THEORY OF COST AND REVENUE

Meaning of the Concept of Cost

A farm uses various inputs for the production of goods and services. The firm has to make payments for
such inputs, as they are not free. The expenditure incurred on these inputs is known as the cost of production
in economics. The concept of cost in economics refers to the total expenditure incurred in producing a
commodity in economics, the cost is the sum total of all explicit costs and implicit costs.
1. Explicit Cost: these are payment (monetary transaction) made to others while running a business that
represents cash outflows. It includes wages, mortgage, rent, utilities, advertisements, raw materials, and
other general, administrative, and sales costs.
2. Implicit Costs: these are not often monetary values a company can easily track. This means that they do not
appear on the general ledger. Many implicit costs are the opportunity costs of deciding on one action over
another. For example, a company that has the choice between training its professionals and investing in a
new line of products loses product value if it trains its professionals or loses the value of qualified
professionals if it pursues a new line of products.

DISTINCTION BETWEEN ECONOMIST’S AND ACCOUNTANT’S VIEW OF COST

An economist views cost in terms of the alternative sacrificed in order to obtain a commodity, or
alternative foregone in order to satisfy a particular want. That is the opportunity cost of pursuing a
particular line of action.
On the other hand, an accountant looks at cost from a different perspective. He sees it in terms of
monetary cost, that is, the amount of money spent on commodities. If NLE 500 is spent on purchasing a
Smart TV, the accountant will look at the monetary terms, while the economist will look at it in terms of
other commodities that could not be bought because of purchasing a Smart TV.
Therefore, the concept of cost in economics includes the actual expenditure on inputs (i.e explicit cost)
and the imputed value of the inputs supplied by the owner (i.e. implicit cost). The sum of the explicit
cost and the implicit cost is the total cost of production of a commodity.
TYPES OF COST

1. Total Cost (TC): it is the total cost incurred by the firm to produce a given quantity of output in

such, it is the overall expenditure involved in producing a given quantity of a commodity. Total

cost is the sum of both variable costs and fixed costs. It is derived by multiplying the unit cost

of production by the total quantity of a commodity produced.

TC = FIXED COST + VARIABLE COST (FC + VC)

TC = Cost x Qty.

MR. MOHAMED SAHR FOFANAH

2. Fixed costs: Fixed costs are those that do not change with the volume of output. The business incurs them
regardless of their level of production. Examples of these include payment of rent, utility expense, interest
expense, taxes on property, insurance, advertisement and promotion, interest on a loan, etc. (they remain the
same even if output increases throughout) they are referred to as Overheads costs or unavoidable costs or
fixed expense. Fixed costs are the costs that must be paid regardless of what level of output the firm
produces. The curve below gives a graphical representation of total fixed cost

Figure 1: Total Fixed Cost Curve

The above diagram shows that, the TFC do not start from the origin zero because before the start of the
production, producer have already incurred the expense. In the diagram above, the fixed cost is NLE 100 at
all quantities produce. This shows that no matter what output produce, the TFC is always constant.
3. Variable costs: are costs that do varies as the output varies. Example transaction fees, hourly wages,
credit card fees, cost of raw material, commission fees, legal fees etc. The costs will vary depending upon
the output that the business generates. Less production will cost fewer expenses, and vice versa, the business
will pay more when its production is greater. Expenses on the purchase of raw materials and payment of
wages are examples of variable costs. The curve below gives a graphical representation of total variable cost

MR. MOHAMED SAHR FOFANAH

 Figure 2: Total Variable Cost Curve

TVC at origin is zero if zero quantity of output is produced. TVC will increase as the output
increases.

RELATIONSHIP BETWEEN TOTAL COST, TOTAL VARIABLE COST, AND TOTAL

FIXED COST

Average Cost (AC): it is the cost of producing each unit of commodity. That is the unit cost of
production. It is calculated as:
Average Cost: Total Cost / Total Output
For example, if the total cost of production is NLE 5,000, and 100 units of the commodity
are produced, the average cost is NLE 50.
4. Marginal Cost (MC): it is the additional cost incurred by producing a commodity, or reduction
in total cost arising from the reduction of total production by one unit. For example, if the total
cost of producing 20 bottles of beer is NLE 18, and the total cost of producing 21 bottles of beer
is NLE 19, the marginal cost is NLE 1. It is also known as the incremental cost.
MC= Change in Total Cost/ Change in Quantity
Or
MC= T C1−T C 0
Q1−Q 0

