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Ryosuke Ishii

The document is a lecture on entrepreneurial economics presented by Ryosuke Ishii, focusing on concepts such as elasticity, welfare, and the impact of taxation on supply and demand curves. It covers various methods of measuring elasticity and the associated changes in consumer and producer surpluses due to market dynamics. Additionally, it discusses how taxation can affect market equilibrium and results in deadweight loss.

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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 = % 𝑄𝑢𝑎𝑛𝑡𝑖𝑡𝑦 𝐶ℎ𝑎𝑛𝑔𝑒 % 𝑃𝑟𝑖𝑐𝑒 𝐶ℎ𝑎𝑛𝑔𝑒 = ( 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 𝑃𝑎𝑓𝑡𝑒𝑟 = 80 Δ𝑃 = −20 𝑄 = 100 𝑄 𝑎𝑓𝑡𝑒𝑟 = 400 Δ𝑄 = 300 Actually, its not just change, its % of Change. 𝑒 = % 𝑄𝑢𝑎𝑛𝑡𝑖𝑡𝑦 𝐶ℎ𝑎𝑛𝑔𝑒 % 𝑃𝑟𝑖𝑐𝑒 𝐶ℎ𝑎𝑛𝑔𝑒 , but how to measure “% of Change”? Mesuring 1: Point Elasticity % 𝑄𝑢𝑎𝑛𝑡𝑖𝑡𝑦 𝐶ℎ𝑎𝑛𝑔𝑒 = Δ𝑄 𝑄 = | 𝑄 𝑎𝑓𝑡𝑒𝑟 − 𝑄 𝑄 | = 300 100 % 𝑃𝑟𝑖𝑐𝑒 𝐶ℎ𝑎𝑛𝑔𝑒 = Δ𝑃 𝑃 = | 𝑃𝑎𝑓𝑡𝑒𝑟 − 𝑃 𝑃 | = | −20 100 | So, 𝑒 = % 𝑄𝑢𝑎𝑛𝑡𝑖𝑡𝑦 𝐶ℎ𝑎𝑛𝑔𝑒 % 𝑃𝑟𝑖𝑐𝑒 𝐶ℎ𝑎𝑛𝑔𝑒 = | (3) ( −1 5 ) | = 15 ≥ 1 (it can be done because the Curve is Linear Function)
