Lectures, week 4
Topic 1.
Consumer Theory 4
(conclusion)
Econ20002 semester 1
Intermediate Microeconomics
Svetlana Danilkina
W4-1
Overview
4. Consumer’s (Individual) Demand
e. revealed preferences
f. paying nurses (labour supply).
g. taxation and labour supply (love story about
tax)
W4-2
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If an individual facing budget line
l1 chooses bundle A rather than
bundle B, A is revealed to be
preferred to B (and all other
points in the l1 budget set).
Likewise, the individual facing
budget line l2 chooses bundle B,
which is thus revealed to be
preferred to bundle D (and all
other bundles in the l2 budget
set).
Therefore, A is preferred to all
market baskets in the green-
shaded area.
If we add “more is better”
assumption, then we know that
all baskets in the pink-shaded
area are preferred to A.
Revealed Preference (PR, Ch.3.4) 4e.
More is better
A and B; B and D; A and D
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Facing budget line l3, the
individual chooses E, which is
revealed to be preferred to A
(because A could have been
chosen).
Likewise, facing line l4, the
individual chooses G, which is
also revealed to be preferred
to A.
If we add convexity
assumption to the “more is
better”, we know that all
bundles in the pink-shaded
area are preferred to A.
Bundle A is preferred to all
bundles in the green-
shaded area (as before).
More is better;
and convexity
Therefore, the indifference curve through
bundle A must lie within the unshaded area.
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When facing the original budget line l1, Roberta chooses point A (10h in the club).
When the fees are altered, she faces budget line l2, which passes through original
bundle A.
Therefore, she will be better off. Why? Bundle A is revealed to be preferred to any
bundle in the original budget set (shaded triangle).
With the new budget set, she can still choose A, but she can also choose among
the points that were not affordable to her before, so she can only become better
off! (It is possible, but unlikely that she will stay at bundle A, so she is weakly better off).
Note that we don’t need to know her indifference curves to conclude that. If we do know
her indifference curves, then we can show her new point B, which lies on a higher
indifference curve, at the tangency point with budget line I2.
EXAMPLE 3.6 REVEALED PREFERENCE FOR RECREATION
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A B
10
Roberta has $100 per week to spend on
recreational activities. When her health
club charges $4 per hour, she chooses
to use it for 10h per week.
The health club changes its fees to $30
fixed fee per week plus $1 per hour.
Is Roberta worse off, better off or
indifferent?
4f. Application – paying nurses
 Nurses in Victoria are mainly employed by the State
Government
 The wage tends to be below the market clearing level –
hence the ‘nurses shortage’
 A key claim against higher wages is that higher wages
would lead nurses to work less, not more, exacerbating
the shortage
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 Issues
 How do we model the decision about how many hours to
work?
 Can a rise in wages lead to less work (backward
bending supply)?
 Is this likely?
Reading: PR, pp.553-5 in 9th Global E (the market supply of inputs)
Background – the labour/leisure choice
 Suppose you have 24 hours per day to work or relax
(you should probably sleep as well). This is your
endowment (given to you by the generous universe).
 You like leisure – relaxing with friends, reading
economics, watching TV, etc. Leisure is a ‘good’ for
you.
 If you work then you receive a wage w and you can
use this money to buy ‘other goods’, OG. The price of
other goods is $1, this is basically your income, to
spend as you please on the stuff you like. But working
means giving up leisure.
 Therefore, you face an individual choice problem.
W4-7
The labour/leisure choice:
the budget set with endowment
qother goods
qleisure, hours24
$1,200
W4-8
Suppose the wage is $50 per hour and the price of
other goods is $1.
You can also think of other goods in terms of $ here:
how many dollars can I spend on other goods?
Then this is your budget set. The (absolute value of)
slope of the budget line is just the wage; $50.
More generally, if you don’t assume that the price of
other goods is 1, the slope is equal to (minus) wage /
price of other goods.
This is an endowment.
slope = -50
The labour/leisure choice
Note that at this optimal choice
your MRS of leisure for other
goods (“income”) is equal to the
wage $50.
$400
16 hours
qother goods
qleisure24 hours
$1,200
W4-9
A
As both leisure and ‘other goods’ are
‘goods’ we can draw standard
indifference curves. Your optimal choice
is given by the tangency condition.
The slope of the budget line is just (minus) the wage; -$50.
