COVENANT UNIVERSITY

ALPHA SEMESTER TUTORIAL KIT (VOL. 2)

P R OG R A M M E : E C O N O M I C S

A L P H A S E M E S T E R

1 0 0 L E V E L

200 LEVEL

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DISCLAIMER

The contents of this document are intended for practice and learning purposes at the

undergraduate level. The materials are from different sources including the internet and the

contributors do not in any way claim authorship or ownership of them. The materials are also not

to be used for any commercial purpose.

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LIST OF COURSES

*CBS211: Mathematics for Business and Social Sciences II

*ECN211: Principles of Economics (Micro)

*ECN212: Principles of Economics (Macro)

*ECN213: History and Structure of the Nigerian Economy

*ECN214: Introduction to Development Economics I

*ECN215: Mathematics for Economists I

ECN216: Labour Economics I

*Not Included

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COVENANT UNIVERSITY

CANAANLAND, KM 10, IDIROKO ROAD

P.M.B 1023, OTA, OGUN STATE, NIGERIA.

TITLE OF EXAMINATION: B.Sc EXAMINATION

COLLEGE: CBSS

SCHOOL: Social Sciences

DEPARTMENT: Economics and Development Studies

SESSION: 2014/2015 SEMESTER: Alpha

COURSE CODE: CBS 211 CREDIT UNIT: 2

COURSE TITLE: Mathematics for Business & Social Sciences II

INSTRUCTION: Answer Question 1 and any other Two. TIME:

2 HOURS

1. (a) Define and give examples of the following matrices:

(i) Symmetric matrix

(ii) Identity matrix

(iii) Triangular matrix

(iv) Diagonal matrix. (1.5marks each)

(b) Given the following matrices: A = 3 6 -2 ; B = 1 2 5

4 0 7 0 -4 6

1 5 9 7 8 -3

Find: (i) |B| (ii) show that A′ + B′ = (A+B)′ (iii) 2A-B (6marks)

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(c) Find the second, third and fourth order derivatives of the following function:

(6marks)

(d) Given that .

Find: (i) (ii) (iii) (6 marks)

(e) Given that , find the limit of as (6marks)

2. (a) Use Cramer’s rule to solve the following simultaneous equations:

4x+3y-z = 7

-6x+2z = 5

9x-y+8z = 10 (10marks)

(b) Find the partial derivative of the function below:

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( , ) 3 4z f x y x y (6marks)

(c) Find the degree of homogeneity of the following functions: (i) (ii)

(4marks)

3. (a) Given that g Find: (i) h

(ii) (iv) (8marks)

(b) Find the first-order derivatives of the following functions:

(i)

(ii) +

(iii)

(iv) (3 marks each)

4. (a) Given that

2 53 2 6

2 2 3

2 3( , , )

x z zf x y z x y z

y x y .

Find: (i) (ii) (iii) (iv) (v) zyf (10marks)

(b) Define the following functions giving an example of each of them:

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(i) Symmetrical Function

(ii) Polynomial Function

(iii) Linear Function

(iv) Multivariate Function (6marks) (c) Find the derivative of the following implicit function:

3 2 25 16 0y x y xy (4marks)

5. (a) Assuming the demand and supply functions in a given market are given as:

Qd → 12 = 5P1+ 2P2 ... ... (1)

Qs → 10 = 20P2 ... ... (2)

(i)Using Gauss Elimination method of matrix algebra, find the inverse. (6 marks)

(ii)Using the inverse obtained from (i) above, obtain the values for P1 and P2. (4 marks)

(b) Find the extreme values of:

(10marks)

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COVENANT UNIVERSITY

CANAAN LAND, KM 10, IDIROKO ROAD,

P.M.B. 1023, OTA, OGUN STATE, NIGERIA

TITLE OF EXAMINATION: B.Sc. DEGREE EXAMINATION

COLLEGE: CBSS DEPARTMENT: ECONOMICS & DEVELOPMENT

STUDIES

SESSION: 2014/2015 SEMESTER: ALPHA SEMESTER

COURSE CODE: ECN 216 COURSE TITLE: LABOUR ECONOMICS I

INSTRUCTION: ANSWER ALL QUESTIONS IN SECTION A AND 2 QUESTIONS

FROM SECTION B DATE:

NOV., 2014

TIME ALLOWED: 2 hours

SECTION A: ANSWER ALL QUESTIONS IN THIS SECTION

(2 marks each)