MR. MOHAMED SAHR FOFANAH

5. Average Fixed Cost (AFC): the average fixed cost is the total fixed cost divided by the output level.

AFC= TFC/Q

6. Average Variable Cost (AVC): this is defined as the total variable cost divided by the output
AVC= TVC/Q

8. Short Run: Short run refers to a production-planning period where at least one input remains fixed while
the rest are subject to change. It works when a business wants to achieve the target within a short duration
due to the sudden or seasonal demand for a specific product. It is the period where at least one factor of
production is fixed. For example, if a gift maker has to manufacture set units of goods for Mr. Fofanah in six
days, it needs to increase labourers and raw materials but not the machinery. In this case, labourers and raw
materials become variable inputs while the machinery remains fixed.
9. Long Run: it is a period where all the resources (factors of production or inputs) can vary. For example, a
business with a one-year lease will have its long run defined as any period longer than a year since it is not
bound by the lease agreement after that year.

Example 1 (WASSCE JUNE 1993 Q2 SECTION “A”).

Cost schedule of a firm

MR. MOHAMED SAHR FOFANAH
 Output Total Total Total Cost Average Average Average Marginal
Fixed Variable Fixed Cost Variable cost Cost
cost
Cost Cost
0 100 0 100 0 100 -
1 100 40 140
2 100 64 164
3 100 80 180
4 100 88 188
5 100 96 196
From the in this table calculate the Average Variable Cost (AVC), Average Total Cost (ATC), and Marginal
Cost (MC) of the firm. Show your working clearly.

Solution

Recopy the table

i. Average total Cost = T o t a l c o s t

Out pu t
( ¿ a ¿) 140 164 180 188 196
100
0
(b) 1
¿
(c) 2
¿
(d) 3
¿
(f) 4
¿
(g) 5
¿
¿
0 140 82 26.7 22 19.2

(i) Average Fixed Cost = T o t a l f i x e d c o s t

out put ¿¿
100 100
100 100
a) AFC0 = b) AFC1 = AFC2 = d) AFC3 =
1
0 ¿ 2
¿ 100
¿ 3
0
c 50 ¿
¿
33.3

100 100
(¿ f ¿) AFC4 = 4
¿
(g) AFC5 = 5
¿
25 20

Marginal Cost = ∆ T o t a l c o st
∆ out put ¿¿

Marginal Cost = T o t a lc o st n e w−T o t al C o s t o l d

o u t p u t n e w−o u t p u t o l d

140− 100

a) 1− 0
¿
40
1
¿
40

MR. MOHAMED SAHR FOFANAH

 164− 140

b) 2− 1
¿
24
1
¿
24

180− 1164

c) 3− 2
¿
16
1
¿
16

188− 180

d) 4 −3
¿
8
1
¿
8

196− 188

(e) 5 −4
¿
8
1
¿
8

To complete the table

Output Total Total Total Cost Average Average Average Marginal

Fixed Variable Fixed Cost Variable cost Cost
cost
Cost Cost
0 100 0 100 0 0 0 -
1 100 40 140 100 40 140 40
2 100 64 164 50 32 82 14
3 100 80 180 33.3 26.7 60 16
4 100 88 188 25 22 47 8
5 100 96 196 20 19.2 39.2 8

Examples 2 (Njala University Agricultural Economics Past Question).

Complete the following Cost structure and answer the questions that follow.

Outp Tota Total Tot Avera Avera Avera Margin

ut l Variab al ge ge ge cost al
Fixe le cost Cos Fixed Variab Cost
d t Cost le
Cost Cost
0 40
1 6
2 11
3 15
4 60

Solution
Total Fixed cost for all the outputs is 40 (these are cost that do not varies/ change if even the outputs/
quantities vary)

MR. MOHAMED SAHR FOFANAH

 Total Variable Cost =
t
o
t
a
l
¿ c
o
s
t
− ¿ t
o
t
a
l
¿ f
i
x
e
d
¿ c
o
s
t
¿

For output0 , the total variable cost is zero since there was no production made
Output4 = 60
− ¿ 40
¿
20

Total Cost =
t
o
t
a
l
¿ f
i
x
e
d
¿ c
o
s
t
+ ¿ t
o
t
a
l
¿ v
a
r
i
a
b
l
e
¿ C
o
s
t

