170902 entrepreneurial economics1

Entrepreneurial Economics

A supplemental lecture on BMA5001

Organized by NUS MBA Entrepreneurship Club

2nd September, 2017

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] sectionis difficult. But this is not today’s scope.

- I have one-day long calculus entrance course as well

ElasticitySee 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

So, the dividend(denominator) should be Price

𝑒 =𝑄𝑢𝑎𝑛𝑡𝑖𝑡𝑦 𝐶ℎ𝑎𝑛𝑔𝑒

𝑃𝑟𝑖𝑐𝑒 𝐶ℎ𝑎𝑛𝑔𝑒

Elasticity

𝑒 =𝑄𝑢𝑎𝑛𝑡𝑖𝑡𝑦 𝐶ℎ𝑎𝑛𝑔𝑒

𝑃𝑟𝑖𝑐𝑒 𝐶ℎ𝑎𝑛𝑔𝑒

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= |

𝑄𝑎𝑓𝑡𝑒𝑟 − 𝑄

% 𝑃𝑟𝑖𝑐𝑒 𝐶ℎ𝑎𝑛𝑔𝑒 =Δ𝑃

𝑃= |

𝑃𝑎𝑓𝑡𝑒𝑟 − 𝑃

% 𝑃𝑟𝑖𝑐𝑒 𝐶ℎ𝑎𝑛𝑔𝑒=

(Δ𝑄𝑄

(Δ𝑃𝑃

Δ𝑄

Δ𝑃

𝑃 = 100

𝑃𝑎𝑓𝑡𝑒𝑟 = 80

Δ𝑃 = −20

𝑄 = 100 𝑄𝑎𝑓𝑡𝑒𝑟 = 400Δ𝑄 = 300

𝐿𝑒𝑡′𝑠 𝑐𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑒 𝑒

←Elasticity of this point

Elasticity

𝑃 = 100

Δ𝑃 = −20

𝑄 = 100 𝑄𝑎𝑓𝑡𝑒𝑟 = 400Δ𝑄 = 300

Actually, its not just change, its % of Change.

Mesuring 1: Point Elasticity

𝑄= |

𝑄| =

𝑃= |

𝑃| = |

% 𝑃𝑟𝑖𝑐𝑒 𝐶ℎ𝑎𝑛𝑔𝑒= |

(−15

)| = 15 ≥ 1

(it can be done because the Curve is Linear Function)

Elasticity

𝑃 = 100

Δ𝑃 = −20

𝑄 = 100 𝑄𝑎𝑓𝑡𝑒𝑟 = 400Δ𝑄 = 300

% 𝑃𝑟𝑖𝑐𝑒 𝐶ℎ𝑎𝑛𝑔𝑒, how to measure “% of Change”?

Mesuring 1: Point Elasticity [advanced]

Or, use 𝑒 =d𝑄

𝑄(this is point elasticity, so make Δ ⇒ 𝑑)

First, make an equation Q = 𝑓(𝑃) form.So, Q = −15𝑃 + 1600

d𝑃= −15, 𝑃 = 100, 𝑄 = 100

|𝑒| =d𝑄

𝑄= −15 = 15 > 1

Elasticity

% 𝑃𝑟𝑖𝑐𝑒 𝐶ℎ𝑎𝑛𝑔𝑒, how to measure “% of Change”?

Mesuring 2: Arc ElasticityIf the price and value change from A to B.We would like to use average as dividend of % change.

𝐴𝑣𝑒𝑟𝑎𝑔𝑒(𝑄)

𝐴𝑣𝑒𝑟𝑎𝑔𝑒(𝑃)So,

(𝑄𝑎𝑓𝑡𝑒𝑟 − 𝑄

𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑄)

(𝑃𝑎𝑓𝑡𝑒𝑟 − 𝑃

𝐴𝑣𝑒𝑟𝑎𝑔𝑒(𝑃))

𝑃 = 100

Δ𝑃 = −20

𝑄 = 100 𝑄𝑎𝑓𝑡𝑒𝑟 = 400

Δ𝑄 = 300

𝑎𝑣𝑒𝑟𝑎𝑔𝑒(𝑄)

𝑎𝑣𝑒𝑟𝑎𝑔𝑒(𝑃)

𝐿𝑒𝑡′𝑠 𝑐𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑒 𝑒!

ElasticityActually, its not just change, its % of Change.

