170902 entrepreneurial economics1

Entrepreneurial Economics
A supplemental lecture on BMA5001
Organized by NUS MBA Entrepreneurship Club
2nd September, 2017
1

About author
Ryosuke ISHII (RYO)
• MIT Microeconomics graded 93%
(on edX, 3 months online course)

Agenda / Topics covered
- How to understand Elasticity
- Why on earth the S/D curves shift by taxation
- Welfare and Dead Weight Loss.
- The secret relation of MRS(Marginal Rate of Substitute)
and indifference curve

Quick questions
- Do you like mathematics?
- How about calculus (especially differential)
- if you are not good at calculus, might [advanced] section
is difficult. But this is not today’s scope.
- I have one-day long calculus entrance course as well

Elasticity
See also; Lecture notes 2 Part A

Elasticity is Sensitivity.
Price Elasticity means how sensitive to price they are?
I change the price Market reacts.
Elasticity

Elasticity
So, the dividend(denominator) should be Price
𝑒 =
𝑄𝑢𝑎𝑛𝑡𝑖𝑡𝑦 𝐶ℎ𝑎𝑛𝑔𝑒
𝑃𝑟𝑖𝑐𝑒 𝐶ℎ𝑎𝑛𝑔𝑒

Elasticity
𝑒 =
𝑄𝑢𝑎𝑛𝑡𝑖𝑡𝑦 𝐶ℎ𝑎𝑛𝑔𝑒
𝑃𝑟𝑖𝑐𝑒 𝐶ℎ𝑎𝑛𝑔𝑒
𝑃
𝑄
𝑃
𝑄
Larger 𝑒 means
Very sensitive
Smaller 𝑒 means
Little sensitive

ElasticityActually, it’s not just change, it’s % of Change.
𝑒 =
% 𝑄𝑢𝑎𝑛𝑡𝑖𝑡𝑦 𝐶ℎ𝑎𝑛𝑔𝑒
% 𝑃𝑟𝑖𝑐𝑒 𝐶ℎ𝑎𝑛𝑔𝑒
, but how to measure “% of Change”?
Mesuring 1: PointElasticity
% 𝑄𝑢𝑎𝑛𝑡𝑖𝑡𝑦 𝐶ℎ𝑎𝑛𝑔𝑒 =
Δ𝑄
𝑄
= |
𝑄 𝑎𝑓𝑡𝑒𝑟 − 𝑄
𝑄
|
% 𝑃𝑟𝑖𝑐𝑒 𝐶ℎ𝑎𝑛𝑔𝑒 =
Δ𝑃
𝑃
= |
𝑃𝑎𝑓𝑡𝑒𝑟 − 𝑃
𝑃
|
So,
𝑒 =
=
(
Δ𝑄
𝑄
)
(
Δ𝑃
𝑃
)
= |
Δ𝑄
Δ𝑃
𝑃
𝑄
|
𝑃
𝑄
𝑃 = 100
𝑃𝑎𝑓𝑡𝑒𝑟 = 80
Δ𝑃 = −20
𝑄 = 100 𝑄 𝑎𝑓𝑡𝑒𝑟 = 400
Δ𝑄 = 300
𝐿𝑒𝑡′ 𝑠 𝑐𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑒 𝑒
←Elasticity of this point

Elasticity
𝑃
𝑄
𝑃 = 100
Δ𝑃 = −20
𝑄 = 100 𝑄 𝑎𝑓𝑡𝑒𝑟 = 400
Δ𝑄 = 300
Actually, its not just change, its % of Change.
𝑒 =
Mesuring 1: Point Elasticity
Δ𝑄
𝑄
= |
𝑄
| =
300
100
Δ𝑃
𝑃
= |
𝑃
| = |
−20
100
|
So,
𝑒 =
= |
(3)
(
−1
5
)
| = 15 ≥ 1
(it can be done because the Curve is Linear Function)

Elasticity
𝑃
𝑄
𝑃 = 100
Δ𝑃 = −20
𝑄 = 100 𝑄 𝑎𝑓𝑡𝑒𝑟 = 400
Δ𝑄 = 300
𝑒 =
, how to measure “% of Change”?
Mesuring 1: Point Elasticity [advanced]
Or, use 𝑒 =
d𝑄
d𝑃
𝑃
𝑄
(this is point elasticity, so make Δ ⇒ 𝑑)
First, make an equation Q = 𝑓(𝑃) form.
So, Q = −15𝑃 + 1600
d𝑄
d𝑃
= −15, 𝑃 = 100, 𝑄 = 100
|𝑒| =
d𝑄
d𝑃
𝑃
𝑄
= −15 = 15 > 1