The labour/leisure choice
Suppose the wage rises to $60 per
hour. Your budget line rotates
outwards. The new choice is point
B. Note that (as drawn) this
involves more ‘other goods’ and
more leisure. A higher wage means
that you work less! (e.g. work 7
hours now so have 17 hours leisure
and $420 income).
More
income
More leisure and less work
qother goods
qleisure24 hours
$1,440
W4-10
A
B
This is TE – total effect.
$1,200
The labour/leisure choice
qother goods
qleisure24 hours
$1,200
W4-11
A
B
To see how this can happen, let’s
break this total effect into
substitution and income effects.
Draw the “fake” budget line with
new slope ($60 per hour) but
tangent to the initial indifference
curve. D
$1,440
The labour/leisure choice: SE
qother goods
qleisure24 hours
$1,200
W4-12
A
BD
The substitution effect will
mean that as wages increase,
the relative price of leisure (in
terms of other goods foregone)
goes up; therefore, you
substitute to less leisure (i.e. to
more work).
SE
$1,440
The labour/leisure choice: IE
qother goods
qleisure24 hours
$1,200
W4-13
A
B
D
But a rise in wage also raises your “real” income. If
both ‘other goods’ and ‘leisure’ are normal goods,
then as your income increases you want more of
both. Therefore, the income effect means you want
more leisure (i.e. you work less).
IE
SE
TE
In Economics, we always assume that leisure is a normal good!
Unless you study workaholics…
Some of you might notice that this
graph of TE, IE and SE looks a bit
different from the one in lecture 3.
This is because in L3 we increase
price while keeping income fixed
(so budget line rotates inward); but
here we increase wage while
keeping an endowment of 24 hours
fixed (so b.l. rotates outward).
$1,440
The labour/leisure choice: labour supply
 So if the wage increases and labour
and ‘other goods’ are both normal
 The substitution effect means you work
more
 The income effect means you work less
 So in general we cannot say that people
will work more as the wage rises!
 This leads to the possibility of a
backward bending labour supply
curve (when income effect is larger than
substitution effect): wage increases, but
people choose to work less.
W4-14
labour
Labour
supply
OG
wage
price
Paying nurses
 So in theory if the State Government did
allow nurses to earn higher wages, each
individual nurse might work less
 There is some evidence that this did occur for
the ‘agency nurses’
 But does this mean a backward bending
supply for all nurses?
 No – it ignores new entry. If a higher wage means
that some people work as nurses rather than in
another profession, then supply of nursing labour
will slope up.
W4-15
Summary
 Breaking price changes into the substitution
and income effects helps us to understand
what drives peoples’ decisions
 It tells us why a higher wage may lead individual
workers to work less and not more.
 It tells us what data we need to check that a policy
will work the way it is meant to work.
W4-16
qother goods
qleisurewage
price-consumption curve when
wage (i.e. price of leisure) changes
Labour – leisure choice for Peter
24 hours
W4-17
OG
OG
wage*(24 - leisure) = price *consumption of other goods
(24 - ) *OGw leisure p q=
If he spends 24 hours working, he
will earn wage*24, and can buy
(wage*24/priceOG ) of other goods.
labour + leisure = 24 hours
4g. Taxation and Labour Supply
the endowment
qOG
qleisurewage
price-consumption curve when
wage (i.e. price of leisure) changes
Labour – leisure choice for Peter
24 hours
W4-18
24
qleisure, hours


Peter’s demand
for leisure
1

slope= 1

leisure1leisure1
qOG
qleisure
Usually, labour supply is very inelastic for primary-
income earners in the family and very elastic for
secondary-income earners.
wage
Peter’s supply of labour is
upward sloping
Labour – leisure choice for Peter
24 h
W4-19
labour, hours
Peter’s supply of
labour
labour + leisure = 24 hours
OG
wage
price
leisure1 labour1 labour1
slope= 1

1

qOG
qleisurewage
Anna’s supply of labour is
backward-bending
Labour – leisure choice for Anna
24 hours
W4-20
labour
Anna’s supply of
labour
labour + leisure = 24 hours
OG
wage
price
21 of 32Copyright © 2015 Pearson Education • Microeconomics • Pindyck/Rubinfeld, 8e, GE
EXAMPLE 14.2 LABOR SUPPLY FOR ONE- AND TWO-EARNER
HOUSEHOLDS
TABLE 14.2 ELASTICITIES OF LABOR SUPPLY (HOURS WORKED)
GROUP
HEAD’S HOURS
WITH RESPECT TO
HEAD’S WAGE
SPOUSE’S HOURS
WITH RESPECT TO
SPOUSE’S WAGE
HEAD’S HOURS
WITH RESPECT TO
SPOUSE’S WAGE
Unmarried males, no children .026
Unmarried females, children .106
Unmarried females, no children .011
One-earner family, children –.078
One-earner family, no children .007
Two-earner family children –.002 –.086 –.004
Two-earner family, no children –.107 –.028 –.059
One of the most dramatic changes in the labor market in the twentieth century
has been the increase in women’s participation in the labor force: 34% of
women in 1950 and 60% in 2010.