1) For individuals who are working, the opportunity cost of an additional hour of leisure

time is ___.

a) b) w c) d) T – h

Where w – wage rate

L – Leisure hours

h – hours worked

T – total hours available

2) The marginal rate of technical substitution (MRTS) is given as the absolute value of

_____________.

a) b) c) d)

3) An increase in the wage that is affecting all employers in an industry will cause labour

demand to ____________

a) increase b) decrease c) fall to zero d) remain

constant

4) All but one of the following are included in the labour force.

a) informal workers b) armed forces personnel c) the unemployed d) first-time

job-seekers

5) The marginal rate of substitution (MRS) is given as the absolute value of __________.

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a) b) c) d)

6) As workers earn more in wages the marginal utility of income _______________.

a) remains constant b) rises c) is unitary d) falls

7) What type of demand is the demand for workers?

a) competitive b) composite c) derived d)

complementary

8) The profit function may be expressed as _______.

a) pq – wE – rK b) wE – pq – rK c) pq + (wE + rK) d) pq – (wE –

rK)

Where w – wage rate

r – rental price of capital

E – total hours hired by the firm

K – capital

p – price per unit of output

q – output

9) The figures below represent Bola and Peter’s indifference curves. Which of them prefers

leisure to more work?

Fig. 1: Bola Fig. 2: Peter

a) Bola b) Peter c) Both d) Neither

U0 U0

U1 U1

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10) The backward bending supply curve emanates due to the domination of the

_____________.

a) scale effect b) substitution effect c) indifference curve d) income

effect

11) When capital and labour are perfect substitutes, the isoquant is ___________.

a) right-angled b) left-angled c) linear d) curved

12) The market labour supply curve is ____________ than the individual labour supply

curve.

a) flatter b) steeper c) more convex d) shorter

13) Empirical studies on the supply of labour by women shows that __________ dominates.

a) scale effect b) substitution effect c) income effect d) backward

bending supply curve

14) The determinants of elasticity of labour demand include all of the following except:

a) Long and short run

b) Labour costs as a proportion of total cost.

c) The elasticity of demand for the product produced.

d) Availability of capital

15) Which of the following best depicts the relationship between the MP and AP curves?

a) MP and AP intersect when MP peaks

b) AP curve lies below MP curve when MP is decreasing

c) MP curve lies above AP curve when AP is decreasing

d) AP curve lies above MP curve when AP is falling

Total 30

marks

SECTION B: ANSWER ANY 2 QUESTIONS FROM THIS SECTION

1) a) What do you understand by the terms isoquant and isocost? Show each clearly with the

aid of graphs.

(6 marks)

b) Given that Dominion Notebook PLC’s production function is :

i) Calculate its output at each level of labour (L) it employs. Input your answers in the

Output (Q) column.

(4 marks)

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ii) Calculate and fill in the Marginal Product (MP) and the Average Product (AP). (5

marks)

iii) Given that the price of each notebook is N20, calculate and fill in the Value of

Marginal Product (VMP) and the Value of Average Product (VAP).

(5 marks)

No. of

workers

(L)

Output

(Q) MP AP

VMP

(N)

VAP

(N)

0

1

2

3

4

5

6

7

8

9

10

Total 20

marks

2) a) Mention five (5) characteristics of an isoquant. (5

marks)

b) Explain with the aid of a diagram the situation where substitution effect dominates as a

result of increase in wage rates.

(7 marks)

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c) Explain with the aid of a diagram the situation where income effect dominates as a

result of increase in wage rates.

(7 marks)

Total 20

marks

3) Inyang’s utility function from consumption (C) and leisure (L) can be expressed as:

The utility function implies that Inyang’s marginal utility for leisure is , and his

marginal utility for consumption is . He has 168 hours in the week available to split

between work and leisure. He earns N500 per hour and receives N13,800 as pocket money

from his father weekly irrespective of how much he works.

a) Graph Inyang’s budget line. (4

marks)

b) What is his budget constraint if he spends 100 hours on leisure? (3

marks)

c) Calculate the value of his marginal rate of substitution. (3

marks)

d) Find Inyang’s utility in utils, given his utility function (i.e. his optimal amount of

consumption and leisure using the utility function).

(3 marks)

e) Show Inyang’s optimal amount of consumption and leisure on a graph using his

budget line and leisure hours from (a) and (b) and his indifference curve from (d).