Elasticity
𝑒 =
, how to measure “% of Change”?
Mesuring 2: Arc Elasticity
If the price and value change from A to B.
We would like to use average as dividend of % change.
Δ𝑄
𝑄
=
𝐴𝑣𝑒𝑟𝑎𝑔𝑒(𝑄)
Δ𝑃
𝑃
=
𝐴𝑣𝑒𝑟𝑎𝑔𝑒(𝑃)
So,
𝑒 =
=
(
𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑄
)
(
)
𝑃
𝑄
𝑃 = 100
Δ𝑃 = −20
𝑄 = 100 𝑄 𝑎𝑓𝑡𝑒𝑟 = 400
Δ𝑄 = 300
𝑎𝑣𝑒𝑟𝑎𝑔𝑒(𝑄)
𝑎𝑣𝑒𝑟𝑎𝑔𝑒(𝑃)
𝐿𝑒𝑡′ 𝑠 𝑐𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑒 𝑒!
𝐴
𝐵

Elasticity
Actually, its not just change, its % of Change.
𝑒 =
Mesuring 2: Arc Elasticity
Δ𝑄
𝑄
=
𝐴𝑣𝑒𝑟𝑎𝑔𝑒(𝑄)
=
300
250
Δ𝑃
𝑃
=
=
−20
90
So,
𝑒 =
=
(
𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑄
)
(
)
= |
1.2 ∗ 9
−2
|
= 5.4
𝑃
𝑄
𝑃 = 100
Δ𝑃 = −20
𝑄 = 100 𝑄 𝑎𝑓𝑡𝑒𝑟 = 400
Δ𝑄 = 300
𝑎𝑣𝑒𝑟𝑎𝑔𝑒(𝑃)
𝑎𝑣𝑒𝑟𝑎𝑔𝑒(𝑄)

Elasticity
Why “%” important? Think about the Case:
𝑃
𝑄
𝑃 = 100
Δ𝑃 = −20
𝑄 = 100
𝑄 𝑎𝑓𝑡𝑒𝑟 = 125
(𝑄, 𝑃) = 100,100
(𝑄 𝑎𝑓𝑡𝑒𝑟, 𝑃𝑎𝑓𝑡𝑒𝑟) = 125,80
(1)What is arc 𝑒 =
?
(2)What is the Revenue before and
after?

Elasticity
𝑃
𝑄
𝑃 = 100
Δ𝑃 = −20
𝑄 = 100
(𝑄, 𝑃) = 100,100
?
𝑒 =
−20/90
25/112.5
= | − 1|
after?
𝑅𝑒𝑣 𝑏𝑒𝑓𝑜𝑟𝑒 = 𝑃𝑄 = 10,000
𝑅𝑒𝑣 𝑎𝑓𝑡𝑒𝑟 = 𝑃𝑎𝑓𝑡𝑒𝑟 𝑄 𝑎𝑓𝑡𝑒𝑟 = 10,000
So, if we define 𝑒 such that,
𝑒 = 1 means Revenue doesn’t change.

Elasticity
𝑃
𝑄
𝑃 = 100
Δ𝑃 = −20
𝑄 = 100
(𝑄, 𝑃) = 100,100
?
𝑒 =
−20/90
25/112.5
= | − 1|
after?
So, if we define 𝑒 such that,
𝑒 = 1 means Revenue doesn’t change.
𝑃𝑄

Elasticity
𝑃
𝑄
𝑃 = 100
Δ𝑃 = −20
𝑄 = 100
(𝑄, 𝑃) = 100,100
(1)
If we think 𝑒 = 5.4 ≫ 1 case.
after?

Elasticity
𝑃
𝑄
𝑃 = 100
Δ𝑃 = −20
𝑄 = 100
(𝑄, 𝑃) = 100,100
(1)
If we think 𝑒 = 5.4 ≫ 1 case.
after?
So, if e > 1,
- Price down gain Revenue
- Price Up lose Revenue

Elasticity
Summary and special case
𝑒 > 1
𝑒 = 1
𝑒 < 1
𝑒 = ∞
𝑒 = 0
If you change price,
Nothing happens.
So, price sensitivity = 0
If you change price
Bit higher than before
Everyone run away.
Bit lower than before
Everyone buy.
So, Infinitely sensitive.
Value Price down Price up
|𝑒| < 1 R decrease↓ R increase↑
|𝑒| = 1 R same R same
|𝑒| > 1 R increase↑ R decrease↓

Elasticity
FYI[advanced]
𝑒 can be changed in Linear curve.
𝑃
𝑄
𝑒 =
d𝑄
d𝑃
𝑃
𝑄
When we take a look at the equation:
This Part is constant.
Because this is Linear function.
So, if 𝑄 ⇒ 𝐿𝑎𝑟𝑔𝑒𝑟 and 𝑃 ⇒ 𝑠𝑚𝑎𝑙𝑙𝑒𝑟
then, 𝑒 ⇒ 𝑠𝑚𝑎𝑙𝑙𝑒𝑟
|𝑒 𝐷| = 1
|𝑒 𝐷| < 1
|𝑒 𝐷| > 1

Welfare can be calculate:
𝑃
𝑄
Consumer Surplus(CS) +
Producer Surplus(PS)
CS
PS
But Why the CS / PS is the
Area on the graph?

𝑃
𝑄
CS
Why the CS can be calculated
by the Area on the graph?
To make the things easy:
- Imagine this market has only 4 people.