One way to describe the work decisions of the various family groups is to
calculate labor supply elasticities. When a higher wage rate leads to fewer
hours worked, the labor supply curve is backward bending: The income effect,
which encourages more leisure, outweighs the substitution effect, which
encourages more work. The elasticity of labor supply is then negative.
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Taxation of Peter: ATO’s nightmare
W4-22
labour
Peter’s supply of
labour
other goods other goods(1 ) (24 - ) *t w leisure p Q− =
Uniform proportional income tax t on labour income is
equivalent to reducing wage from w to (1- t)w.
Tax revenue = tw*labour.
If government increases
tax rate, then they get
more money per $dollar
earned, but people can
choose to work less and
earn less income.
If overall income can
decrease, so can tax
revenue!


w p
(1 )t w p−
Does Peter like tax?
W4-23
labour
Peter’s
supply of
labour
When tax rate increases, Peter works less and enjoys
more leisure. But he is not happy about it! His utility
went down.
qOG
qleisure
24 hours
before tax
with tax
w p
(1 )t w p−


Taxation of Anna: ATO loves her
W4-24
labour
Anna’s supply of
labour
When government
increases tax rate, Anna
chooses to work more
(on backward-bending
part of her labour curve).
Tax revenue increases
when tax rate goes up –
she pays more per
$dollar earned and works
more, earning higher
(pre-tax) income!
Anna’s supply of labour is
backward-bending
w p
(1 )t w p−


Taxation of Anna: does she love tax?
W4-25
labour
Anna’s supply
of labour
w p
(1 )t w p−
When tax rate increases, Anna works more and has
less leisure. But she is not happy about it! Her utility
went down.
qOG
qleisure
24 hours
before tax
with tax


Taxation dilemma
If all people are like Anna, increasing tax rates will lead to
higher tax revenue.
If all people are like Peter – then there is a trade-off:
increasing tax rate increases revenue per dollar earned,
but people respond by working less and earning less
money, so there is less income to tax.
Taxation can kill economic activity – most people will
respond like Peter and will choose to work less and less,
or move to the country with better tax laws.
Some people will try to hide their earnings – which is
illegal, making tax enforcement quite expensive.
It is also possible to hire a very good accountant, who will
make sure that you claim all deductions and use all
loopholes – this is not illegal.
Also you can fund a special interest group that would
lobby government for tax breaks and concessions in
exchange for political support – not pretty. W4-26
The Relationship of U.S. Tax Revenue and
the Marginal Tax Rate
W4-27
W4-28
Note to future high-ranking
government officials:
just because you want more tax
revenue does not mean that you can
get it.
Or should – you can end up spending
it on stupid programs.
W4-29
Producer Theory 1
Topic 2.
Econ20002 semester 1
Intermediate Microeconomics
Svetlana Danilkina Lecture 4
Overview
1. Production
a. producer theory; production decisions of firms
b. production technology; SR and LR; fixed and variable
inputs
c. production function in SR:
 production function
 marginal and average products
 law of diminishing marginal returns
 relationship between MP and AP
 law of diminishing marginal returns and
technological progress: Malthus was wrong
d. production function in LR:
 MP of labour and MP of capital
 isoquants; MRTS
 special cases: perfect substitutes; fixed-
proportions
 Increasing, decreasing and constant returns to
scale W4-30
W4-31
1a. Producer Theory
 In Topic1. Consumer Theory we talked about
behaviour of consumers – their preferences,
restrictions and choices. They constitute the
demand side of the market.
 Now, let’s look at the supply side – producers.
 Producer theory studies how firms make
production decisions – how to choose inputs
correctly to minimise costs.
