Cost/Revenue Analysis

UUNZ Institute of Business 1
520
The Economic Environment
Lecture 6
Facilitator: Don Samarasinghe
Cost/Revenue Analysis

Key concepts
• The production process
• Fixed and variable inputs
• Short run vs long run
• The production function
• Marginal product
• The law of diminishing returns
• Economic and accounting costs
• Short run cost curves
• Revenue analysis
• Break-even and shutdown points
• Long run cost curves
• Scales of production

The production process

Fixed and variable inputs
• A fixed input is any resource for which the
quantity cannot change during the period
of time under consideration.
“Those difficult to increase within a reasonable
time span”
Example
The physical size of a firm’s plant and the
production capacity of heavy machines cannot
easily change within a short period time.

Fixed and variable inputs (cont…)
• A variable input is any resource for which
the quantity can change during the period
of time under consideration.
“ Those much more easily supplied in
increasing numbers”
Example
Managers can hire fewer or more workers during a
given year. They can also change the amount of
materials and electricity used in production.

Short-run versus long-run
• Distinction doesn’t depend on any specific no of
days, months or years
• However, it depends on the ability to vary the
quantity of inputs or resources used in
production

Short-run versus long-run (cont…)
• Short-run is a period of time so short that
there is at least one fixed input.
E.g. During a short run a firm can increase out put
by hiring more workers(variable input), while the
size of the firm’s profit (fixed input) remains
unchanged. The firm’s plant is the most difficult
input to change quickly.

Short-run versus long-run (cont…)
• Long-run is a period of time so long that all
inputs are variable.
In the long run, the firm can build new factories or
purchase new machinery. New firm can enter the
industry, an existing firms may leave the industry.

Short Run Costs
(i.e. there is always at least one
type of fixed input)

The production function

The production function (cont…)
• The relationship between the maximum
amounts of output a firm can produce and
various quantities of inputs.
• The diagram on the next slide is a typical
production function, where output rises
according to how many people are
employed.

The production function (cont…)
= Q

Marginal product
• The change in total output produced by
adding one unit of a variable input, with all
other inputs used being held constant, that
is:
– How much does output rise when an extra
worker is employed?
MP =

Marginal product
Labour input(number of
workers per day)
Total output(bushels of
grapes perday)
Marginal
product(bushels of
grapes per day)
0 0
1 10
2 22
3 33
4 42
5 48
6 50
0.5
1.5

The marginal product curve
0
2
4
6
8
10
12
14
1 2 3 4 5 6
0.5 1.5 2.5 3.5 4.5 5.5
MP
Q

Cont…
Increasing returns
Increasing returns
Output results from the
combined use of fixed and
variable inputs.
Each successive unit of labour
adds more to the output than
previous labour
But, all units are equal and
Total output increases
because, extra unit of labour are
needed to operate the
machinery
At some stage, sufficient labour
will be employed to operate All
the equipment
Additional units of labour can still
contribute to output(e.g. Working
a shift at times)
However this cannot go forever
In a certain time period , extra
output provided by additional
labour units becomes smaller
and smaller
Total output continue to grow
but at a diminishing rate

The law of diminishing returns
• The principle that beyond some point the
marginal product decreases as additional
units of a variable factor are added to a
fixed factor.
• Note: the law assumes there are fixed
inputs – it is therefore a short-run concept.

Land
(hectares)
Fertiliser input
(tonnes)
Total production of
Corn (bushels)
MP (bushels)
1 0 1000
1 1 1250
1 2 1550
1 3 1900
1 4 2200
1 5 2450
1 6 2600
1 7 2650
1 8 2650
1 9 2600
(cont…)

• Identify “Increasing marginal returns”,
“Diminishing marginal returns”, and
“Negative marginal returns”
(cont…)

Decisions of a firm
• A firms supply curve is related to cost
and an increase in costs will shift the
supply curve to the left.
Total
cost
Total
fixed
cost
Total
variable
cost

Economic and accounting costs
Accounting costs
• The actual (explicit)
costs involved in
production
• E.g. Mortgage, rent,
power, raw materials,
wages, etc.
Economic costs
• Accounting cost
(explicit) + the
opportunity costs
(implicit) of the
resources used.
• E.g. The rent lost by
the owner of a factory
whose firm currently
uses the building

Total cost concepts
• Total fixed costs(TFC) are costs that do
not vary as output varies and that must
be paid even if output is zero.
• Even a firm produces nothing, it must
still pay rent, interest on loans,
mortgage, property taxes and fire
insurance.
• TFC can possibly change in the long
run, e.g. the council set new rates, rent
arrangements come up for review.

Total variable costs
• Total variable costs(TVC) are costs that
are zero when output is zero and vary
as output varies.
E.g.
Wages for hourly workers, electricity, fuel
and raw materials.

Total cost
• Thus total cost(TC) is the sum of total
fixed cost and total variable cost at each
level of output.
TC = TFC + TVC

Total cost (cont…)

Average fixed and variable costs
• Average fixed cost (AFC) – total fixed
cost divided by the quantity of output
produced:
• Average variable cost (AVC) – total
variable cost divided by the quantity of
output produced:
Q
Q

Average total cost
• Total cost divided by the quantity of output
produced
ATC = AFC + AVC = TC
Q

Marginal cost
• Marginal analysis asks how much costs
rise when an additional unit of output is
produced.
• MC = the change in total cost when one
unit of output is produced
MC = TC = TVC
QQ