𝑃
𝑄
Imagine this “Apple” market has only 4 people(buyer/consumer).
And each of them have a budget to get an Apple.
So, the Demand Curve will be:
This budget means: maximum how much willing to pay to get an Apple.
$100
80
50
40
Name Budget
Akira $100
Chieko $80
Rocky $50
Tomo $40
1 2 3 4

𝑃
𝑄
If the price of an apple become $60 what will happen?
Name Budget
Akira $100
Chieko $80
Rocky $50
Tomo $40
$100
80
50
40
60
1 2 3 4

𝑃
𝑄
If the price of an apple become $60 what will happen?
2 people can buy an apple each.
And the consumer surplus each is below:
Because the Budget means maximum how much willing to pay to get an Apple.
Name Budget
Akira $100
Chieko $80
Rocky $50
Tomo $40
$100
80
50
40
60
1 2 3 4
$40
$20

𝑃
𝑄
CS
This is because the CS can be calculated
by the Area on the graph.

Producer Surplus(PS) can be calculated same way.
𝑃
𝑄
PS

𝑃
𝑄
Imagine this Apple market has 4 sellers.
The sellers differ their cost structure so,
COST = MINIMUM How much they want to charge is below:
That means if the price is equal to the Cost, it means they can get No profit.
$100
80
50
40
Name Cost
Neha $40
Federico $50
Joe $80
David $100
1 2 3 4

𝑃
𝑄
If the price set as $60,
What will happen?
$100
80
50
40
Name Cost
Neha $40
Federico $50
Joe $80
David $100
1 2 3 4
60

𝑃
𝑄
Neha got $20 profit while Federico got $10
So the profit = Producer Surplus is $30
$100
80
50
40
Name Cost
Neha $40
Federico $50
Joe $80
David $100
1 2 3 4
60
$20 $10

𝑃
𝑄
Neha got $20 profit while Federico got $10
So the profit = Producer Surplus is $30
$100
80
50
40
1 2 3 4
60
$20 $10
Revenue
60
20
COST− = 𝑝𝑟𝑜𝑓𝑖𝑡

So, Welfare can be calculate:
𝑃
𝑄
Consumer Surplus(CS) +
Producer Surplus(PS)
CS
PS

How tax change D/S curves
and the Dead Weight Loss
See also; Lecture notes 2 Part B

Government can decide from which side (Demand/Supply)
The Government collect tax.
The curve affects depends of the decision.
𝑃
𝑄
Supply Curve
Demand Curve
Let’s us think about
Government decides that
They collect tax from
Buyer(demand side)
And the tax is $10 each goods.

Demand Side Taxation: 3 steps thinking:
𝑃
𝑄
Supply Curve
Demand Curve Before
1.Demand Curve should be affected.
2.Demand must be lower than
before, because they should pay
+$10 each than market price.
3.So, taxation makes Demand curve
shift inward.
Demand Curve After
We could understand if we take a look at
𝑄 𝑏𝑒𝑓𝑜𝑟𝑒, 𝑃𝑏𝑒𝑓𝑜𝑟𝑒 = (0,100)
Should become
𝑄 𝑎𝑓𝑡𝑒𝑟, 𝑃𝑎𝑓𝑡𝑒𝑟 = (0,90)
Because 𝑃𝑎𝑓𝑡𝑒𝑟 + 𝑡𝑎𝑥 = 𝑃𝑏𝑒𝑓𝑜𝑟𝑒
100
90

Who, how much, really bear?
𝑃
𝑄
Supply Curve
Demand Curve Before
After Taxation, we got new
Equilibrium (𝑃𝑎𝑓𝑡𝑒𝑟, 𝑄 𝑎𝑓𝑡𝑒𝑟)
But, what consumers really pay is:
𝑃𝑎𝑓𝑡𝑒𝑟 + 𝑡𝑎𝑥 = 𝑃𝑅𝐸𝐴𝐿
𝑃𝑅𝐸𝐴𝐿 − 𝑃𝑏𝑒𝑓𝑜𝑟𝑒 = 𝑡𝑎𝑥 𝑐𝑜𝑛𝑠𝑢𝑚𝑒𝑟
𝑃𝑏𝑒𝑓𝑜𝑟𝑒 − 𝑃𝑎𝑓𝑡𝑒𝑟 = 𝑡𝑎𝑥 𝑝𝑟𝑜𝑑𝑢𝑐𝑒𝑟
𝑡𝑎𝑥 𝑐𝑜𝑛𝑠𝑢𝑚𝑒𝑟 + 𝑡𝑎𝑥 𝑝𝑟𝑜𝑑𝑢𝑐𝑒𝑟 = 𝑡𝑎𝑥
Demand Curve After
𝑃𝑏𝑒𝑓𝑜𝑟𝑒
𝑃𝑎𝑓𝑡𝑒𝑟
𝑃𝑅𝐸𝐴𝐿

Let’s calculate for this example!
𝑃
𝑄
𝑃𝑆 = 5𝑄
Demand Curve Before
Demand curve before tax:
𝑃 𝐷 𝑏 = 120 − 3𝑄
Supply Curve before tax:
𝑃𝑆 = 5𝑄
𝒕𝒂𝒙 = $𝟖 for Consumers
What is:
𝑃 𝐷 𝑏 = 120 − 3𝑄