Elasticity 𝑃 𝑄 𝑃 = 100 𝑃𝑎𝑓𝑡𝑒𝑟 = 80 Δ𝑃 = −20 𝑄 = 100 𝑄 𝑎𝑓𝑡𝑒𝑟 = 400 Δ𝑄 = 300 𝑒 = % 𝑄𝑢𝑎𝑛𝑡𝑖𝑡𝑦 𝐶ℎ𝑎𝑛𝑔𝑒 % 𝑃𝑟𝑖𝑐𝑒 𝐶ℎ𝑎𝑛𝑔𝑒 , 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 = % 𝑄𝑢𝑎𝑛𝑡𝑖𝑡𝑦 𝐶ℎ𝑎𝑛𝑔𝑒 % 𝑃𝑟𝑖𝑐𝑒 𝐶ℎ𝑎𝑛𝑔𝑒 , 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. % 𝑄𝑢𝑎𝑛𝑡𝑖𝑡𝑦 𝐶ℎ𝑎𝑛𝑔𝑒 = Δ𝑄 𝑄 = 𝑄 𝑎𝑓𝑡𝑒𝑟 − 𝑄 𝐴𝑣𝑒𝑟𝑎𝑔𝑒(𝑄) % 𝑃𝑟𝑖𝑐𝑒 𝐶ℎ𝑎𝑛𝑔𝑒 = Δ𝑃 𝑃 = 𝑃𝑎𝑓𝑡𝑒𝑟 − 𝑃 𝐴𝑣𝑒𝑟𝑎𝑔𝑒(𝑃) So, 𝑒 = % 𝑄𝑢𝑎𝑛𝑡𝑖𝑡𝑦 𝐶ℎ𝑎𝑛𝑔𝑒 % 𝑃𝑟𝑖𝑐𝑒 𝐶ℎ𝑎𝑛𝑔𝑒 = ( 𝑄 𝑎𝑓𝑡𝑒𝑟 − 𝑄 𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑄 ) ( 𝑃𝑎𝑓𝑡𝑒𝑟 − 𝑃 𝐴𝑣𝑒𝑟𝑎𝑔𝑒(𝑃) ) 𝑃 𝑄 𝑃 = 100 𝑃𝑎𝑓𝑡𝑒𝑟 = 80 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 = % 𝑄𝑢𝑎𝑛𝑡𝑖𝑡𝑦 𝐶ℎ𝑎𝑛𝑔𝑒 % 𝑃𝑟𝑖𝑐𝑒 𝐶ℎ𝑎𝑛𝑔𝑒 , but how to measure “% of Change”? Mesuring 2: Arc Elasticity % 𝑄𝑢𝑎𝑛𝑡𝑖𝑡𝑦 𝐶ℎ𝑎𝑛𝑔𝑒 = Δ𝑄 𝑄 = 𝑄 𝑎𝑓𝑡𝑒𝑟 − 𝑄 𝐴𝑣𝑒𝑟𝑎𝑔𝑒(𝑄) = 300 250 % 𝑃𝑟𝑖𝑐𝑒 𝐶ℎ𝑎𝑛𝑔𝑒 = Δ𝑃 𝑃 = 𝑃𝑎𝑓𝑡𝑒𝑟 − 𝑃 𝐴𝑣𝑒𝑟𝑎𝑔𝑒(𝑃) = −20 90 So, 𝑒 = % 𝑄𝑢𝑎𝑛𝑡𝑖𝑡𝑦 𝐶ℎ𝑎𝑛𝑔𝑒 % 𝑃𝑟𝑖𝑐𝑒 𝐶ℎ𝑎𝑛𝑔𝑒 = ( 𝑄 𝑎𝑓𝑡𝑒𝑟 − 𝑄 𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑄 ) ( 𝑃𝑎𝑓𝑡𝑒𝑟 − 𝑃 𝐴𝑣𝑒𝑟𝑎𝑔𝑒(𝑃) ) = | 1.2 ∗ 9 −2 | = 5.4 𝑃 𝑄 𝑃 = 100 𝑃𝑎𝑓𝑡𝑒𝑟 = 80 Δ𝑃 = −20 𝑄 = 100 𝑄 𝑎𝑓𝑡𝑒𝑟 = 400 Δ𝑄 = 300 𝑎𝑣𝑒𝑟𝑎𝑔𝑒(𝑃) 𝑎𝑣𝑒𝑟𝑎𝑔𝑒(𝑄)
Elasticity Why “%” important? Think about the Case: 𝑃 𝑄 𝑃 = 100 𝑃𝑎𝑓𝑡𝑒𝑟 = 80 Δ𝑃 = −20 𝑄 = 100 𝑄 𝑎𝑓𝑡𝑒𝑟 = 125 (𝑄, 𝑃) = 100,100 (𝑄 𝑎𝑓𝑡𝑒𝑟, 𝑃𝑎𝑓𝑡𝑒𝑟) = 125,80 (1)What is arc 𝑒 = % 𝑄𝑢𝑎𝑛𝑡𝑖𝑡𝑦 𝐶ℎ𝑎𝑛𝑔𝑒 % 𝑃𝑟𝑖𝑐𝑒 𝐶ℎ𝑎𝑛𝑔𝑒 ? (2)What is the Revenue before and after?