 Producer Theory is similar to Consumer Theory:
1. Production Technology
2. Cost Constraints
3. Input Choices
1. Preferences
2. Budget Constraints
3. Consumption Choices
32 of 30Copyright © 2013 Pearson Education, Inc. • Microeconomics • Pindyck/Rubinfeld, 8e.
Why Do Firms Exist?
Firms and Their Production Decisions
Firms offer a means of coordination that is extremely
important and would be sorely missing if workers operated
independently.
Firms eliminate the need for every worker to negotiate every
task that he or she will perform, and bargain over the fees
that will be paid for those tasks.
Firms can avoid this kind of bargaining by having managers
that direct the production of salaried workers—they tell
workers what to do and when to do it, and the workers (as
well as the managers themselves) are simply paid a weekly
or monthly salary.
W4-32
W4-33
1b. Production Technology
 Firm converts inputs such as labour, materials, energy, and
capital into outputs: the goods and services for sale
 We can divide inputs (they are called the factors of
production) into the broad categories of labor, capital and
materials:
 Labor (L): skilled workers (managers, carpenters,
engineers) and less-skilled workers (agricultural workers,
construction labourers.)
 Capital (K): land, buildings (factories, stores), machinery
and other equipment (machinery, trucks).
 Materials: include steel, plastics, electricity, water, and any
other goods that the firm buys and transforms into final
products.
W4-34
Production Function; SR and LR
• Suppose that firm uses two inputs: capital K and labour L to
produce single output q.
• The production technology is described by the production
function q = f(K,L).
• The production function q = f(K,L) shows the maximum
possible output q that can be produced with a given amount of
inputs (K and L).
• i.e. it assumes that inputs are used efficiently by the firm.
How output responds to changes in the amount of
inputs:
Short run: a period of time such that at least one factor of
production cannot be changed.
This factor is called fixed input. The other inputs that can
be changed in the short run are called variable inputs.
Long run: a period of time needed so that firm can vary all
inputs (so all inputs are variable).
W4-35
Short run and long run: Example
If a woman is unhappy,
first, she should change her haircut,
then her apartment,
and if the above doesn’t help, her boyfriend.
folk wisdom
Let’s discuss this rule from economic point of view.
The production function :
haircut, apartment, boyfriend happiness
Long run: can change haircut, apartment and boyfriend
Short run (before expiration date of the lease on the apartment):
can’t change apartment!
So if you already had a haircut, and still unhappy, it is time for a
new boyfriend (significant other)
W4-36
1c. Properties of the production
function in the short run
In the short run, usually the capital is fixed:
and labour is variable.K K=
Marginal product of labour:
additional output produced when one
extra unit of labour is employed.
L
K K
q qMP
L L=
∆ ∂
= =
∆ ∂
Short run production function:
Average product of labour:
output per unit of labour used L K K
qAP
L =
=
( , )q f K L=
Note that both average and marginal product of labour
depends on how much capital is used. They are usually higher
when more capital is used.
37 of 30Copyright © 2013 Pearson Education, Inc. • Microeconomics • Pindyck/Rubinfeld, 8e.
Short Run: Production with One
Variable Input (Labor)
TABLE 6.1 PRODUCTION WITH ONE VARIABLE INPUT
AMOUNT OF
LABOR (L)
AMOUNT OF
CAPITAL (K)
TOTAL
OUTPUT (q)
AVERAGE
PRODUCT (q/L)
MARGINAL PRODUCT
(Δq/ΔL)
0 10 0 — —
1 10 10 10 10
2 10 30 15 20
3 10 60 20 30
4 10 80 20 20
5 10 95 19 15
6 10 108 18 13
7 10 112 16 4
8 10 112 14 0
9 10 108 12 −4
10 10 100 10 −8
W4-37
W4-38
q
L84 62
30
80
112
108
Short run production function: ( , )q f K L=
A
B
D
E
W4-39
q
L84 62
30
80
112
108
Average product of labour:
output per unit of labour used, keeping
capital constant
L
K K
qAP
L =
=
average product =
slope of the line from
the origin
at A: AP = 30/2 = 15
at B: AP = 80/4 = 20
A
B
D
E
W4-40
q
L84 62
30
80
112
108
Average product of labour:
output per unit of labour used, keeping
capital constant
L
K K
qAP
L =
=
A
average product = slope
of the line from the origin.
first increases, then
decreases (after point C)
C
B
D
E
W4-41
q
L84 62
30
80
112
108 L
K K
qAP
L =
=
A
average product = slope
of the line from the origin.