𝑃
𝑄
𝑃𝑆 = 5𝑄
Demand Curve Before
Calculate before Equilibrium,
𝑃𝑏𝑒𝑓𝑜𝑟𝑒 = 75, 𝑄 𝑏𝑒𝑓𝑜𝑟𝑒 = 15
The new demand curve will be
𝑃 𝐷 𝑎
= 112 − 3𝑄
𝑃𝑎𝑓𝑡𝑒𝑟 = 70, 𝑄 𝑎𝑓𝑡𝑒𝑟 = 14
But, what consumers really pay is:
𝑃𝑎𝑓𝑡𝑒𝑟 + 𝑡𝑎𝑥 = 𝑃𝑅𝐸𝐴𝐿 = 78
𝑃𝑅𝐸𝐴𝐿 − 𝑃𝑏𝑒𝑓𝑜𝑟𝑒 = 𝑡𝑎𝑥 𝑐𝑜𝑛𝑠𝑢𝑚𝑒𝑟 = 3
𝑃𝑏𝑒𝑓𝑜𝑟𝑒 − 𝑃𝑎𝑓𝑡𝑒𝑟 = 𝑡𝑎𝑥 𝑝𝑟𝑜𝑑𝑢𝑐𝑒𝑟 = 5
𝑡𝑎𝑥 𝑐𝑜𝑛𝑠𝑢𝑚𝑒𝑟 + 𝑡𝑎𝑥 𝑝𝑟𝑜𝑑𝑢𝑐𝑒𝑟 = 𝑡𝑎𝑥Demand Curve After
𝑃 𝐷 𝑏 = 120 − 3𝑄

Next: supply side taxation:
𝑃
𝑄
Supply Curve
Demand Curve
Let’s us think about
Government decides that
They collect tax from
Seller(Supply side)

Supply Side Taxation: 3 steps thinking:
𝑃
𝑄
Supply Curve
Demand Curve
1.Supply Curve should be affected.
2.The price must be higher than
before, because sellers should pay
+$10 each after the deal made.
3.So, taxation makes supply curve
shift upward.
We could understand if we take a look at
𝑄 𝑏𝑒𝑓𝑜𝑟𝑒, 𝑃𝑏𝑒𝑓𝑜𝑟𝑒 = (0,10)
Should become
𝑄 𝑎𝑓𝑡𝑒𝑟, 𝑃𝑎𝑓𝑡𝑒𝑟 = (0,20)
Because 𝑃𝑎𝑓𝑡𝑒𝑟 − 𝑡𝑎𝑥 = 𝑃𝑏𝑒𝑓𝑜𝑟𝑒

𝑃
𝑄
Supply Curve
Demand Curve
After Taxation, we got new
Equilibrium (𝑃𝑎𝑓𝑡𝑒𝑟, 𝑄 𝑎𝑓𝑡𝑒𝑟)
𝑃𝑎𝑓𝑡𝑒𝑟 is what consumers pay.
But, what sellers really get:
𝑃𝑎𝑓𝑡𝑒𝑟 − 𝑡𝑎𝑥 = 𝑃𝑅𝐸𝐴𝐿
𝑃𝑎𝑓𝑡𝑒𝑟−𝑃𝑏𝑒𝑓𝑜𝑟𝑒= 𝑡𝑎𝑥 𝑐𝑜𝑛𝑠𝑢𝑚𝑒𝑟
𝑃𝑏𝑒𝑓𝑜𝑟𝑒 − 𝑃𝑅𝐸𝐴𝐿 = 𝑡𝑎𝑥 𝑝𝑟𝑜𝑑𝑢𝑐𝑒𝑟

𝑃
𝑄
𝑃𝑆 = 5𝑄
Demand Curve
Demand curve before tax:
𝑃 𝐷 𝑏 = 120 − 3𝑄
Supply Curve before tax:
𝑃𝑆 = 5𝑄
𝑡𝑎𝑥 = $8 for Sellers.
What is:
𝑃 𝐷 𝑏 = 120 − 3𝑄

𝑃
𝑄
Supply Curve
Demand Curve
𝑃𝑆 𝐵
= 5𝑄
𝑃 𝐷 = 120 − 3𝑄
𝑃𝑆 𝐴
= 5𝑄 + 8
𝑃𝑏𝑒𝑓𝑜𝑟𝑒 = 75, 𝑄 𝑏𝑒𝑓𝑜𝑟𝑒 = 15
The new supply curve will be
𝑃𝑆 𝐴
= 5𝑄 + 8
𝑃𝑎𝑓𝑡𝑒𝑟 = 78, 𝑄 𝑎𝑓𝑡𝑒𝑟 = 14
But, what sellers really get is:
𝑃𝑎𝑓𝑡𝑒𝑟 − 𝑡𝑎𝑥 = 𝑃𝑅𝐸𝐴𝐿 = 70
𝑃𝑎𝑓𝑡𝑒𝑟−𝑃𝑏𝑒𝑓𝑜𝑟𝑒= 𝑡𝑎𝑥 𝑐𝑜𝑛𝑠𝑢𝑚𝑒𝑟 = 3
𝑃𝑏𝑒𝑓𝑜𝑟𝑒 − 𝑃𝑅𝐸𝐴𝐿 = 𝑡𝑎𝑥 𝑝𝑟𝑜𝑑𝑢𝑐𝑒𝑟 = 5

