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PPE611S - PRINCIPLES OF PRODUCTION ECONOMICS - 1ST OPP - JUNE 2023 |
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n Am I BI A u n IVE RSITY
OF SCIEn CE Ano TECHn OLOGY
FACULTYOF HEALTH, NATURAL RESOURCESAND APPLIED SCIENCES
SCHOOLOF AGRICULTUREAND NATURALRESOURCESSCIENCES
DEPARTMENT OF AGRICULTURALSCIENCESAND AGRIBUSINESS
QUALIFICATION: BACHELOROF SCIENCEIN AGRICULTURE
QUALIFICATION CODE:07BAGA
LEVEL: 7
COURSECODE: PPE621S
COURSENAME: PRINCIPLESOF PRODUCTION
ECONOMICS
SESSION:
DURATION:
JUNE 2023
3 HOURS
PAPER:
MARKS:
THEORY
100
FIRSTOPPORTUNITY EXAMINATION QUESTION PAPER
EXAMINER{S) DR DAVID UCHEZUBA
MODERATOR: DR THINAH M0YO
INSTRUCTIONS
1. This paper consists of three sections: Section 1 has ten (10) multiple choice questions,
section 2 is made up of ten (10) open fill-in-the-space questions, and Section three is the
essay-type questions.
2. Answer ALL questions in blue or black ink.
3. Start each question on a new page in your answer booklet.
4. Questions relating to this paper may be raised in the initial 30 minutes after the start of
the examination. Thereafter, students must use their initiative to deal with any perceived
error or ambiguities & any assumption made should be clearly stated.
THIS QUESTION PAPERCONSISTSOF 8 PAGES(Including this front page)
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Sectionl Multiple choice question (10 Marks)
Question 1
Which of the following statements is incorrect about the production horizon?
A). The period of production for which inputs are engaged.
B). The production period for which some costs are fixed.
C). The production period for which all costs are variable.
D). The production period for which no input is varied.
Question 2
Production activities that are independent of one another are known as
A). Homoperiodic production
B). Homothetic production
C). Homogenous production
D). Heterogenous production
Question 3
Which of the following is not a factor of production?
A). Capital
B). Skill
C). Labour
D). Wages
Question 4
Which of the following is not part of a producer's main objective?
A). Minimise cost.
B). Minimise risk.
C) Maximise utility
D) Maximise profit
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Question 5
What is incorrect about the production function, y = f(x,, .......x11),
A}. The function is a combination of only one input.
B). The function f links input with output.
C). The x s are a combination of input to produce output.
D). The output is linearly related to the input.
Question 6
Which of the following statements is incorrect about the production function in Figure 1?
y
TPP
X
Figure 1. Production function
A). It is a non-linear function.
B). It is subject to the law of diminishing marginal returns.
C). It has a constant return to scale.
D}. At maximum TPP, the rate of change of the output is zero.
Question 7
Find the value of output (TPP)for the following production function, y = 4x 2 + 3x3 -16
when the input level is 2 units.
A).22
B).24
C).25
D}.20
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Question 8
Suppose a production
function
is
y
= x + 4x 2
-3x
3
.
Find the
function
for the average
physical product.
A). y = 8x-6x 2
B). y = l + 8x + 6x 2
C). y = l-8x-6x 2
D). y = l + 8x-6x 2
Question 9
Which statement is incorrect? At the boundary of stage I and II,
A). The total physical product is increasing at an increasing rate.
B). The elasticity of production is equal to one.
C). The marginal and average physical products are equal.
D). The total physical product is increasing at a decreasing rate.
Question 10
Which of the following is correct about the total physical product (TPP)growth curve?
A). It is concave to the horizontal axis before the inflexion point and convex to the horizontal
axis after inflexion.
B). It is convex to the horizontal axis before the inflexion point and concave to the horizontal
axis at maximum TPP.
C). It is concave to the horizontal axis before the inflexion point and concave to the
horizontal axis at maximum TPP.
D). It is convex to the horizontal axis before the inflexion point and convex to the horizontal
axis at maximum TPP.