Mesuring 2: Arc Elasticity

𝐴𝑣𝑒𝑟𝑎𝑔𝑒(𝑄)=

𝐴𝑣𝑒𝑟𝑎𝑔𝑒(𝑃)=

(𝑄𝑎𝑓𝑡𝑒𝑟 − 𝑄

𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑄)

(𝑃𝑎𝑓𝑡𝑒𝑟 − 𝑃

𝐴𝑣𝑒𝑟𝑎𝑔𝑒(𝑃))

= |1.2 ∗ 9

𝑃 = 100

Δ𝑃 = −20

𝑄 = 100 𝑄𝑎𝑓𝑡𝑒𝑟 = 400

Δ𝑄 = 300

𝑎𝑣𝑒𝑟𝑎𝑔𝑒(𝑃)

𝑎𝑣𝑒𝑟𝑎𝑔𝑒(𝑄)

ElasticityWhy “%” important? Think about the Case:

𝑃 = 100

Δ𝑃 = −20

𝑄 = 100

𝑄𝑎𝑓𝑡𝑒𝑟 = 125

(𝑄, 𝑃) = 100,100

(𝑄𝑎𝑓𝑡𝑒𝑟, 𝑃𝑎𝑓𝑡𝑒𝑟) = 125,80

(1)What is arc 𝑒 =% 𝑄𝑢𝑎𝑛𝑡𝑖𝑡𝑦 𝐶ℎ𝑎𝑛𝑔𝑒

% 𝑃𝑟𝑖𝑐𝑒 𝐶ℎ𝑎𝑛𝑔𝑒?

(2)What is the Revenue before and after?

𝑃 = 100

Δ𝑃 = −20

𝑄 = 100

(𝑄, 𝑃) = 100,100

𝑒 =−20/90

25/112.5= | − 1|

𝑅𝑒𝑣𝑏𝑒𝑓𝑜𝑟𝑒 = 𝑃𝑄 = 10,000

𝑅𝑒𝑣𝑎𝑓𝑡𝑒𝑟 = 𝑃𝑎𝑓𝑡𝑒𝑟𝑄𝑎𝑓𝑡𝑒𝑟 = 10,000

So, if we define 𝑒 such that,𝑒 = 1 means Revenue doesn’t change.

Elasticity

𝑃 = 100

Δ𝑃 = −20

𝑄 = 100

(𝑄, 𝑃) = 100,100

𝑒 =−20/90

25/112.5= | − 1|

So, if we define 𝑒 such that,𝑒 = 1 means Revenue doesn’t change.

𝑃𝑄

Why “%” important? Think about the Case:

Elasticity

𝑃 = 100

Δ𝑃 = −20

𝑄 = 100

(𝑄, 𝑃) = 100,100

(1)If we think 𝑒 = 5.4 ≫ 1 case.

Why “%” important? Think about the Case:

𝑃 = 100

Δ𝑃 = −20

𝑄 = 100

(𝑄, 𝑃) = 100,100

(1)If we think 𝑒 = 5.4 ≫ 1 case.

So, if e > 1, - Price down gain Revenue- Price Up lose Revenue

ElasticitySummary and special case

𝑒 > 1

𝑒 = 1𝑒 < 1

𝑒 = ∞

𝑒 = 0

If you change price,Nothing happens.So, price sensitivity = 0

If you change priceBit higher than beforeEveryone run away.

Bit lower than beforeEveryone 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↓

ElasticityFYI[advanced]𝑒 can be changed in Linear curve.

𝑒 =d𝑄

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

|𝑒𝐷| = 1

|𝑒𝐷| < 1

|𝑒𝐷| > 1

Surplus and Welfare

Welfare can be calculate:

Consumer Surplus(CS) + Producer Surplus(PS)

But Why the CS / PS is the Area on the graph?

Why the CS can be calculated by the Area on the graph?

To make the things easy:

- Imagine this market has only 4 people.

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.

Name Budget

Akira $100

Chieko $80

Rocky $50

Tomo $40

1 2 3 4

If the price of an apple become $60 what will happen?

Name Budget

Akira $100

Chieko $80

Rocky $50

Tomo $40

1 2 3 4

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

1 2 3 4

$40$20

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

Producer Surplus(PS) can be calculated same way.

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.

Name Cost

Neha $40

Federico $50

Joe $80

David $100

1 2 3 4

If the price set as $60,What will happen?