Let’s Calculate CS and PS before tax
𝑃
𝑄
Supply Curve
Demand Curve
𝑃𝑆 𝐵
= 5𝑄
𝑃 𝐷 = 120 − 3𝑄
CS
PS

Let’s Calculate CS and PS before tax
𝑃
𝑄
Supply Curve
Demand Curve
𝑃𝑆 𝐵
= 5𝑄
𝑃 𝐷 = 120 − 3𝑄
CS
PS
𝑄 𝑏𝑒𝑓𝑜𝑟𝑒 = 15 , 𝑃𝑏𝑒𝑓𝑜𝑟𝑒 = 75
𝑄 𝑏𝑒𝑓𝑜𝑟𝑒 = 15
𝑃𝑏𝑒𝑓𝑜𝑟𝑒 = 75
120
0
𝐶𝑆 =
(120 − 75) × 15
2
= 337.5
𝑃𝑆 =
(75 − 0) × 15
2
= 562.5

Let’s Calculate CS and PS after tax $8 (for producer)
𝑃
𝑄
Supply Curve
Demand Curve
𝑃𝑆 𝐵
= 5𝑄
𝑃 𝐷 = 120 − 3𝑄
𝑄 𝑏𝑒𝑓𝑜𝑟𝑒
= 15
120
0
𝑃𝑆 𝐴
= 5𝑄 + 8
𝑃𝑅𝐸𝐴𝐿 = 70
𝑄 𝑎𝑓𝑡𝑒𝑟
= 14

𝑃
𝑄
Supply Curve
Demand Curve
𝑃𝑆 𝐵
= 5𝑄
𝑃 𝐷 = 120 − 3𝑄
120
0
𝑃𝑆 𝐴
= 5𝑄 + 8
CS
PS
The Welfare should be calculated based on
- What consumer really pay
- What producer really get
So, for consumers they really pay
for producers they really get
Yes, taxation makes price difference
Between consumers and producers.𝑄 𝑏𝑒𝑓𝑜𝑟𝑒
= 15
= 14

𝑃
𝑄
Supply Curve
Demand Curve
𝑃𝑆 𝐵
= 5𝑄
𝑃 𝐷 = 120 − 3𝑄
120
0
𝑃𝑆 𝐴
= 5𝑄 + 8
𝐶𝑆 𝑎𝑓𝑡𝑒𝑟
𝑃𝑆 𝑎𝑓𝑡𝑒𝑟
𝐶𝑆 𝑎𝑓𝑡𝑒𝑟 =
(120 − 78) × 14
2
= 294
𝑃𝑆 𝑎𝑓𝑡𝑒𝑟 =
(70 − 0) × 14
2
= 490
= 15
= 14

Let’s Calculate Sum of Tax, collected from market.
𝑃
𝑄
Supply Curve
Demand Curve
𝑃𝑆 𝐵
= 5𝑄
𝑃 𝐷 = 120 − 3𝑄
120
0
𝑃𝑆 𝐴
= 5𝑄 + 8
Where is tax and why?
= 15
= 14

Let’s Calculate Sum of Tax, collected from market.
𝑃
𝑄
Supply Curve
Demand Curve
𝑃𝑆 𝐵
= 5𝑄
𝑃 𝐷 = 120 − 3𝑄
120
0
𝑃𝑆 𝐴
= 5𝑄 + 8
consumers really pay
producers really get
The difference is a tax so
𝑃𝑎𝑓𝑡𝑒𝑟 − 𝑃𝑅𝐸𝐴𝐿 = 𝑡𝑎𝑥 each consumption.
And the quantity is 𝑄 𝑎𝑓𝑡𝑒𝑟 = 14.
So
Sum of Tax = 78 − 70 × 14 = 112𝑄 𝑏𝑒𝑓𝑜𝑟𝑒
= 15
= 14

Compare before and after
𝑃
𝑄
Demand Curve
0
𝑄 𝑏𝑒𝑓𝑜𝑟𝑒𝑄 𝑎𝑓𝑡𝑒𝑟
𝑃
𝑄
CS
PS
0
before after

Dead Weight Loss
𝑃
𝑄
Demand Curve
0
𝑄 𝑏𝑒𝑓𝑜𝑟𝑒𝑄 𝑎𝑓𝑡𝑒𝑟
𝑃
𝑄
CS
PS
0
before after
This is
Dead Weight Loss
This is a Social Welfare Loss that caused by tax