TC0 = 40
+ ¿ 0
¿
40

TC1 = 40 + 6 = 46
TC2 = 40 +11 = 51
TC3= 40 + 15 = 55
TC4= 40+ 20 = 60

(ii) Average total Cost = T o t a l c o s t

Out pu t
A
T
C0
¿
40
0
¿
0

A
T
C1
¿
46
1
¿
46

A
T
C 2
¿
51
2
¿
25.5

A
T
C3
¿
55
3
¿
18.3

A
T
C 4
¿
64
4
¿
10.7

(iii) Average total Cost = T o t a l V a r i a b l e c o st

Out put
A
v
C 0
¿
0
0
¿
0

A
V
C 1
¿
6
1
¿
6

A
V
C 2
¿
1 1
2
¿
5.5

A
T
C 3
¿
15
3
¿
5

A
T
C 4
¿
20
4
¿
5

MR. MOHAMED SAHR FOFANAH

 (iv) Average Fixed Cost = T o t a l f i x e d c o s t
out put ¿¿
T
F
C0
¿
40
0
¿
0

T
F
C1
¿
40
1
¿
40

T
F
C2
¿
40
2
¿
20

T
F
C3
¿
40
3
¿
13.3

T
F
C 4
¿
40
4
¿
10

Marginal Cost = ∆ T o t a l c o st
∆out put

Marginal Cost = T o t a lc o st n e w−T o t al C o s t o l d

o u t p u t n e w−o u t p u t o l d

MC0 = zero
46 − 40

MC1 = 1− 0
¿
6
1
¿
6

51− 46

MC2 = 2− 1
¿
5
1
¿
5

55− 51

MC3 = 3− 2
¿
4
1
¿
4

60− 55

MC4 = 4 −3
¿
5
1
¿
5

Output Total Total Total Cost Average Average Average Marginal

Fixed Variable Fixed Cost Variable cost Cost
cost
Cost Cost
0 40 0 40 0 0 0 -
1 40 6 46 40 46 6 6
2 40 11 51 20 25.5 5.5 5
3 40 15 55 13.3 18.3 5 4

MR. MOHAMED SAHR FOFANAH

 4 40 20 60 10 10.7 5 5

CONCEPT OF REVENUE
Revenue is the amount that a firm receives from the sale of the output. In other words, it is the receipts that a
firm obtains from selling its products.

TYPES OF REVENUE

1. Total Revenue
TR is the amount of money that a firm receives for the offer of goods and services in the market. Total
revenue is the gross revenue that a firm receives from selling an output. A firm’s total revenue can be
calculated as the number/quantity of goods sold multiplied by the price. The TR includes the product of the
quantity sold and the price.

TR = Q x P
Were,

TR – Total Revenue

Q – Quantity of sale (units sold)

P – Price per unit of output

2. Total Or Gross Profit

A firm calculates its total or gross profit by subtracting total cost (TC) from the total revenue (TR).

Profit = TR- TC

Profit is maximized when the marginal revenue is equal to the marginal cost i.e., when MR= MC, profit is
maximized.

3. Average Revenue

AR is used as a price in a perfectly competitive market. This can be found by the ratio of the firm’s total
revenue and the number of goods sold.

AR =TR/Q

Were,

AR – Average Revenue

TR – Total Revenue

Q – Total units sold

MR. MOHAMED SAHR FOFANAH

 4. Marginal Revenue (MR)

MR refers to the extra money received by selling one additional unit of the commodity. It is an addition to
the total revenue of a firm as new additional units are sold. By selling an additional unit, a firm earns
additional revenue that adds to the total revenue and this addition to revenue is called MR.

It is calculated as:

MR = TRn – TRn-1

Or

MR =ΔTR/ΔQ

Were,

MR – Marginal Revenue

ΔTR – Change in the Total revenue

ΔQ – Change in the units sold

TRn – Total Revenue of n units

TRn-1 – Total Revenue of n-1 units

Example 3 (WASSCE 1997 SECTION “A” Q2.)

Table of a Firm Total Revenue and Cost

Quantit Total Margin Tota Margin

y of Revenu al l al Cost
Yams e Revenu Cost (MC)
(kg) (TR) e (MC
(MR) )
0 0 - 5 -
1 M 9 8 3
2 18 9 6 T
3 O 6 21 5
4 28 Q 25 4
5 30 2 25 U
6 P 1 25 0
7 28 -3 S 1
8 24 R 24 -2

Use the table to answer the

following questions:
a) Complete the table by calculating the missing figures M, O, P, Q, R, S, T, U?

b) At what output is profit maximized?

MR. MOHAMED SAHR FOFANAH

c) Calculate the profit when the quantity sold is 5

d) At what output does MC begin to rise?

Solution

a) TRn = TRn-1 + MRn

Where TRn is the Total Revenue New/ Current total revenue

TRn-1 is the previous / old total Revenue

MRn is the Current Marginal revenue / new marginal revenue

To find the value of M

TRn-1 = 0, MRn = 9, TRn = ?