(3 marks)

f) Assuming Inyang’s father increases his weekly pocket money to N15,000, graph his

new budget line against the previous one.

(4 marks)

Total 20

marks

4) a) Using a well-labeled diagram, explain the short run demand for labour. (6

marks)

c) With the aid of a detailed graph, explain the labour market equilibrium, showing the

points where firms demand more than the available number of workers and vice versa.

(6 marks)

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d) A profit-maximizing firm’s produces 1000 units of output and sells them at N85 per

unit. The firm pays its 10 workers N400 per hour for 3 man-hours of labour. If the firm

has 12 machines in place, which it rents at a cost of N100 each per hour:

i) What is the total man-hours hired? (2

marks)

ii) Calculate the firm’s total revenue. (2

marks)

iii) Find the total cost incurred the firm. (2

marks)

iv) Calculate the firm’s profit. (2

marks)

Total 20

marks

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16) Define the following, showing the respective calculations/graphs as appropriate: (15

marks)

i) Reservation wage

ii) Indifference curve

iii) Elasticity of labour demand

iv) Elasticity of labour supply

v) Labour force

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COVENANT UNIVERSITY

ECN 216 - LABOUR ECONOMICS I

2014/2015 ACADEMIC SESSION, ALPHA SEMESTER

EXAMINATION MARKING GUIDE

SECTION A

1) C

2) C

3) B

4) A

5) B

6) D

7) C

8) A

9) A

10) D

11) C

12) A

13) B

14) D

15) D

SECTION B

1) a) What do you understand by the terms isoquant and isocost? Show each clearly with the

aid of graphs.

(6 marks)

An Isoquant describes the possible combinations of labour and capital that produce the

same level of output.

(1 mark)

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An Isocost line indicates the possible combinations of labour and capital the firm can hire

given a specified budget. It indicates equally costly combinations of inputs.

(1 mark)

b) Given that Dominion Notebook PLC’s production function is :

Employment

q1

q0

K

E

Y

2 marks

2 marks

15

i) Calculate its output at each level of labour (L) it employs. Input your answers in the

Output (Q) column.

(4 marks)

When , then

When , then

When , then

When , then

When , then

When , then

When , then

When , then

When , then

When , then

When , then

(3 marks for showing working, 1 mark for inputting answers in the table – 4

marks total)

ii) Calculate and fill in the Marginal Product (MP) and the Average Product (AP). (5

marks)

( mark)

At is unknown

At

At

At

At

At

16

At

At

At

At

At

(2 marks for showing working and inputting answers in the

table)

( mark)

At is unknown

At

At

At 41

At

At

At

At

At

At

At

(2 marks for showing working and inputting answers in the

table)

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iii) Given that the price of each notebook is N20, calculate and fill in the Value of

Marginal Product (VMP) and the Value of Average Product (VAP).

(5 marks)

( mark)

At is unknown

At

At

At

At

At

At

At

At

At

At

(2 marks for showing working and inputting answers in the

table)

( mark)

At is unknown

At

At

At

At

At

At

At

18

At

At

At

(2 marks for showing working and inputting answers in the

table)

No. of

workers

(L)

Output

(Q) MP AP

VMP

(N)

VAP

(N)

0 0 - - - -

1 47 47 47 940 940

2 88 41 44 820 880

3 123 35 41 700 820

4 152 29 38 580 760

5 175 23 35 460 700

6 192 17 32 340 640

7 203 11 29 220 580

8 208 5 26 100 520

9 207 -1 23 -20 460

10 200 -7 20 -140 400

Total 20 marks

2) a) Mention five (5) characteristics of an isoquant. (5

marks)

Must be downward sloping

Cannot intercept

Higher isoquants indicate more output

They are convex to the origin

They have a slope known as MRTS (marginal rate of technical substitution)

Averages are better than extremes

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(1 mark each for 5 points – 5 marks

total)

b) Explain with the aid of a diagram the situation where substitution effect dominates as

a result of increase in wage rates.

(7 marks)

When wage increases, it makes leisure more expensive, therefore, the individual

substitutes more work for leisure (substitution effect).

In the diagram, the substitution effect is depicted as the curve shifts from point Q to point

R.

If substitution effect is greater than income effect, then hours of work increases when

wage rate increases.