Name Cost

Neha $40

Federico $50

Joe $80

David $100

1 2 3 4

Neha got $20 profit while Federico got $10So the profit = Producer Surplus is $30

Name Cost

Neha $40

Federico $50

Joe $80

David $100

1 2 3 4

60$20 $10

Neha got $20 profit while Federico got $10So the profit = Producer Surplus is $30

1 2 3 4

60$20 $10

Revenue

COST− = 𝑝𝑟𝑜𝑓𝑖𝑡

So, Welfare can be calculate:

Consumer Surplus(CS) + Producer Surplus(PS)

How tax change D/S curvesand the Dead Weight LossSee 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.

Supply Curve

Demand Curve

Let’s us think aboutGovernment decides thatThey collect tax from Buyer(demand side)And the tax is $10 each goods.

Demand Side Taxation: 3 steps thinking:

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

𝑄𝑏𝑒𝑓𝑜𝑟𝑒, 𝑃𝑏𝑒𝑓𝑜𝑟𝑒 = (0,100)

Should become

𝑄𝑎𝑓𝑡𝑒𝑟 , 𝑃𝑎𝑓𝑡𝑒𝑟 = (0,90)

Because 𝑃𝑎𝑓𝑡𝑒𝑟 + 𝑡𝑎𝑥 = 𝑃𝑏𝑒𝑓𝑜𝑟𝑒

Who, how much, really bear?

Supply Curve

Demand Curve Before

After Taxation, we got new Equilibrium (𝑃𝑎𝑓𝑡𝑒𝑟 , 𝑄𝑎𝑓𝑡𝑒𝑟)

But, what consumers really pay is:𝑃𝑎𝑓𝑡𝑒𝑟 + 𝑡𝑎𝑥 = 𝑃𝑅𝐸𝐴𝐿

𝑃𝑅𝐸𝐴𝐿 − 𝑃𝑏𝑒𝑓𝑜𝑟𝑒 = 𝑡𝑎𝑥𝑐𝑜𝑛𝑠𝑢𝑚𝑒𝑟

𝑃𝑏𝑒𝑓𝑜𝑟𝑒 − 𝑃𝑎𝑓𝑡𝑒𝑟 = 𝑡𝑎𝑥𝑝𝑟𝑜𝑑𝑢𝑐𝑒𝑟

𝑡𝑎𝑥𝑐𝑜𝑛𝑠𝑢𝑚𝑒𝑟 + 𝑡𝑎𝑥𝑝𝑟𝑜𝑑𝑢𝑐𝑒𝑟 = 𝑡𝑎𝑥Demand Curve After

𝑃𝑏𝑒𝑓𝑜𝑟𝑒

𝑃𝑎𝑓𝑡𝑒𝑟

𝑃𝑅𝐸𝐴𝐿

Let’s calculate for this example!

𝑃𝑆 = 5𝑄

Demand Curve Before

Demand curve before tax:𝑃𝐷𝑏 = 120 − 3𝑄

Supply Curve before tax:𝑃𝑆 = 5𝑄

𝒕𝒂𝒙 = $𝟖 for Consumers

What is:𝑃𝑅𝐸𝐴𝐿 − 𝑃𝑏𝑒𝑓𝑜𝑟𝑒 = 𝑡𝑎𝑥𝑐𝑜𝑛𝑠𝑢𝑚𝑒𝑟

𝑃𝐷𝑏 = 120 − 3𝑄

𝑃𝑆 = 5𝑄

Demand Curve Before

Calculate before Equilibrium, 𝑃𝑏𝑒𝑓𝑜𝑟𝑒 = 75, 𝑄𝑏𝑒𝑓𝑜𝑟𝑒 = 15

The new demand curve will be𝑃𝐷𝑎

= 112 − 3𝑄

𝑃𝑎𝑓𝑡𝑒𝑟 = 70, 𝑄𝑎𝑓𝑡𝑒𝑟 = 14

But, what consumers really pay is:𝑃𝑎𝑓𝑡𝑒𝑟 + 𝑡𝑎𝑥 = 𝑃𝑅𝐸𝐴𝐿 = 78

𝑃𝑅𝐸𝐴𝐿 − 𝑃𝑏𝑒𝑓𝑜𝑟𝑒 = 𝑡𝑎𝑥𝑐𝑜𝑛𝑠𝑢𝑚𝑒𝑟 = 3

𝑃𝑏𝑒𝑓𝑜𝑟𝑒 − 𝑃𝑎𝑓𝑡𝑒𝑟 = 𝑡𝑎𝑥𝑝𝑟𝑜𝑑𝑢𝑐𝑒𝑟 = 5

𝑡𝑎𝑥𝑐𝑜𝑛𝑠𝑢𝑚𝑒𝑟 + 𝑡𝑎𝑥𝑝𝑟𝑜𝑑𝑢𝑐𝑒𝑟 = 𝑡𝑎𝑥Demand Curve After

𝑃𝐷𝑏 = 120 − 3𝑄

Next: supply side taxation:

Supply Curve

Demand Curve

Let’s us think aboutGovernment decides thatThey collect tax from Seller(Supply side)

Supply Side Taxation: 3 steps thinking:

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

𝑄𝑏𝑒𝑓𝑜𝑟𝑒, 𝑃𝑏𝑒𝑓𝑜𝑟𝑒 = (0,10)

Should become

𝑄𝑎𝑓𝑡𝑒𝑟 , 𝑃𝑎𝑓𝑡𝑒𝑟 = (0,20)

Because 𝑃𝑎𝑓𝑡𝑒𝑟 − 𝑡𝑎𝑥 = 𝑃𝑏𝑒𝑓𝑜𝑟𝑒

Supply Curve

Demand Curve

After Taxation, we got new Equilibrium (𝑃𝑎𝑓𝑡𝑒𝑟 , 𝑄𝑎𝑓𝑡𝑒𝑟)

𝑃𝑎𝑓𝑡𝑒𝑟 is what consumers pay.

But, what sellers really get:𝑃𝑎𝑓𝑡𝑒𝑟 − 𝑡𝑎𝑥 = 𝑃𝑅𝐸𝐴𝐿

𝑃𝑎𝑓𝑡𝑒𝑟−𝑃𝑏𝑒𝑓𝑜𝑟𝑒= 𝑡𝑎𝑥𝑐𝑜𝑛𝑠𝑢𝑚𝑒𝑟

𝑃𝑏𝑒𝑓𝑜𝑟𝑒 − 𝑃𝑅𝐸𝐴𝐿 = 𝑡𝑎𝑥𝑝𝑟𝑜𝑑𝑢𝑐𝑒𝑟

𝑡𝑎𝑥𝑐𝑜𝑛𝑠𝑢𝑚𝑒𝑟 + 𝑡𝑎𝑥𝑝𝑟𝑜𝑑𝑢𝑐𝑒𝑟 = 𝑡𝑎𝑥

𝑃𝑆 = 5𝑄

Demand Curve

Demand curve before tax:𝑃𝐷𝑏 = 120 − 3𝑄

Supply Curve before tax:𝑃𝑆 = 5𝑄

𝑡𝑎𝑥 = $8 for Sellers.