TRn = 0+9= 9

To find the value of O

TRn-1 = 18, MRn = 6, TRn =?

TRn = 18+6 = 24

To find the value of P

TRn-1 = 30, MRn = 1, TRn =?

TRn = 30+1= 31

MRn = TRn - TRn-1

To find the value of Q

MRn =?, TRn =28, TRn-1 = O (but O= 24),

TRn = 28-24= 4

To find the value of R

MRn =?, TRn =24, TRn-1 = 28

TRn = 24-28= -4

MR. MOHAMED SAHR FOFANAH

 TCn = TCn-1 + MCn

Where TCn is the Total Cost New/ Current total cost

TCn-1 is the previous / old total cost

MCn is the Current Marginal cost / new marginal cost

To find the value of S

TCn-1 = 25, MCn = 1, TCn = ?

TRn = 25+1= 26

MRn = TCn - TCn-1

To find the value of T

MCn =?, TCn =6, TCn-1 = 8

TRn = 6 - 8= -2

To find the value of U

MCn =?, TCn =25, TCn-1 = 25

TRn = 25 - 25= 0

b) Profit is maximized when the Marginal Revenue is equal to the Marginal Cost i.e. (MR= MC)

Therefore, the profit is maximized at output 4kg of yam

c) Profit = TR – TC

Profit = NLE30 – NLE25

Profit = NLE 5

d) The marginal revenue begins to rise at output 1

Example 4: (WASSCE 2018 SECTION “A” Q2)

The cost and output schedule of a firm is shown in the table below.
Output (kg) 0 15 35 60 85

Variable ($) 0 30 55 75 90

MR. MOHAMED SAHR FOFANAH

 Total cost ($) 15 45 70 90 105

Total revenue 0 30 70 120 170

($)

a) Using the data in the table above, at each level of output, calculate the firms i) Marginal revenue (ii)
Marginal cost

b) At what output level did the firm: i) break even ii) make the highest profit iii) attain equilibrium

c) Identify the market structure in which the firm operates. #

Solution

a) Marginal revenue = Marginal Revenue = ∆ T o t a l R e v e n u e

∆out put

Marginal Cost = T o t a lr e v e n u e n e w−T o t a lr e v e n u e o ld

o u t p u t n e w−o u t p u t o l d

MR0 = zero
3 0− 0

MR15 = 1 5− 0
¿
30
15
¿
2

7 0− 3 0

MR35 = 3 5− 1 5
¿
40
20
¿
2

120− 70

MR60 = 60− 35
¿
50
25
¿
2

170− 120

MR85= 85− 60
¿
50
25
¿
2

Marginal Cost = ∆ T o t a l c o st
∆out put

Marginal Cost = T o t a lc o st n e w−T o t al C o s t o l d

o u t p u t n e w−o u t p u t o l d

MC0 = zero
45 − 15

MC1 = 15− 0
¿
30
15
¿
2

70− 45

MC2 = 35− 15
¿
25
20
¿
1.25

MR. MOHAMED SAHR FOFANAH

 90− 70

MC3 = 60− 35
¿
20
25
¿
0.8

105− 90

MC4 =
85− 60
¿
15
25
¿
0.6

Output (kg) 0 15 35 60 85

Variable ($) 0 30 55 75 90

Total cost ($) 15 45 70 90 105

Total revenue 0 30 70 120 170

($)

Marginal 0 2 2 2 2
Revenue

Marginal Cost 0 2 1.25 0.8 0.6

b. Breakeven (the point where there is no profit nor loss i.e., TR=TC)

Therefore, we have a breakeven at output 35 (TR= 70, TC= 70)

EXAMPLE 5 (WASSCE 2004 SECTION “A” Q2)

The table below represents the output level of a particular firm producing soft drinks. Use the information in
the table to answer the questions that follows.
Output 0 12 23 36 48 58
(unit)

Give the cost equation of the firm in Naira as C= 20 + 2q where C is total cost and q is quantity produced,
calculate:

a) The total cost of producing (i) 12 units of output (ii) 36 units of output

b) The average cost when (i) 48 units were produced (ii) 58 units were produced.

c) The \marginal cost when (i) 23 units were produced (ii) 36 units were produced.

d) If the firm in operating in a perfectly competitive market and the market price is N5 per unit, determine the
profit when, (i) 23 – units are produced (ii) 48 units are produced. o

MR. MOHAMED SAHR FOFANAH

MR. MOHAMED SAHR FOFANAH