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

https://www.youtube.com/watch?v=bE9NdTNi5-w


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 productLabour 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

1 2 3 4 5 60

2

4

6

8

10

12

14

0.5 1.5 2.5 3.5 4.5 5.5

MP

Q

https://www.youtube.com/watch?v=CfioxJ4E_h4


Cont…

Increasing returns

Increasing returnsOutput 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 andTotal 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

The law of diminishing returns (cont…)


• Identify “Increasing marginal returns”, “Diminishing marginal returns”, and “Negative marginal returns”

The law of diminishing 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:

AFC = TFC

AVC = TVC

Q

Q


Average total cost

• Total cost divided by the quantity of output produced

ATC = AFC + AVC = TCQ


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 = TVCQQ


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 = TRQ


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

https://www.youtube.com/watch?v=ZihWEVWCJYk

https://www.youtube.com/watch?v=4zGooWkYJG4


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 300Its total revenue will be $8 x 300 = $2400Its total variable costs will be $8 x 300 = $2400It 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 curveSRATC = 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 curve𝐿𝑅𝐴𝐶=𝐿𝑅𝑇𝐶𝑄


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.

https://www.youtube.com/watch?v=VDZTBxhlSTE

https://www.youtube.com/watch?v=56dpnShzRhs


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

• A situation in which the long-run average 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

• A situation in which the long-run average 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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