What is:𝑃𝑅𝐸𝐴𝐿 − 𝑃𝑏𝑒𝑓𝑜𝑟𝑒 = 𝑡𝑎𝑥𝑐𝑜𝑛𝑠𝑢𝑚𝑒𝑟

𝑃𝐷𝑏 = 120 − 3𝑄

Supply Curve

Demand Curve

𝑃𝑆𝐵= 5𝑄

𝑃𝐷 = 120 − 3𝑄

𝑃𝑆𝐴= 5𝑄 + 8

Calculate before Equilibrium, 𝑃𝑏𝑒𝑓𝑜𝑟𝑒 = 75, 𝑄𝑏𝑒𝑓𝑜𝑟𝑒 = 15

The new supply curve will be𝑃𝑆𝐴

= 5𝑄 + 8

𝑃𝑎𝑓𝑡𝑒𝑟 = 78, 𝑄𝑎𝑓𝑡𝑒𝑟 = 14

But, what sellers really get is:𝑃𝑎𝑓𝑡𝑒𝑟 − 𝑡𝑎𝑥 = 𝑃𝑅𝐸𝐴𝐿 = 70

𝑃𝑎𝑓𝑡𝑒𝑟−𝑃𝑏𝑒𝑓𝑜𝑟𝑒= 𝑡𝑎𝑥𝑐𝑜𝑛𝑠𝑢𝑚𝑒𝑟 = 3

𝑃𝑏𝑒𝑓𝑜𝑟𝑒 − 𝑃𝑅𝐸𝐴𝐿 = 𝑡𝑎𝑥𝑝𝑟𝑜𝑑𝑢𝑐𝑒𝑟 = 5

𝑡𝑎𝑥𝑐𝑜𝑛𝑠𝑢𝑚𝑒𝑟 + 𝑡𝑎𝑥𝑝𝑟𝑜𝑑𝑢𝑐𝑒𝑟 = 𝑡𝑎𝑥

Dead Weight Loss

Let’s Calculate CS and PS before tax

Supply Curve

Demand Curve

𝑃𝑆𝐵= 5𝑄

𝑃𝐷 = 120 − 3𝑄

Let’s Calculate CS and PS before tax

Supply Curve

Demand Curve

𝑃𝑆𝐵= 5𝑄

𝑃𝐷 = 120 − 3𝑄

Calculate before Equilibrium, 𝑄𝑏𝑒𝑓𝑜𝑟𝑒 = 15 , 𝑃𝑏𝑒𝑓𝑜𝑟𝑒 = 75

𝑄𝑏𝑒𝑓𝑜𝑟𝑒 = 15

𝑃𝑏𝑒𝑓𝑜𝑟𝑒 = 75

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)

Supply Curve

Demand Curve

𝑃𝑆𝐵= 5𝑄

𝑃𝐷 = 120 − 3𝑄

𝑄𝑏𝑒𝑓𝑜𝑟𝑒

𝑃𝑆𝐴= 5𝑄 + 8

𝑃𝑅𝐸𝐴𝐿 = 70

𝑄𝑎𝑓𝑡𝑒𝑟

Supply Curve

Demand Curve

𝑃𝑆𝐵= 5𝑄

𝑃𝐷 = 120 − 3𝑄

𝑃𝑆𝐴= 5𝑄 + 8

The Welfare should be calculated based on- What consumer really pay- What producer really get

So, for consumers they really pay𝑃𝑎𝑓𝑡𝑒𝑟 = 78

for producers they really get𝑃𝑅𝐸𝐴𝐿 = 70

Yes, taxation makes price differenceBetween consumers and producers.

Supply Curve

Demand Curve

𝑃𝑆𝐵= 5𝑄

𝑃𝐷 = 120 − 3𝑄

𝑃𝑆𝐴= 5𝑄 + 8

𝐶𝑆𝑎𝑓𝑡𝑒𝑟

𝑃𝑆𝑎𝑓𝑡𝑒𝑟

𝐶𝑆𝑎𝑓𝑡𝑒𝑟 =(120 − 78) × 14

2= 294

𝑃𝑆𝑎𝑓𝑡𝑒𝑟 =(70 − 0) × 14

2= 490

Let’s Calculate Sum of Tax, collected from market.

Supply Curve

Demand Curve

𝑃𝑆𝐵= 5𝑄

𝑃𝐷 = 120 − 3𝑄

𝑃𝑆𝐴= 5𝑄 + 8

Where is tax and why?

Let’s Calculate Sum of Tax, collected from market.

Supply Curve

Demand Curve

𝑃𝑆𝐵= 5𝑄

𝑃𝐷 = 120 − 3𝑄

𝑃𝑆𝐴= 5𝑄 + 8

consumers really pay𝑃𝑎𝑓𝑡𝑒𝑟 = 78

producers really get𝑃𝑅𝐸𝐴𝐿 = 70

The difference is a tax so𝑃𝑎𝑓𝑡𝑒𝑟 − 𝑃𝑅𝐸𝐴𝐿 = 𝑡𝑎𝑥 each consumption.

And the quantity is 𝑄𝑎𝑓𝑡𝑒𝑟 = 14.

So Sum of Tax = 78 − 70 × 14 = 112𝑄𝑏𝑒𝑓𝑜𝑟𝑒

Compare before and after

Demand Curve

𝑄𝑏𝑒𝑓𝑜𝑟𝑒𝑄𝑎𝑓𝑡𝑒𝑟

before after

Dead Weight Loss

Demand Curve

𝑄𝑏𝑒𝑓𝑜𝑟𝑒𝑄𝑎𝑓𝑡𝑒𝑟

before after

This is Dead Weight Loss

This is a Social Welfare Loss that caused by tax

Before After Δ = 𝐴𝑓𝑡𝑒𝑟 − 𝐵𝑒𝑓𝑜𝑟𝑒

ConsumerSurplus

ProducerSurplus

Tax+112

Social Welfare 900 896-4

Dead Weight Loss

Summary

𝐶𝑆 = 337.5

𝑃𝑆 = 562.5

𝐶𝑆𝑎𝑓𝑡𝑒𝑟 = 294

𝑃𝑆𝑎𝑓𝑡𝑒𝑟 = 490

𝑇𝑎𝑥 = 112

Consumer Theory

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

Budget Constrain (make sure both axis is Q)

