This document discusses production costs and functions. It covers: 1. Short-run and long-run production, where factors of production are fixed in the short-run. Diminishing returns can occur in the short-run as adding more variable inputs yields lower marginal products. 2. Returns to scale in the long-run, where all factors are variable. Increasing, decreasing, and constant returns to scale depend on the relationship between input and output percentage changes. 3. Cost concepts including fixed, variable, average, marginal, and total costs. Fixed costs do not vary with output while variable costs do. Marginal cost is the change in total cost from one extra unit of output.

1. Costs
Introduction to production
We take it for granted that goods and services will be available for us to buy as and when
we need them. But production and supplying to the market is often a complicated business.
Production Functions
The production function relates the quantity of factor inputs to the volume of output that
result. We use three measures of production and productivity.
o Total product (or total output). In manufacturing industries such as motor vehicles and
DVD players, it is straightforward to measure how much output is being produced. But
in service or knowledge industries, where output is less “tangible” it is harder to
measure productivity.
o Average product measures output per-worker-employed or output-per-unit of capital.
o Marginal product is the change in output from increasing the number of workers used
by one person, or by adding one more machine to the production process in the short
run.
The length of time required for the long run varies from sector to sector. In the nuclear power industry for
example, it can take many years to commission new nuclear power plant and capacity. This is something
the UK government has to consider as it reviews our future sources of energy.
Short Run Production Function
The short run is a time period where at least one factor of production is in fixed supply. We
normally assume that the quantity of plant and machinery is fixed and that production can be
altered through changing variable inputs such as labour, raw materials and energy.
The time periods used in economics differ from one industry to another, for example, the
short-run for the electricity generation industry or telecommunications differs from magazine
publishing and local sandwich bars. If you are starting out in business with a new venture
selling sandwiches and coffees to office workers, how long is your short run? And how long is
your long run? The long run could be as short as a few days – enough time to lease a new van
and a sandwich-making machine!
Diminishing Returns

2. In the short run, the law of diminishing returns states that as we add more units of a variable
input to fixed amounts of land and capital, the change in total output will at first rise and
then fall. Diminishing returns to labour occurs when marginal product of labour starts to fall.
This means that total output will be increasing at a decreasing rate.
What might cause marginal product to fall? One explanation is that, beyond a certain point,
new workers will not have as much capital equipment to work with so it becomes diluted
among a larger workforce. An example is shown below.
We assume that there is a fixed supply of capital (20 units) available in the production
process to which extra units of labour are added.
• Initially, marginal product is rising – e.g. the 4th worker adds 26 to output and the 5th
worker adds 28 and the 6th worker increases output by 29.
• Marginal product then starts to fall. The 7th worker supplies 26 units and the 8th worker
just 20 added units. At this point production demonstrates diminishing returns.
The Law of Diminishing Returns
Capital Input Labour Input Total Output Marginal Product Average Product of Labour
20 1 5 5
20 2 16 11 8
20 3 30 14 10
20 4 56 26 14
20 5 85 28 17
20 6 114 29 19
20 7 140 26 20
20 8 160 20 20
20 9 171 11 19
20 10 180 9 18
Average product rises as long as the marginal product is greater than the average – for
example when the seventh worker is added the marginal gain in output is 26 and this drags
the average up from 19 to 20 units. Once marginal product is below the average as it is with
the ninth worker employed (where marginal product is only 11) then the average must decline.
Total
Output
(Q)
Units of Labour Employed (L)
(Q)Slope of the curve gives the
marginal product of labour
Diminishing returns are apparent
here – total output is rising but at a
decreasing rate

3. Criticisms of the Law of Diminishing Returns
How realistic is this assumption of diminishing returns? Surely ambitious and successful
businesses will do their level best to avoid such a problem emerging? It is now widely
recognised that the effects of globalisation and the ability of trans-national businesses to
source their inputs from more than one country and engage in transfers of business
technology, makes diminishing returns less relevant as a concept. Many businesses are multi-
plant meaning that they operate factories in different locations – can switch output to meet
changing demand.
Long Run Production - Returns to Scale
In the long run, all factors of production are variable. How the output of a business responds
to a change in factor inputs is called returns to scale.
Numerical example of long run returns to scale
Units of
Capital
Units of
Labour
Total
Output
% Change in
Inputs
% Change in
Output
Returns to Scale
20 150 3000
40 300 7500 100 150 Increasing
60 450 12000 50 60 Increasing
80 600 16000 33 33 Constant
100 750 18000 25 13 Decreasing
• In our example when we double the factor inputs from (150L + 20K) to (300L + 40K)
then the percentage change in output is 150% - there are increasing returns to scale.
• In contrast, when the scale of production is changed from (600L + 80K0 to (750L +
100K) then the percentage change in output (13%) is less than the change in inputs
(25%) implying a situation of decreasing returns to scale.
• Increasing returns to scale occur when the % change in output > % change in inputs
• Decreasing returns to scale occur when the % change in output < % change in inputs
• Constant returns to scale occur when the % change in output = % change in inputs
The nature of the returns to scale affects the shape of a business’s long run average cost
curve.
Finding an optimal mix between labour and capital
In the long run businesses will be looking to find an optimal output that combines labour and
capital in a way that maximises productivity and therefore reduces unit costs towards their
lowest level. This may involve a process of capital-labour substitution where capital machinery
and new technology replaces some of the labour input. In many industries over the years we
have seen a rise in the capital intensity of production - good examples include farming,
banking and retailing.
Calculating the costs of a firm