Before After Δ = 𝐴𝑓𝑡𝑒𝑟 − 𝐵𝑒𝑓𝑜𝑟𝑒
Consumer
Surplus
-43.5
Producer
Surplus
-72.5
Tax
+112
Social Welfare 900 896
-4
Dead Weight Loss
Summary
𝐶𝑆 = 337.5
𝑃𝑆 = 562.5
𝐶𝑆 𝑎𝑓𝑡𝑒𝑟 = 294
𝑃𝑆 𝑎𝑓𝑡𝑒𝑟 = 490
𝑇𝑎𝑥 = 112

We all are facing trade-offs
- Because fundamental assumption economist have is
“people are facing trade-off”
The management of society’s resources is important
because resources are scarce. Scarcity means that society
has limited resources and therefore cannot produce all the
goods and services people wish to have.
-Nicholas Gregory Mankiw
See also
https://en.wikiquote.org/wiki/Greg_Mankiw#Ch._1._Ten_Principles_of_Economics

Budget constrain.
• You have a budget. Say $96/week.
• You will allocate this money to
maximize your utility.
• Imagine you are living in hell, which has
only 2 goods: Pizza and Movie.
• And you should allocate all the money.
• Pizza = $16, Movie=$8

Budget Constrain (make sure both axis is Q)
- Pizza($16 each) and Movie($8 each)
- Your weekly budget is $96
- Let’s draw a line and equation
𝑀𝑜𝑣𝑖𝑒
𝑃𝑖𝑧𝑧𝑎
𝑄
𝑄
12
6

Budget Constrain (make sure both axis is Q)
- Your weekly budget is $96
𝑄
𝑄
6
12
But this curve is nothing to do
With your Utility.
(imagine, if you hate movie)
16𝑄 𝑝𝑖𝑧𝑧𝑎 + 8𝑄 𝑚𝑜𝑣𝑖𝑒 = $96
Don’t think this equation by looking curve.
Just think 𝑃𝑟𝑖𝑐𝑒 × 𝑄𝑢𝑎𝑛𝑡𝑖𝑡𝑖𝑦 = 𝐵𝑢𝑑𝑔𝑒𝑡, 𝐶𝑜𝑠𝑡

Consumer’s preference and Utility
If you are rational consumer,(Lecture note 3)
• Complete binary ordering
• Between any two bundles of goods, a consumer
can tell whether she prefers one to another or indifferent.
• Reflectivity
• Any bundle is just as good as any other identical bundle.
• Transitivity
• If a consumer prefers bundle 1 to bundle 2 and prefers bundle 2 to
bundle 3, then she must prefer bundle 1 to bundle 3.
• Non-satiation
• Consumers prefer more units of a good than less.

Consumer’s preference and Utility
- Holding a pizza makes you happy
- but it’s non- linear.
- in this case, for example, 𝑈 = 𝑄 𝑃𝑖𝑧𝑧𝑎
𝑝𝑖𝑧𝑧𝑎
𝑄
𝑈𝑡𝑖𝑙𝑖𝑡𝑦
12
2
4
5
5

Marginal Utility
When we have 0 Pizza and get +1 pizza,
Our utility increase 0 to 1
If we already have 4 pizza and get +1.
How much our utility change?
𝑄
12
2
4
5
5

Marginal Utility
If we already have 4 pizza and get 1.
How much our utility change?
𝑈4 = 4 = 2
𝑈5 = 5
𝑈5 − 𝑈4 = 5 − 2 = 0.236. .
While the 1st pizza increase U=1
If we imagine real situation,
The utility change of 5th pizza
Might nearly zero.𝑝𝑖𝑧𝑧𝑎
𝑄
12
2
4
5
5

Marginal Utility [advance]
is a the additional satisfaction a consumer gains from
consuming one more unit of a good or service.*
𝑀𝑈 𝑝𝑖𝑧𝑧𝑎 =
𝜕𝑈
𝜕𝑄 𝑝𝑖𝑧𝑧𝑎
=
1
2 𝑄 𝑝𝑖𝑧𝑧𝑎
*http://www.investopedia.com/terms/m/marginalutility.asp
𝑄
12
2
4
5
5

Indifference curve
Imagine your utility function, not only Pizza, but a combination
Of Pizza and Movie 𝑈 = 𝑄 𝑀 𝑄 𝑃.
And indifference means 𝑈 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡. 𝑠𝑎𝑦, 𝑈 = 2
𝑄
𝑄
12
6

Indifference curve
And indifference means 𝑈 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡. 𝑠𝑎𝑦, 𝑈 = 2 𝑎𝑛𝑑 3
𝑄
𝑄
12
4
2
2 4 93
𝑈 = 𝑄 𝑀 𝑄 𝑃 = 2

Indifference curve
And indifference means 𝑈 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡. 𝑠𝑎𝑦, 𝑈 = 2 𝑎𝑛𝑑 3
𝑄
𝑄
12
4
2
2 4 93
𝑈 = 𝑄 𝑀 𝑄 𝑃 = 3

MRS(Marginal Rates of Substitute) on Indifference curve
Think about 𝑈 = 2 = 𝑄 𝑀 𝑄 𝑃.
𝑄
𝑄
12
4
2
2 4 93
𝑈 = 𝑄 𝑀 𝑄 𝑃 = 2
𝐴
𝐵
𝐶
When you are point A
You have Movie, Pizza = (1,4)
And this is indifferent with point B
Which is Movie, Pizza = (2,2)
That means you can give up
2 pizza to get 1 more movie.
In mathematical form,
MRSPointA =
Δ𝑌
Δ𝑋
=
2−4
2−1
= −2

