
F7
0
x2
x1
A
B
1
1
0.50
0.50
Figure 2. An Input Set
EXAMINATION CONTINUES ON NEXT PAGE
Page 5 of 15
Semester Two Final Examinations, 2018 ECON3340 Productivity and Efficiency Analysis
(8) If a firm maximises profit, then:
(a) it must also maximise return to the dollar.
(b) it must be operating on the boundary of the production possibilities set.
(c) the manager must value outputs and inputs at market prices.
(d) All of the above.
(e) None of the above.
(9) Consider the output set depicted in Figure 3. If (a) firms are price takers in output markets,
(b) output prices are strictly positive, and (c) the price of output 1 is greater than the price
of output 2, then the revenue maximising point:
(a) is point A.
(b) is point B.
(c) is point C.
(d) cannot be determined from the information given.
(e) None of the above.F9
0
q2
q1
A
C
B
1
1
Figure 3. An Output Set
(10) If firms are price setters in input markets and inverse demand functions are nondecreasing
in inputs, then cost-minimising input combinations:
(a) may lie above the boundary of the input set.
(b) always lie on the boundary of the input set.
(c) may lie below the boundary of the input set.
(d) are also productivity-maximising input combinations.
(e) None of the above.
EXAMINATION CONTINUES ON NEXT PAGE
Page 6 of 15
Semester Two Final Examinations, 2018 ECON3340 Productivity and Efficiency Analysis
(11) The input-oriented technical efficiency of a manager can be viewed as:
(a) a proper input index.
(b) a proper TFP index.
(c) the cost efficiency of the manager divided by his/her input-oriented allocative inefficiency.
(d) All of the above.
(e) None of the above.
(12) The output-oriented mix efficiency of a manager can be viewed as:
(a) an output-oriented measure of how well he/she has captured economies of input substitution.
(b) the component of revenue efficiency that remains after accounting for output-oriented
allocative efficiency.
(c) the component output-oriented technical and mix efficiency that remains after accounting
for output-oriented technical efficiency.
(d) All of the above.
(e) None of the above.
(13) Measures of technical, scale and mix efficiency (TSME) and output-oriented technical efficiency
(OTE) for six firms are reported in Table 2. The output-oriented mix efficiency of firm E is:
(a) 0.078.
(b) 0.512
(c) 1.000.
(d) something that cannot be determined from the information given.
(e) None of the above.
Table 2. Input Quantity Index Numbers
Firm TSME OTE
A 0.334 0.652
B 0.337 1.000
C 1.000 1.000
D 1.000 1.000
E 0.078 1.000
F 0.388 0.500
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Semester Two Final Examinations, 2018 ECON3340 Productivity and Efficiency Analysis
(14) Consider the following linear program:
min
µ,λ11,...,λIt
{
µ :
I∑
h=1
t∑
r=1
λhrqhr ≥ qit,
I∑
h=1
t∑
r=1
λhrzhr ≤ zit,
µxit ≥
I∑
h=1
t∑
r=1
λhrxhr,
I∑
h=1
t∑
r=1
λhr = 1, λhr ≥ 0 for all h and r
}
,
where qit is a vector of outputs, xit is a vector of inputs, and zit is a vector of environmental
variables. The value of µ at the optimum is an estimate of input-oriented:
(a) allocative efficiency.
(b) mix efficiency.
(c) technical efficiency.
(d) scale efficiency
(e) None of the above.
(15) Which of the following statements is true?
(a) Estimates of scale efficiency can be obtained by dividing estimates of technical efficiency
obtained under a VRS assumption by corresponding estimates of technical efficiency
obtained under a CRS assumption.
(b) If inputs are not strongly disposable, then the coefficients of the input variables in
locally-linear output and input distance functions are nonnegative.
(c) If production possibilities sets are not convex, then there is no linear programming
duality theory to link the primal and dual forms of piecewise frontier models.
(d) All of the above.
(e) None of the above.
(16) An analyst has used data on two outputs, two inputs and one environmental variable to
analyse the performance of a group of firms. Relevant R script and output is presented in
Figure 4. The variable Z is a measure of:
(a) technical efficiency.
(b) revenue efficiency.
(c) technical, scale and mix efficiency.
(d) environmental change.
(e) None of the above.
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Semester Two Final Examinations, 2018 ECON3340 Productivity and Efficiency Analysis
Figure 4. R Script and Output
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Semester Two Final Examinations, 2018 ECON3340 Productivity and Efficiency Analysis
(17) An analyst has used data on two-input-two-output firms to test the null hypothesis that the
average efficiency of firms operating in a relatively poor production environment (defined as
an environment where the value of an environmental variable, z, is less than the mean) is no
greater than the average efficiency of firms operating in a relatively favourable environment.