First increases, then
decreases (after point C)
C
L
APL
W4-42
q
L84 62
30
80
112
108 marginal product =
slope of the tangent
line
First increases, then
decreases.
A
B
D
E
Marginal product of labour:
additional output produced when one
extra unit of labour is employed.
L
K K
q qMP
L L=
∆ ∂
= =
∆ ∂
W4-43
q
L862
30
80
112
108
marginal product =
slope of the tangent
line
First increases, then
decreases.A
B
D
E
L
MPL
F
L
K K
q qMP
L L=
∆ ∂
= =
∆ ∂
W4-44
Marginal product: diminishing
marginal returns
q
L84 62
3
0
8
0
112
108
A
B
D
E
L
MPL
F
marginal product of labour:
 When labour input is small, MPL
increases when labour increases,
due to specialisation
 When labour input is large, MPL
decreases when labour increases:
when there are too many workers,
some become less effective.
Law of diminishing marginal
returns:
When more and more labour is
hired, but capital is fixed, marginal
product of labour will eventually start
decreasing
W4-45
 When marginal product
is above the average
product, the average
product is increasing
 When MP is below the
AP, the average product
is decreasing
 When MP is equal the
AP, the average product
reaches its maximum.
 MP curve crosses AP
curve from above where
AP is at its maximum.
q
L
E
L
APL,
MPL
F
C
Relationship between marginal
and average products
APL
MPL
46 of 30Copyright © 2013 Pearson Education, Inc. • Microeconomics • Pindyck/Rubinfeld, 8e.
THE EFFECT OF TECHNOLOGICAL
IMPROVEMENT
Figure 6.2
Labor productivity (output per unit of
labor) can increase if there are
improvements in technology, even
though any given production process
exhibits diminishing returns to labor.
As we move from point A on curve O1
to B on curve O2 to C on curve O3 over
time, labor productivity increases.
The Law of Diminishing Marginal Returns
● law of diminishing marginal returns Principle that as the use of
an input increases with other inputs fixed, the resulting additions to output will
eventually decrease.
W4-46
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The law of diminishing marginal returns
was central to the thinking of political
economist Thomas Malthus (1766–1834).
Malthus predicted that as both the
marginal and average productivity of labor
fell and there were more mouths to feed,
mass hunger and starvation would result.
Malthus was wrong (although he was right
about the diminishing marginal returns to
labor).
Over the past century, technological
improvements have dramatically altered
food production in most countries
(including developing countries, such as
India). As a result, the average product of
labor and total food output have
increased.
Hunger remains a severe problem in some
areas, in part because of the low
productivity of labor there.
EXAMPLE 6.2 MALTHUS AND THE FOOD CRISIS
TABLE 6.2 INDEX OF WORLD FOOD PRODUCTION PER CAPITA
YEAR INDEX
1948-52 100
1961 115
1965 119
1970 124
1975 125
1980 127
1985 134
1990 135
1995 135
2000 144
2005 151
2009 155
Once upon a time, there was Malthus… W4-47
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Cereal yields have increased. The average world price of food increased
temporarily in the early 1970s but has declined since.
EXAMPLE 6.2 MALTHUS AND THE FOOD CRISIS
CEREAL YIELDS AND THE WORLD PRICE OF FOOD
Figure 6.4
… and he was wrong! W4-48
W4-49
1d. LR production: two variable inputs
• Firm uses two inputs: capital K and labour L to produce single
output q.
• The production technology is described by the production
function q = f(K,L) . It shows the maximum possible output q
that can be produced with a given amount of inputs (K and L) .
• The marginal product of labour shows an increase in output due
to one unit increase in labour holding capital fixed.
• The marginal product of capital shows an increase in output
due to one unit increase in capital holding labour fixed.
• Most production technologies exhibit diminishing marginal products
( , ) ( , )
K
L L L L
q f K L q f K LMP
K K K K= =
∆ ∆ ∂ ∂
= = = =
∆ ∆ ∂ ∂
( , ) ( , )
L
K K K K
q f K L q f K LMP
L L L L= =
∆ ∆ ∂ ∂
= = = =
∆ ∆ ∂ ∂
W4-50
for production function q = f(K,L) = K3L4
= = (,) = 324
= = (,) = 433
W4-51
The isoquant
L
K
20010050
20
45
100
q = 500
isoquant
We can represent the production
technology by using isoquants.