4. Next we look at production costs. In the short run, because at least one factor of production
is fixed, output can be increased only by adding more variable factors.
Fixed costs
Fixed costs do not vary directly with the level of output
Most businesses operate with a significant fixed cost component. Examples of fixed costs
include the rental costs of buildings; the costs of leasing or purchasing capital equipment such
as plant and machinery; the annual business rate charged by local authorities; the costs of full-
time contracted salaried staff; the costs of meeting interest payments on loans; the
depreciation of fixed capital (due solely to age) and also the costs of business insurance.
Basically any business with significant capacity will have high fixed costs; perhaps the classic
example is an airline with a large number of routes, or a vehicle manufacturer that spends
millions of pounds building a new factory and installing expensive and bulky capital
equipment.
Fixed costs are the overhead costs of a business.
Key points:
 Total fixed costs (TFC) these remain constant as output increases
 Average fixed cost (AFC) = total fixed costs divided by output
Average fixed costs must fall continuously as output increases because total fixed costs
are being spread over a higher level of production. In industries where the ratio of fixed to
variable costs is extremely high, there is great scope for a business to exploit lower fixed
costs per unit if it can produce at a big enough size. Consider the Sony PS3 or the new iPhone
where the fixed costs of developing the product are enormous, but these costs can be divided
by millions of individual units sold across the world. Successful product launches and huge
volume sales can make a huge difference to the average total costs of production.
Please note! A change in fixed costs has no effect on marginal costs. Marginal costs relate
only to variable costs!
Variable Costs
Variable costs are costs that vary directly with output – when output is zero, variable costs
will be zero but as production increases, total variable cost will rise.
Examples of variable costs include the costs of raw materials and components, the wages of
part-time staff or employees paid by the hour, the costs of electricity and gas and the
depreciation of capital inputs due to wear and tear.
Average variable cost (AVC) = total variable costs (TVC) /output (Q)
Average Total Cost (ATC or AC)
• Average total cost is the cost per unit produced
• Average total cost (ATC) = total cost (TC) / output (Q)
Marginal Cost
Marginal cost is the change in total costs from increasing output by one extra unit.

5. The marginal cost of supplying an extra unit of output is linked with the marginal productivity
of labour. The law of diminishing returns implies that marginal cost will rise as output
increases. Eventually, rising marginal cost will lead to a rise in average total cost. This happens
when the rise in AVC is greater than the fall in AFC as output (Q) increases.
A numerical example of short run costs is shown in the table below. Fixed costs are assumed to
be constant at £200. Variable costs increase as more output is produced.
Output
(Q)
Total Fixed
Costs (TFC)
Total Variable
Costs (TVC)
Total Cost Average Cost
Per Unit
Marginal Cost
(the change in total cost
from a one unit change
in output)
(TC= TFC +
TVC)
(AC = TC/Q)
0 200 0 200
50 200 100 300 6 2
100 200 180 400 4 2
150 200 230 450 3 1
200 200 260 460 2.3 0.2
250 200 280 465 1.86 0.1
300 200 290 480 1.6 0.3
350 200 325 525 1.5 0.9
400 200 400 600 1.5 1.5
450 200 610 810 1.8 4.2
500 200 750 1050 2.1 4.8
• In our example, average cost per unit is minimised at a range of output - 350 and 400
units.
• Thereafter, because the marginal cost of production exceeds the previous average, so
the average cost rises (for example the marginal cost of each extra unit between 450
and 500 is 4.8 and this increase in output has the effect of raising the cost per unit
from 1.8 to 2.1).
An example of fixed and variable costs in equation format
If for example, the short-run total costs of a firm are given by the formula
SRTC = $(10 000 + 5X2) where X is the level of output.
• The firm’s total fixed costs are $10,000
• The firm’s average fixed costs are $10,000 / X
• If the level of output produced is 50 units, total costs will be $10,000 + $2,500 =
$12,500