Relevant R script and output is presented in Figure 5. Assume the inefficiency effects are
independent exponential random variables. The value of the test statistic is:
(a) 0.522.
(b) 1.250.
(c) 1.916.
(d) 2.105.
(e) None of the above.
Figure 5. R Script and Output
(18) Growth accountants typically assume that:
(a) input sets are homothetic.
(b) inputs are strongly disposable.
(c) technical change is implicit Hicks input neutral.
(d) All of the above.
(e) None of the above.
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Semester Two Final Examinations, 2018 ECON3340 Productivity and Efficiency Analysis
(19) Consider the deterministic frontier model yit = β0 + β1xit − uit where xit is not random
and uit is an independent G(P, σu) random variable with P > 2. Which of the following
statements is true?
(a) The ordinary least squares estimator for β0 is unbiased.
(b) The corrected ordinary least squares estimator for β1 is asymptotically efficient.
(c) The maximum likelihood estimator for β1 is asymptotically normal.
(d) All of the above.
(e) None of the above.
(20) Consider the following regression relationship:
yi = 5 + 0.6 lnx1i + 0.3 lnx2i − ui
where yi denotes the logarithm of the output of firm i, x1i and x2i denote inputs of capital
and labour, and ui ≥ 0 is an output oriented technical inefficiency effect. Consider a firm
that uses one unit of capital and two units of labour to produce fifty units of output. The
output-oriented technical efficiency of the manager is:
(a) 0.237.
(b) 0.274.
(c) 0.772.
(d) 1.
(e) None of the above.
(21) Consider the following output-oriented deterministic frontier model:
yit = α +
M∑
m=1
βm lnxmit − uit
where yit is the logarithm of the aggregate output of firm i in period t, xmit is an input, and
uit ≥ 0 is a random variable with the following properties:
LS1 E(uit) = µ ≥ 0 for all i and t.
LS2 var(uit) ∝ σ2u for all i and t.
LS3 cov(uit, uks) = 0 if i 6= k or t 6= s.
LS4 uit is uncorrelated with the explanatory variables.
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Semester Two Final Examinations, 2018 ECON3340 Productivity and Efficiency Analysis
A researcher has used R to generate the results in Figure 6. The corrected ordinary least
squares (COLS) estimate of α is:
(a) -0.485.
(b) 0.372.
(c) 1.230.
(d) something that cannot be determined from the information given.
(e) None of the above.
Figure 6. R Script and Output
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Semester Two Final Examinations, 2018 ECON3340 Productivity and Efficiency Analysis
(22) Which of the following statements is true?
(a) Stochastic frontier models are underpinned by the assumption that the functional forms
of relevant distance, revenue and cost functions are known.
(b) Except in restrictive special cases, stochastic frontier models cannot be used to compute
primal TFP index numbers.
(c) The presence of statistical noise does not affect our ability to give an economic interpretation
to the parameters in stochastic frontier models.
(d) All of the above.
(e) None of the above.
(23) The statistical noise component in a stochastic frontier model:
(a) can generally be interpreted as a productivity index.
(b) is a normally distributed random variable.
(c) is generally included to account for functional form errors, measurement errors, and
omitted variable errors.
(d) All of the above.
(e) None of the above.
(24) Consider the following stochastic frontier model:
ln q1it = α + δ ln zit +
M∑
m=1
βm lnxmit − φ ln(q2it/q1it) + vit − uit
where qnit is the n-th output of firm i in period t, xmit is the m-th input, vit represents
statistical noise, and uit ≥ 0 is a random variable representing technical inefficiency. A
researcher has used observations on five firms in five time periods to estimate the parameters
of this model. The results are reported in Figure 7. She subsequently uses these results to
estimate the statistical noise component. Her estimate of v11 is:
(a) -1.223
(b) -0.950.
(c) 0.305.
(d) 0.578.
(e) None of the above.
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Semester Two Final Examinations, 2018 ECON3340 Productivity and Efficiency Analysis
Figure 7. R Script and Output
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Semester Two Final Examinations, 2018 ECON3340 Productivity and Efficiency Analysis
(25) Stochastic production frontier models are often estimated using maximum likelihood methods
because:
(a) least squares estimators are biased in finite samples.
(b) maximum likelihood methods can be used to make valid finite sample inferences concerning
levels of efficiency.
(c) maximum likelihood methods involve fewer assumptions than least squares methods.
(d) least squares methods cannot be used to impose equality restrictions on the unknown
model parameters.
(e) None of the above.
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