- Pizza($16 each) and Movie($8 each)- Your weekly budget is $96

But this curve is nothing to do With your Utility.(imagine, if you hate movie)

16𝑄𝑝𝑖𝑧𝑧𝑎 + 8𝑄𝑚𝑜𝑣𝑖𝑒 = $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 = 𝑄𝑃𝑖𝑧𝑧𝑎

𝑝𝑖𝑧𝑧𝑎

𝑈𝑡𝑖𝑙𝑖𝑡𝑦

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?

Marginal UtilityIf 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

Marginal Utility [advance]

is a the additional satisfaction a consumer gains from consuming one more unit of a good or service.*

𝑀𝑈𝑝𝑖𝑧𝑧𝑎 =𝜕𝑈

𝜕𝑄𝑝𝑖𝑧𝑧𝑎=

2 𝑄𝑝𝑖𝑧𝑧𝑎

*http://www.investopedia.com/terms/m/marginalutility.asp

Indifference curve

Imagine your utility function, not only Pizza, but a combination

Of Pizza and Movie 𝑈 = 𝑄𝑀𝑄𝑃.

And indifference means 𝑈 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡. 𝑠𝑎𝑦, 𝑈 = 2

Indifference curve

And indifference means 𝑈 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡. 𝑠𝑎𝑦, 𝑈 = 2 𝑎𝑛𝑑 3

2 4 93

𝑈 = 𝑄𝑀𝑄𝑃 = 2

Indifference curve

And indifference means 𝑈 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡. 𝑠𝑎𝑦, 𝑈 = 2 𝑎𝑛𝑑 3

2 4 93

MRS(Marginal Rates of Substitute) on Indifference curve

Think about 𝑈 = 2 = 𝑄𝑀𝑄𝑃.

2 4 93

When you are point AYou have Movie, Pizza = (1,4)And this is indifferent with point BWhich is Movie, Pizza = (2,2)That means you can give up2 pizza to get 1 more movie.

In mathematical form,

MRSPointA =Δ𝑌

Δ𝑋=

2−1= −2

MRS(Marginal Rates of Substitute) and Marginal Utility

[advance]

2 4 93

𝑀𝑅𝑆 =𝛥𝑌

𝛥𝑋=

𝑀𝑈𝑋

𝑀𝑈𝑌Because MU is a the additional satisfaction a consumer gains from consuming one more unit of a good or service.If 𝑀𝑈𝑃𝐼𝑍𝑍𝐴 = 1, which means if you got 1 more,pizza your utility change +1.

So, if you got 1 Pizza, get +𝑀𝑈𝑃𝐼𝑍𝑍𝐴 as an additional UtilityAnd, you got 1 Movie, get +𝑀𝑈𝑀𝑜𝑣𝑖𝑒 as an additional Utility.How to determine MRS from MU?

MRS(Marginal Rates of Substitute) and Marginal Utility

[advance] So, if you got 1 Pizza, get +𝑀𝑈𝑃𝐼𝑍𝑍𝐴 = 1And, at a same point,

you got 1 Movie, get +𝑀𝑈𝑀𝑜𝑣𝑖𝑒 = 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=

𝑀𝑈𝑋

𝑀𝑈𝑌

2 4 93

Budget constrain and MRS

Return back to Indifference curve and Budget constrain.

When the tangent of budget constrainEquals to MRS, the utility within the budget constrain become maximum.

2 4 93

Budget constrain and MRS1. How to calculate tangent of Budget constrain?