Total product (Q) TFC($) TVC TC MC AFC AVC ATC
0 100 0 100
1 100 50 150 50 100 50 150
2 100 84 184 34 50 42 92
3 100 108 208 24 33 36 69
4 100 127 227 19 25 32 57
5 100 150 250 23 20 30 50
6 100 180 280 30 17 30 47
7 100 218 318 38 14 31 45
8 100 266 366 48 13 33 46
9 100 325 425 59 11 36 47
10 100 400 500 75 10 40 50
11 100 495 595 95 9 45 54
12 100 612 712 117 8 51 59

Revenue Analysis
• Revenue is the income received from the sale
of receipts or goods.
• Total revenue (TR) is the sum of the income
received from the sale of total goods (TR =
price x quantity = P x Q)
• AR = TR/Q

Revenue Analysis (Cont…)
• Marginal revenue (MR) is the additional
revenue obtained by selling one more
additional unit.
MR = TR
Q

Average
and
marginal
costs
 Cost curves (generally U shaped) are
always plotted with output (Q) on the
horizontal axis
 They can be plotted on a one graph

Note the marginal-average rule
• When MC < ATC, ATC falls.
• When MC > ATC, ATC rises.
• When MC = ATC, ATC is at its minimum
point where the technical optimum output
occurs. At the point resources are
efficiently combined.

Break-even and shutdown points

Break-even point
• This is the point where price is equal to
average cost or P=ATC
• At this price the firm is covering all of its
economic costs (recall this is accounting
cost plus opportunity cost)
• In economics when a firm is at a
breakeven point it is said to be earning a
normal profit.

Break-even point (Cont…)
PRICE $
COST $
REVENUE $
QUANTITY
ATC
AVC
MC
10
300
If this firm is receiving a
price of $10 and is selling
a quantity of 300, its total
revenue will be?
So we have a Total Revenue (TR) of $3000 and a Total
Cost (TC) of $3000 at an output of 300 units. TR – TC =
Profit OR $3000 - $3000 = 0 or BREAK EVEN

Shutdown point
• Recall that Total Cost =FC + VC
• If a firm can’t even receive a price to cover the VC of
producing a good then it should shutdown.
• In this case though it will still have to pay its fixed costs
• At any price point between shutdown (above AVC) and
breakeven at least the firm will receive a contribution to cover
FC so it will continue to operate.
• While shut down, the firm might keep its factory, pay fixed
costs, and hope for higher prices soon
• If the firm does not believe market condition will improve, it
will avoid fixed costs by going out of business
SHUTDOWN is where P (selling price) = AVC

Shutdown point (cont…)
PRICE $
COST $
REVENUE $
QUANTITY
ATC
AVC
MC
10
300
8
This firm is receiving a price of $8 and is selling a quantity of 300
Its total revenue will be $8 x 300 = $2400
Its total variable costs will be $8 x 300 = $2400
It should SHUTDOWN, there is no sense in opening the doors.

Shutdown point (cont…)
PRICE $
COST $
REVENUE $
QUANTITY
ATC
AVC
MC
10
300
8
What does the shaded area in the diagram represent?
If you identified this area as total FC at output 300 you are right! So you will see that at the
Shutdown point of $8.00 the firm is not covering any of its FC. At any price between $8 and $10 it
will at least be able to pay off some of its Fixed Costs (FC) so it makes sense to keep operating.
At least in the short term and until the price in the market improves.

Long Run Costs
(i.e. all inputs can be varied)
The long run total cost (LRTC) curve graphs the minimum
cost of producing any quantity if all inputs are variable and
can be chosen

Long-run production costs
• In the long run, a firm can vary the quantity
of all inputs:
e.g. build a larger factory; expand onto
new land.
• In the short run, there was no need to vary
fixed inputs, or no time to do so.
• The long run allows greater planning for
the expected level of production.

Q1
Suppose a company estimates that it will be
producing an output level of 6 units per hour
for the faceable future (long run). Which
plant size should the company choose?
Q2
What if the production is expected to be 12
units per hour?
The plant size represented by a firm in the long run
depends on the expected level of production

The long-run average cost curve
SRATC = Short Run Average Total Cost S=Small, M=medium, l=large
The long run total cost curve
will be the lower “envelope”
of the short run cost curves
This is drawn as a smooth
curve given that a continuum
of plant sizes are available.

The long-run average cost curve
(cont…)
The curve that traces the lowest cost per unit at
which a firm can produce any level of output when
the firm can build any desired plant size.
= Firm’s planning curve

Scales of production
• The long-run average cost curve is
U-shaped.
• This reflects returns to scale – three types
are recognised:
– Economies of scale (LRAC falls as output
rises)
– Constant returns to scale
– Diseconomies of scale (LRAC rises as output
rises).

Scales of production (cont…)
The long run average cost (LRAC) curves tells us
whether the particular production function exhibits
increasing, decreasing or constant returns to scale.

Example
• A single firm will expand to larger plant
size by increasing all factors of production.
If increasing the plant size leads to lower
unit costs, we have economies of scale
but if this leads to higher units costs we
have diseconomies of scale.
Scales of production (cont…)

Economies of scale
• A situation in which the long-run average
cost curve declines as the firm increases
output
• Sources of economies of scale:
– The division of labour and the use of
specialisation are increased
– More efficient use of capital equipment
– Advanced technology
– Better management, marketing, etc.

Constant returns to scale
cost curve does not change as the firm
increases output.
• Sources of cconstant returns to scale
- When a firm double its production, it
can simply replicate its plants
-So, ALRTC will not change and output
will simply increase

Diseconomies of scale
cost curve rises as the firm increases
output
• Sources of diseconomies of scale:
– Managers may become less efficient and less
able to monitor output of workers
– Barriers to communication
– Workers may become slack

Cost/Revenue Analysis

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