Elasticity Why “%” important? Think about the Case: 𝑃 𝑄 𝑃 = 100 𝑃𝑎𝑓𝑡𝑒𝑟 = 80 Δ𝑃 = −20 𝑄 = 100 𝑄 𝑎𝑓𝑡𝑒𝑟 = 125 (𝑄, 𝑃) = 100,100 (𝑄 𝑎𝑓𝑡𝑒𝑟, 𝑃𝑎𝑓𝑡𝑒𝑟) = 125,80 (1)What is arc 𝑒 = % 𝑄𝑢𝑎𝑛𝑡𝑖𝑡𝑦 𝐶ℎ𝑎𝑛𝑔𝑒 % 𝑃𝑟𝑖𝑐𝑒 𝐶ℎ𝑎𝑛𝑔𝑒 ? 𝑒 = −20/90 25/112.5 = | − 1| (2)What is the Revenue before and 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 𝑃𝑎𝑓𝑡𝑒𝑟 = 80 Δ𝑃 = −20 𝑄 = 100 𝑄 𝑎𝑓𝑡𝑒𝑟 = 125 (𝑄, 𝑃) = 100,100 (𝑄 𝑎𝑓𝑡𝑒𝑟, 𝑃𝑎𝑓𝑡𝑒𝑟) = 125,80 (1)What is arc 𝑒 = % 𝑄𝑢𝑎𝑛𝑡𝑖𝑡𝑦 𝐶ℎ𝑎𝑛𝑔𝑒 % 𝑃𝑟𝑖𝑐𝑒 𝐶ℎ𝑎𝑛𝑔𝑒 ? 𝑒 = −20/90 25/112.5 = | − 1| (2)What is the Revenue before and 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. 𝑃𝑄 Why “%” important? Think about the Case:
Elasticity 𝑃 𝑄 𝑃 = 100 𝑃𝑎𝑓𝑡𝑒𝑟 = 80 Δ𝑃 = −20 𝑄 = 100 (𝑄, 𝑃) = 100,100 (1) If we think 𝑒 = 5.4 ≫ 1 case. (2)What is the Revenue before and after? 𝑄 𝑎𝑓𝑡𝑒𝑟 = 400 Why “%” important? Think about the Case:
Elasticity Why “%” important? Think about the Case: 𝑃 𝑄 𝑃 = 100 𝑃𝑎𝑓𝑡𝑒𝑟 = 80 Δ𝑃 = −20 𝑄 = 100 (𝑄, 𝑃) = 100,100 (1) If we think 𝑒 = 5.4 ≫ 1 case. (2)What is the Revenue before and after? 𝑅𝑒𝑣 𝑏𝑒𝑓𝑜𝑟𝑒 = 𝑃𝑄 = 10,000 𝑅𝑒𝑣 𝑎𝑓𝑡𝑒𝑟 = 𝑃𝑎𝑓𝑡𝑒𝑟 𝑄 𝑎𝑓𝑡𝑒𝑟 = 32,000 So, if e > 1, - Price down gain Revenue - Price Up lose Revenue 𝑄 𝑎𝑓𝑡𝑒𝑟 = 400
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
Surplus and Welfare
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: 𝑃𝑅𝐸𝐴𝐿 − 𝑃𝑏𝑒𝑓𝑜𝑟𝑒 = 𝑡𝑎𝑥 𝑐𝑜𝑛𝑠𝑢𝑚𝑒𝑟 𝑃𝑏𝑒𝑓𝑜𝑟𝑒 − 𝑃𝑎𝑓𝑡𝑒𝑟 = 𝑡𝑎𝑥 𝑝𝑟𝑜𝑑𝑢𝑐𝑒𝑟 𝑃𝑏𝑒𝑓𝑜𝑟𝑒 𝑃𝑎𝑓𝑡𝑒𝑟 𝑃 𝐷 𝑏 = 120 − 3𝑄
Let’s calculate for this example! 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 𝑃𝑏𝑒𝑓𝑜𝑟𝑒 𝑃𝑎𝑓𝑡𝑒𝑟 𝑃𝑅𝐸𝐴𝐿 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
Supply Side Taxation: 3 steps thinking: 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 𝑡𝑎𝑥 𝑐𝑜𝑛𝑠𝑢𝑚𝑒𝑟 + 𝑡𝑎𝑥 𝑝𝑟𝑜𝑑𝑢𝑐𝑒𝑟 = 𝑡𝑎𝑥 𝑃𝑏𝑒𝑓𝑜𝑟𝑒 𝑃𝑎𝑓𝑡𝑒𝑟 𝑃𝑅𝐸𝐴𝐿