𝑄𝑚𝑜𝑣𝑖𝑒

𝑄𝑝𝑖𝑧𝑧𝑎

2 4 93

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

2Qmovie + $6

And it is known −P𝑀𝑜𝑣𝑖𝑒

Ppizza= −

Budget constrain and MRS[advance]

2 4 93

𝑈 = 𝑄𝑀𝑄𝑃

2. How to calculate MRS

𝑀𝑅𝑆 = −𝛥𝑌

𝛥𝑋= −

𝑀𝑈𝑋

𝑀𝑈𝑌= −

𝜕𝑈𝜕𝑄𝑋

𝜕𝑈𝜕𝑄𝑌

= −(

𝜕𝑈𝜕𝑄𝑀𝑂𝑉𝐼𝐸

(𝜕𝑈

𝜕𝑄𝑃𝑖𝑧𝑧𝑎)

If we calculate it…

Budget constrain and MRS[advance]

2 4 93

2. How to calculate MRS

𝑀𝑅𝑆 = −𝛥𝑌

𝛥𝑋= −

𝑀𝑈𝑋

𝑀𝑈𝑌= −

𝜕𝑈𝜕𝑄𝑋

𝜕𝑈𝜕𝑄𝑌

= −(

𝜕𝑈𝜕𝑄𝑀𝑂𝑉𝐼𝐸

(𝜕𝑈

𝜕𝑄𝑃𝑖𝑧𝑧𝑎)

𝑎𝑛𝑑𝜕𝑈

𝜕𝑄𝑃=

𝑄𝑀

2 𝑄𝑀𝑄𝑃

,𝜕𝑈

𝜕𝑄𝑀=

𝑄𝑃

2 𝑄𝑀𝑄𝑃

So, 𝑀𝑅𝑆 = −𝑄𝑃

𝑄𝑀

So, where is the optimal? (Max U under the badget)

2 4 93

2. How to calculate MRS𝑀𝑅𝑆 = tangent

So, 𝑀𝑅𝑆 = −𝑄𝑃

𝑄𝑀, 𝑎𝑛𝑑 𝑡𝑎𝑛𝑔𝑒𝑛𝑡 = −

P𝑀𝑜𝑣𝑖𝑒

Ppizza= −

therefore, −𝑄𝑃

𝑄𝑀= −

𝑃𝑃= −

2↔ 2𝑄𝑃 = 𝑄𝑀

Using above, the equation (𝑎) should be16𝑄𝑝𝑖𝑧𝑧𝑎 + 16𝑄𝑝𝑖𝑧𝑧𝑎 = $96

𝑆𝑜𝑙𝑣𝑒 𝑖𝑡 𝑎𝑛𝑑 𝑄𝑝 = 3, 𝑄𝑀 = 6

𝑈 = 𝑄𝑀𝑄𝑃 = 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]

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 theLuckiest 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↓

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 cakeBefore you sleep.The demand increase.This is Income Effect.

Cakes$5↓

Pastry$2

Remember Budget constrain

𝑄𝑚𝑜𝑣𝑖𝑒

2 4 93

- Pizza($16 each) and Movie($8 each)- imagine, the Movie become cheaper ($6 each)

1 How your budget constrain change?2 What is your newequation?

2 4 93

It become like this. So what?

16𝑄𝑚𝑜𝑣𝑖𝑒

2 4 93

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.

16𝑄𝑝𝑖𝑧𝑧𝑎 + 6𝑄𝑚𝑜𝑣𝑖𝑒 = $96𝐴

Move the new Budget constrain to tangent of

Indifference curve.

2 4 93

We would like to parallel translate thisRed Line, a new budget constrain, to aTangent 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)”

Indifference curve.

2 4 93

This is called 𝑆𝑢𝑏𝑠𝑡𝑖𝑡𝑢𝑡𝑖𝑜𝑛 𝐸𝑓𝑓𝑒𝑐𝑡Because, the change of movie price cause theChange of ratio of Pizza and Movie.And the new tangent on the same indifference curveas before, represent the effect of change ratio only.

Indifference curve.

2 4 93

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.

2 4 93

This is called 𝐼𝑛𝑐𝑜𝑚𝑒 𝐸𝑓𝑓𝑒𝑐𝑡

The change (cheaper) of movie priceMakes you richer (you can buy more goodsby same budget).This is also change your demand.

Summary of Income Effect and substitution effect

2 4 93

SubstitutionEffect

IncomeEffect

Total Effect

Pizza became Relatively expensive.

So decrease.

Consumers become Richer

So the amount of consumption

increase

Depends onSub/income

effect.

Movie(Cheaper)

Movie became Relatively

cheap.So increase.

DemandIncrease.

Want to learn more?

• See Entrepreneurial Economics #2!

• https://www.slideshare.net/ryouen/170925-entrepreneurial-economics2

ReferenceNUS 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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