MRS(Marginal Rates of Substitute) and Marginal Utility
[advance]
𝑄
𝑄
12
4
2
2 4 93
𝑈 = 𝑄 𝑀 𝑄 𝑃 = 2
𝐴
𝐵
𝐶
𝑀𝑅𝑆 =
𝛥𝑌
𝛥𝑋
=
𝑀𝑈 𝑋
𝑀𝑈 𝑌
Because MU is a the additional satisfaction a consumer
gains from consuming one more unit of a good or service.
If 𝑀𝑈 𝑃𝐼𝑍𝑍𝐴 = 1, which means if you got 1 more,
pizza your utility change +1.
So, if you got 1 Pizza, get +𝑀𝑈 𝑃𝐼𝑍𝑍𝐴 as an additional Utility
And, you got 1 Movie, get +𝑀𝑈 𝑀𝑜𝑣𝑖𝑒 as an additional Utility.
How to determine MRS from MU?
𝑄
12
2
4
5
5

MRS(Marginal Rates of Substitute) and Marginal Utility
[advance] So, if you got 1 Pizza, get +𝑀𝑈 𝑃𝐼𝑍𝑍𝐴 = 1
And, at a same point,
you got 1 Movie, get +𝑀𝑈 𝑀𝑜𝑣𝑖𝑒 = 2
They can get rid of 2 pizza and get 1 movie.
This means your Trade-ratio Pizza and Movie is
+1 Movie is 2 times better off than +1 Pizza.
So, 𝑀𝑅𝑆 =
𝛥𝑌
𝛥𝑋
=
𝑀𝑈 𝑋
𝑀𝑈 𝑌
𝑄
𝑄
12
4
2
2 4 93
𝑈 = 𝑄 𝑀 𝑄 𝑃 = 2
𝐴
𝐵
𝐶
𝑄
12
2
4
5
5

Budget constrain and MRS
Return back to Indifference curve and
Budget constrain.
When the tangent of budget constrain
Equals to MRS, the utility within
the budget constrain become maximum.
𝑄
𝑄
12
4
2
2 4 93
𝑈 = 𝑄 𝑀 𝑄 𝑃 = 2

Budget constrain and MRS
1. How to calculate tangent of Budget constrain?
𝑄 𝑚𝑜𝑣𝑖𝑒
𝑄 𝑝𝑖𝑧𝑧𝑎
12
4
2
2 4 93
6
According to the graph,
Y axis = Qpizza and X axis = Qmovie
So, let’s make the equation
𝑌 = 𝑎𝑋 + 𝑏 format that is
Qpizza = 𝑎Qmovie + 𝑏 format.
16Qpizza + 8Qmovie = $96 ↔
Qpizza = −
1
2
Qmovie + $6
And it is known −
P 𝑀𝑜𝑣𝑖𝑒
Ppizza
= −
P 𝑋
PY

Budget constrain and MRS[advance]
𝑄
𝑄
12
4
2
2 4 93
𝑈 = 𝑄 𝑀 𝑄 𝑃
2. How to calculate MRS
𝑀𝑅𝑆 = −
𝛥𝑌
𝛥𝑋
= −
𝑀𝑈 𝑋
𝑀𝑈 𝑌
= −
𝜕𝑈
𝜕𝑄 𝑋
𝜕𝑈
𝜕𝑄 𝑌
= −
(
𝜕𝑈
𝜕𝑄 𝑀𝑂𝑉𝐼𝐸
)
(
𝜕𝑈
𝜕𝑄 𝑃𝑖𝑧𝑧𝑎
)
If we calculate it…

Budget constrain and MRS[advance]
𝑄
𝑄
12
4
2
2 4 93
𝑀𝑅𝑆 = −
𝛥𝑌
𝛥𝑋
= −
𝑀𝑈 𝑋
𝑀𝑈 𝑌
= −
𝜕𝑈
𝜕𝑄 𝑋
𝜕𝑈
𝜕𝑄 𝑌
= −
(
𝜕𝑈
𝜕𝑄 𝑀𝑂𝑉𝐼𝐸
)
(
𝜕𝑈
𝜕𝑄 𝑃𝑖𝑧𝑧𝑎
)
𝑎𝑛𝑑
𝜕𝑈
𝜕𝑄 𝑃
=
𝑄 𝑀
2 𝑄 𝑀 𝑄 𝑃
,
𝜕𝑈
𝜕𝑄 𝑀
=
𝑄 𝑃
2 𝑄 𝑀 𝑄 𝑃
So, 𝑀𝑅𝑆 = −
𝑄 𝑃
𝑄 𝑀