An isoquant is the set of all
possible combinations of inputs that
are just sufficient to produce a
given amount of output:
f(K,L) = q
W4-52
The isoquant map
L
K
20010050
20
45
100
500
An isoquant is the set of all
possible combinations of
inputs that are just
sufficient to produce a
given amount of output:
f(K,L) = q
Just like indifference curves for consumer!
300
1205
W4-53
The slope of an isoquant is MRTS
= the ratio of marginal products
L
K
ΔL (negative)
ΔK
(positive) MRTS = (MPL / MPK)
diminishing MRTS if convex isoquants
The marginal rate of technical substitution
(MRTS) measures the rate at which one input can be
substituted for another without changing the amount of
output produced. It is equal to minus the slope of the
isoquant.
q = 500
isoquant
Δq = MPK ΔK + MPL ΔL = 0
Slope = ΔK/ ΔL = - MPL / MPK
Slope is negative, MRTS is positive
54 of 30Copyright © 2013 Pearson Education, Inc. • Microeconomics • Pindyck/Rubinfeld, 8e.
MARGINAL RATE OF
TECHNICAL SUBSTITUTION
Figure 6.6
Like indifference curves,
isoquants are downward
sloping and convex. The
slope of the isoquant at
any point measures the
marginal rate of technical
substitution—the ability of
the firm to replace capital
with labor while
maintaining the same level
of output.
On isoquant q2, the MRTS
falls from 2 to 1 to 2/3 to
1/3.
W4-54
LK
isoquant
MRTS = 1
MRTS = 3
MRTS = 0.5
MRTS is equal to the negative of the slope of an isoquant
W4-55
LK
isoquant q = 1
MRTS = 1
MRTS = 2/0.5=4
MRTS = 0.2/5=0.04
for production function q = KL:
MPL = K, MPK = L, MRTSLK = K/L
W4-56
0.5 5
2
1
1
0.2
W4-57
Special production function:
inputs are perfect substitutes
L
K
10050
70
100
 Isoquants are straight
lines
 the rate at which capital
and labour can be
substituted for each other
to produce the same
output is the same no
matter what level of
inputs is being used
 MRTS is constant
 Example: q = 5K + 3L
Just like goods that are perfect substitutes for consumer
W4-58
Special production function:
fixed-proportions prod. function
L
K
27
45
 Isoquants are L-shaped
 Labour and capital need to
be used in exact
proportions – adding more
capital only or more labour
only does not increase
output
 MRTS is 0 on horizontal
parts and infinite on
vertical part
 Example: q = min {3K, 5L}
Just like goods that are perfect complements for consumer
3
5
W4-59
Properties of the production function
q=f(K,L) in the long run: Returns to scale
In the long run all factors can be varied
Returns to scale:
what happens if we increase all inputs by factor t (t > 1)?
For example, double or triple inputs?
compare to MP (increase one factor holding the others fixed)
 constant returns to scale: f(tK, tL) = tf(K, L)
replication
 increasing returns to scale: f(tK, tL) > tf(K, L)
benefits from specialization
 decreasing returns to scale: f(tK, tL) < tf(K, L)
replication is not possible
W4-60
q = 1
10 30
q = 2
q = 3
20
8
24
16
CRS – constant return to scale
K
L
f(tK, tL) = tf(K, L), t >1
replication
Double inputs =>
double output
Isoquants are
evenly spaced
What about
perfect substitutes
technology
q = 5K + 3L?
W4-61
q = 1
10 15
q = 2
q = 3
17.5
8
14
12
IRS – increasing return to scale
K
L
f(tK, tL) > tf(K, L), t >1
benefits from
specialization
Double inputs =>
more than double output
Isoquants move
closer together as
output increases
What about
production function
q = KL?
W4-62
q = 1
10 30
q = 2
20
8
24
16
DRS – decreasing return to scale
K
L
f(tK, tL) < tf(K, L), t >1
replication is not possible
Double inputs =>
less than double output
Isoquants move
further apart as
output increases
q = 3
What about
production function
= + ?
W4-63
q = 2
10 16 30
q = 4
q = 6
20
8
24
16
varying return to scale
K
L
First IRS, then DRS:
q = 5
from q=2 to q=4:
inputs increased by
60%, output
doubled => IRS
from q=4 to q=5:
inputs increased by
25%, output by
25% => CRS
from q=5 to q=6:
inputs increased by
50%, output by 20%
=> DRS
W4-64
If your short run plans are
always different from your
long run plan, how could you
achieve your long run goals?