In the figure, hours of leisure decreased overall from 70 to 65 hours, implying that hours

of work increased overall from 40 to 45 hours.

The diagram shows an individual’s behaviour who commits more time to work

when wage rate increases. This is reflected by the decrease in leisure time from

70hours to 65hours. Thus, substitution effect dominates here.

(2 marks for 2 valid points, 4 marks

maximum)

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c) Explain with the aid of a diagram the situation where income effect dominates as a

result of increase in wage rates.

(7 marks)

When wage increases, it raises the individual’s opportunities, thereby making the

individual to increase his/her leisure (income effect).

In the diagram, income effect is depicted as the curve shifts from point P to point Q.

If income effect is greater than substitution effect, then hours of work decreases when

wage rate increases.

In the figure, hours of leisure increased overall from 70 to 75 hours, implying that hours

of work decreased overall from 40 to 35 hours.

The diagram shows an individual’s behaviour who commits lesser time to work

when wage rate increases. This is reflected by the increase in leisure time from

70hours to 75hours. Thus, income effect dominates here.

(2 marks for 2 valid points, 4 marks maximum)

Total 20 marks

3) Inyang’s utility function from consumption (C) and leisure (L) can be expressed as:

The utility function implies that Inyang’s marginal utility for leisure is , and his

marginal utility for consumption is . He has 168 hours in the week available to split

between work and leisure. He earns N500 per hour and receives N13,800 as pocket money

from his father weekly irrespective of how much he works.

3 marks

3 marks

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a) Graph Inyang’s budget line. (4

marks)

Non-labour income (V) = N13,800

Wage rage (w) = N500/hour

Total hours available (T) = 168 hours

wT (N500 x 168hrs) = N84,000 (1

mark)

wT + V (N84,000 + N13,800)=N97,800 (1

mark)

b) What is his budget constraint if he spends 100 hours on leisure? (3

marks)

C = wh + V or C = w (T – L) + V (1 mark)

C = N500 (168 – 100) + N13,800

C = N500 (68) + N13,800

C = N34,000 + N13,800

C = N47,800 (2 marks)

c) Calculate the value of his marginal rate of substitution. (3

marks)

MRS = MUL (1 mark)

MUC

MUL =

=

= 48210

MUC =

=

= 40

MRS = 48210 (1 mark)

40

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MRS = 1205.25 (1 mark)

d) Find Inyang’s utility in utils, given his utility function (i.e. his optimal amount of

consumption and leisure using the utility function). (3

marks)

(1 mark)

= (1 mark)

=

U = utils (1 mark)

e) Show Inyang’s optimal amount of consumption and leisure on a graph using his

budget line and leisure hours from (a) and (b) and his indifference curve from (d).

(3 marks)

f) Assuming Inyang’s father increases his weekly pocket money to N15,000, graph

his new budget line against the previous one.

(4 marks)

Total 20 marks

4) a) Using a well-labeled diagram, explain the short run demand for labour. (6

marks)

The short-run demand curve for labour is downward sloping.

A drop in the wage from $22 to $18 increased the firm’s employment from 8 to 9

workers

An increase in the price of output will however, shift the VMP curve

upward/outward from VMP1 to VMP2

(3 marks for 3 valid

points)

b) With the aid of a detailed graph, explain the labour market equilibrium, showing the

points where firms demand more than the available number of workers and vice versa.

(6 marks)

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c) A profit-maximizing firm’s produces 1000 units of output and sells them at N85 per

unit. The firm pays its 10 workers N400 per hour for 3 man-hours of labour. If the firm

has 12 machines in place, which it rents at a cost of N100 each per hour:

i) What is the total man-hours hired?

Total man-hours (E) = 10 workers at 3 hours each

Total man-hours (E) = 10 x 3 = 30 hours (2 marks)

ii) Calculate the firm’s total revenue.

Total Revenue (TR) = pq = Price x Quantity

= N85 x 1,000 units

TR = N85,000 (2 marks)

iii) Find the total cost incurred the firm.

Total Cost (TC) = wE + rK

= (wage x total man-hours) + (rental price of capital x capital)

= (N400 x 30 hours) + (N100 x 12)

= N12,000 + N1,200

TC = N13,200 (2 marks)

iv) Calculate the firm’s profit.

Profit = TR – TC

= N85,000 – N13,200

= N71,800 (2 marks)

Total 20 marks

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