So, where is the optimal? (Max U under the badget)
𝑄
𝑄
12
4
2
2 4 93
𝑀𝑅𝑆 = tangent
So, 𝑀𝑅𝑆 = −
𝑄 𝑃
𝑄 𝑀
, 𝑎𝑛𝑑 𝑡𝑎𝑛𝑔𝑒𝑛𝑡 = −
P 𝑀𝑜𝑣𝑖𝑒
Ppizza
= −
P 𝑋
PY
therefore, −
𝑄 𝑃
𝑄 𝑀
= −
P 𝑀
𝑃 𝑃
= −
1
2
↔ 2𝑄 𝑃 = 𝑄 𝑀
Using above, the equation (𝑎) should be
16𝑄 𝑝𝑖𝑧𝑧𝑎 + 16𝑄 𝑝𝑖𝑧𝑧𝑎 = $96
𝑆𝑜𝑙𝑣𝑒 𝑖𝑡 𝑎𝑛𝑑 𝑄 𝑝 = 3, 𝑄 𝑀 = 6
𝑈 = 𝑄 𝑀 𝑄 𝑃 = 18

http://www.wolframalpha.com/input/?i=3Dplot+Z%3Dsqrt(XY),+X%3D0+to+10,+Y%3D0+to+10
Indifference curve in the 3D format
[advance]
𝑈 = 𝑄 𝑀 𝑄 𝑃 = 4

Income effect and
Substitution effect

Let us think in Qualitative first.
You like Cake very much.
But cake cost you $5 each and
Sweet pastry cost you $2 each.
So, everyday you eat
(morning) 1 pastry $2
(lunch) 2 pastry $4
(dinner) 1 cake $5
In total, you spend $11 every day.
Cakes
$5
Pastry
$2

One day, you thought you are the
Luckiest girl in the world!
Cakes are sold just $1 today!
So, decide
(morning) 1 cake $1
(lunch) 2 cake $2
(dinner) 1 cake $1
This is substitution effect.
You like more cake than Pastry.
Cakes
$5
↓
$1
Pastry
$2

In the end of the day,
You calculate.
(morning) 1 cake $1
(lunch) 2 cake $2
(dinner) 1 cake $1
In total just $4 you use.
While everyday spend $11
So, you decide to buy more cake
Before you sleep.
The demand increase.
This is Income Effect.
Cakes
$5
↓
$1
Pastry
$2

Remember Budget constrain
12
4
2
2 4 93
6
- imagine, the Movie become cheaper ($6 each)
1 How your budget constrain change?
2 What is your newequation?
16

12
4
2
2 4 93
6
It become like this. So what?
16

12
4
2
2 4 93
6
It become like this.
This difference is Total Effect.
The demand of Movie increase.
And the demand of Pizza also increase.
Let’s break down in into income/substitution.
16
16𝑄 𝑝𝑖𝑧𝑧𝑎 + 6𝑄 𝑚𝑜𝑣𝑖𝑒 = $96𝐴
𝐵

Move the new Budget constrain to tangent of
Indifference curve.
12
4
2
2 4 93
6
16
We would like to parallel translate this
Red Line, a new budget constrain, to a
Tangent of indifferent curve before.
If we do so, we got point 𝐶on indifferent curve before.
The change point A to 𝐶 implies the effect caused by
“the change of price ratio : from ($16,$8) to ($16, $6)”
𝐴
𝐵
𝐶

Indifference curve.
12
4
2
2 4 93
6
16
This is called 𝑆𝑢𝑏𝑠𝑡𝑖𝑡𝑢𝑡𝑖𝑜𝑛 𝐸𝑓𝑓𝑒𝑐𝑡
Because, the change of movie price cause the
Change of ratio of Pizza and Movie.
And the new tangent on the same indifference curve
as before, represent the effect of change ratio only.

Indifference curve.
12
4
2
2 4 93
6
16
Remember this 𝑆𝑢𝑏𝑠𝑡𝑖𝑡𝑢𝑡𝑖𝑜𝑛 𝐸𝑓𝑓𝑒𝑐𝑡 works negative
for Pizza.
Decreasing the cost of movie means
Pizza became relatively expensive.
So, the effect works negative in general.

12
4
2
2 4 93
6
This is called 𝐼𝑛𝑐𝑜𝑚𝑒 𝐸𝑓𝑓𝑒𝑐𝑡
The change (cheaper) of movie price
Makes you richer (you can buy more goods
by same budget).
This is also change your demand.
16

Summary of Income Effect and substitution effect
12
4
2
2 4 93
6
Substitution
Effect
Income
Effect
Total Effect
Pizza
Pizza became
Relatively
expensive.
So decrease.
Consumers
become Richer
So the amount of
consumption
increase
Depends on
Sub/income
effect.
Movie
(Cheaper)
Movie became
Relatively
cheap.
So increase.
Demand
Increase.

Want to learn more?
• See Entrepreneurial Economics #2!
• https://www.slideshare.net/ryouen/170925-entrepreneurial-
economics2

Reference
NUS MBA BMA5001 Lecture Note 2, 3
Principles of Microeconomics (Mankiw's Principles of Economics)
MITx: 14.100x Microeconomics
https://en.wikiquote.org/wiki/Greg_Mankiw#Ch._1._Ten_Principles_of_Economics

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