6. Case Study: The Marginal Cost of Oil
The marginal cost of oil is the expense of
extracting an extra barrel of crude oil
from below the ground. It is a widely held
belief among economists who specialize in
commodity prices that the long-run market
price of something is determined
fundamentally by the marginal cost of
production. The resources that can be
tapped at lowest cost are often done so
first, and then as it becomes progressively
harder to unearth such resources the
market price must rise to provide an
economic incentive to do so.
One problem is that, because oil is a non-
renewable resource lying in geological
structures that vary enormously in location, weather, depth and many other variables, the cost
of extracting new supplies is hard to determine. Many OPEC countries – especially Saudi
Arabia – have access to relatively cheap and elastic supplies of oil. But the same cannot be
said of crude oil producers in Canada's tar sands and oil companies who have sunk huge
amounts of money into exploiting the oil available in deep-water facilities off the west coast
of Africa or in Brazil.
When the market value is
much higher than marginal
cost, oil producers extract a
high level of producer surplus
for each barrel that makes it
to the oil refineries. The fact
is that for many oil-exporting
countries, the price for each
barrel of crude oil extracted
needs to be higher than the
marginal cost of production
for national governments to
generate sufficient income to
pay for ambitious public
spending projects. So
whereas the Saudi
government can expect to
balance its budget when
world oil prices are hovering
at around $55 per barrel, prices need to be closer to $70 a barrel for the Russian
government to earn enough oil revenues to pay for their state spending. And that figure rises
to more than $95 a barrel for countries such as Iran and Venezuela.
Oil companies need to know that the price they can command in the market will be
persistently above the marginal extraction cost in order to cover the fixed costs of production
and the expected rate of profit demanded by shareholders.
Source: EconoMax, October 2008
US dollars
World Crude Oil Price - US Dollars Per Barrel
Source: Reuters EcoWin
03 04 05 06 07 08 09
0
10
20
30
40
50
60
70
80
90
100
110
120
130
140
150
USdollarsperbarrel
0
10
20
30
40
50
60
70
80
90
100
110
120
130
140
150
Million barrels per day, source of data is the OECD
World Oil Supply and Demand
World oil demand, millions of barrels per day
World oil supply, millions of barrels per day
Source: OECD
86 88 90 92 94 96 98 00 02 04 06 08
millions
55
60
65
70
75
80
85
90
Millionbarrelsperday(millions)
55
60
65
70
75
80
85
90

8. Short Run Cost Curves
When diminishing returns set in (beyond output Q1) the marginal cost curve starts to rise.
Average total cost continues to fall until output Q2 where the rise in average variable cost
equates with the fall in average fixed cost. Output Q2 is the lowest point of the ATC curve for
this business in the short run. This is known as the output of productive efficiency.
A change in variable costs
A rise in the variable costs of production – perhaps due to a rise in oil and gas prices or a rise
in the national minimum wage - leads to an upward shift both in marginal and average total
cost. The firm is not able to supply as much output at the same price. The effect is that of an
inward shift in the supply curve of a business in a competitive market.
Costs
Output (Q)
Average Fixed
Cost (AFC)
Average
Variable Cost
(AVC)
Average Total
Cost (ATC)
Marginal Cost
(MC)
If marginal cost is below average cost then average must be falling. Even if MC is rising, AC falls
if MC <AC. For this reason, MC curve intersects the AC curve at the lowest point of the AC
curve. Diminishing returns starts to occur when marginal cost starts to rise.
Q1 Q2

9. An increase in fixed costs has no effect on the variable costs of production. This means that
only the average total cost curve shifts. There is no change on the marginal cost curve leading
to no change in the profit maximising price and output of a business. The effects of an increase
in the fixed or overhead costs of a business are shown in the diagram below.
Suggestions for background reading on changes in business costs
Dry cleaners facing rising costs (BBC news, June 2008)
Grain prices are squeezing bakers (BBC news, April 2008)
Costs
Output (Q)
AC1
MC
AC2 (after rise
in fixed costs)
Costs
Output (Q)
Average
Variable Cost
(AVC1)
Average Total
Cost (ATC1)
Marginal Cost
(MC1)
MC2 AC2
AVC2

10. High costs fuel record loss for British Airways (BBC news, May 2009)
Pub industry hit by rising costs (BBC news, September 2008)