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Section 2 Fill in the space questions (10 Marks)
1. lfthe ist derivative of a TPP function is positive, the function __________
_
2. If the ist derivative of a TPP function is negative, the function __________
_
3. If the ist derivative of a TPPfunction is zero-----------------
4. If the ist derivative of the TPP function is zero and the 2nd derivative is negative ___ _
5. If the ist derivative of TPPfunction is zero, and the 2nd is positive ________
_
6. If both the ist and 2nd derivative of TPPfunction are zero-------------
7. lfthe ist derivative of TPPfunction is zero and the 2nd derivative does not exist----
8. If the 2nd derivative of the TPP function is positive ______________
_
9. If the 2nd derivative of the TPP function is negative ______________
_
10. If the 2nd derivative of the TPPfunction is zero----------------
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Section 3 Essay-type questions (80 Marks)
Question 1
Distinguish between the following;
1.1. Function coefficient and partial elasticity of production.
1.2. Economies and diseconomies of scale.
1.3. Constant and increasing return to scale.
1.4. Production and production function.
1.5. Explain all the underlying assumptions of production economics.
(20 Marks)
(2 Marks)
(2 Marks)
(2 Marks)
(2 Marks)
(12 Marks)
Question 2
(20 Marks)
2.1. Consider the following production function, y = lOx + 20x 2 -16x 3 • Derive a function for
2.1.1. The average physical product.
(2 Marks)
2.1.2. The marginal physical product.
(2 Marks)
2.2. At what level of input would the following reach maximum?
2.2.1. The marginal physical product.
(2 Marks)
2.2.2. The average physical product.
(2 Marks)
2.2.3. The total physical product.
(5 Marks)
2.3. Draw a graph to represent the production functions derived above and indicate the
boundary of stage II and stage Ill.
(5 Marks)
2.4. At what stage of the production is the elasticity of production equal to one? (1 Mark)
2.5. At what point on the production frontier does the law of diminishing returns kick in?
(1 Mark)
Question 3
3.1. Given the demand function p = I 00- 2Q,
3.1.1. Express total revenue as a function of quantity demanded (output).
3.1.2. For what value of output (Q) is the total revenue maximum?
3.1.3. What is the maximum value of total revenue?
3.1.4. Sketch a graph to show the output level and the total revenue.
(20 Marks)
(2 Marks)
(2 Marks)
(2 Marks)
(2 Marks)
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3.2. Given that the fixed costs are 1000 and the variable costs are 4 per unit and the demand
function is given as
p =l0-2Q
3.2.1 Express the total cost as a function ofthe output (Q).
(2 Marks)
3.2.2. Express total revenue as a function of output (Q).
(2 Marks)
3.2.3. Express the profit as a function of output (Q).
(2 Marks)
3.2.4. For what values of output does the firm break even?
(2 Marks)
3.2.5. What is the maximum profit?
(2 Marks)
3.2.6. Plot a graph to show the output levels, breakeven point and total profit. (2 Marks)
Question 4
(20 Marks}
4.1. Find the level of corn yield with four units of capital and three units of labour using the
following production function.
4.1.1 Y = K 05 L12.
(1 Mark)
4.1.2. Y = K 16 L08
(1 Mark)
4.2. The budget constraint of a Tomato farmer is N$10000, per unit cost of fertiliser, is N$40
and per unit cost of seed is N$30.
4.2.1. Find the possible combination of the inputs that the farmer should utilise that gives the
same cost outlay.
(4 Marks)
4.2.2. Sketch the lsocost line.
(2 Marks)
4.3. Find the necessary and sufficient conditions for the maximisation of the production
functions.
= + y
IO Xi
10X2 -
2
xl -
Xi
(4 Marks)
4.4. Check if these conditions in 4.3 are met.
4.5. For the production function, y = -2x 1 -2x 2 -2x~ - Xi+ lOx1x2 , find,
4.5.1. J;
(2 Marks)
(1 Mark)
4.5.2. Iii
(1 Mark)
4.5.3. li2
(1 Mark)
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4.5.4. /2
4.5.5. /2,
4.5.6. /22
END
(1 Mark)
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