Let’s calculate for this example! 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: 𝑃𝑅𝐸𝐴𝐿 − 𝑃𝑏𝑒𝑓𝑜𝑟𝑒 = 𝑡𝑎𝑥 𝑐𝑜𝑛𝑠𝑢𝑚𝑒𝑟 𝑃𝑏𝑒𝑓𝑜𝑟𝑒 − 𝑃𝑎𝑓𝑡𝑒𝑟 = 𝑡𝑎𝑥 𝑝𝑟𝑜𝑑𝑢𝑐𝑒𝑟 𝑃𝑏𝑒𝑓𝑜𝑟𝑒 𝑃𝑎𝑓𝑡𝑒𝑟 𝑃 𝐷 𝑏 = 120 − 3𝑄
Supply Side Taxation: 3 steps thinking: 𝑃 𝑄 Supply Curve Demand Curve 𝑃𝑏𝑒𝑓𝑜𝑟𝑒 𝑃𝑎𝑓𝑡𝑒𝑟 𝑃𝑅𝐸𝐴𝐿 𝑃𝑆 𝐵 = 5𝑄 𝑃 𝐷 = 120 − 3𝑄 𝑃𝑆 𝐴 = 5𝑄 + 8 Calculate before Equilibrium, 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 𝑡𝑎𝑥 𝑐𝑜𝑛𝑠𝑢𝑚𝑒𝑟 + 𝑡𝑎𝑥 𝑝𝑟𝑜𝑑𝑢𝑐𝑒𝑟 = 𝑡𝑎𝑥
Dead Weight Loss
Let’s Calculate CS and PS before tax 𝑃 𝑄 Supply Curve Demand Curve 𝑃𝑏𝑒𝑓𝑜𝑟𝑒 𝑃𝑎𝑓𝑡𝑒𝑟 𝑃𝑅𝐸𝐴𝐿 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 Calculate before Equilibrium, 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 𝑃𝑏𝑒𝑓𝑜𝑟𝑒 = 75 120 0 𝑃𝑆 𝐴 = 5𝑄 + 8 𝑃𝑎𝑓𝑡𝑒𝑟 = 78 𝑃𝑅𝐸𝐴𝐿 = 70 𝑄 𝑎𝑓𝑡𝑒𝑟 = 14
Let’s Calculate CS and PS after tax $8 (for producer) 𝑃 𝑄 Supply Curve Demand Curve 𝑃𝑆 𝐵 = 5𝑄 𝑃 𝐷 = 120 − 3𝑄 𝑃𝑏𝑒𝑓𝑜𝑟𝑒 = 75 120 0 𝑃𝑆 𝐴 = 5𝑄 + 8 𝑃𝑎𝑓𝑡𝑒𝑟 = 78 𝑃𝑅𝐸𝐴𝐿 = 70 CS PS The Welfare should be calculated based on - What consumer really pay - What producer really get So, for consumers they really pay 𝑃𝑎𝑓𝑡𝑒𝑟 = 78 for producers they really get 𝑃𝑅𝐸𝐴𝐿 = 70 Yes, taxation makes price difference Between consumers and producers.𝑄 𝑏𝑒𝑓𝑜𝑟𝑒 = 15 𝑄 𝑎𝑓𝑡𝑒𝑟 = 14
Let’s Calculate CS and PS after tax $8 (for producer) 𝑃 𝑄 Supply Curve Demand Curve 𝑃𝑆 𝐵 = 5𝑄 𝑃 𝐷 = 120 − 3𝑄 𝑃𝑏𝑒𝑓𝑜𝑟𝑒 = 75 120 0 𝑃𝑆 𝐴 = 5𝑄 + 8 𝑃𝑎𝑓𝑡𝑒𝑟 = 78 𝑃𝑅𝐸𝐴𝐿 = 70 𝐶𝑆 𝑎𝑓𝑡𝑒𝑟 𝑃𝑆 𝑎𝑓𝑡𝑒𝑟 𝐶𝑆 𝑎𝑓𝑡𝑒𝑟 = (120 − 78) × 14 2 = 294 𝑃𝑆 𝑎𝑓𝑡𝑒𝑟 = (70 − 0) × 14 2 = 490 𝑄 𝑏𝑒𝑓𝑜𝑟𝑒 = 15 𝑄 𝑎𝑓𝑡𝑒𝑟 = 14
Let’s Calculate Sum of Tax, collected from market. 𝑃 𝑄 Supply Curve Demand Curve 𝑃𝑆 𝐵 = 5𝑄 𝑃 𝐷 = 120 − 3𝑄 𝑃𝑏𝑒𝑓𝑜𝑟𝑒 = 75 120 0 𝑃𝑆 𝐴 = 5𝑄 + 8 𝑃𝑎𝑓𝑡𝑒𝑟 = 78 𝑃𝑅𝐸𝐴𝐿 = 70 Where is tax and why? 𝑄 𝑏𝑒𝑓𝑜𝑟𝑒 = 15 𝑄 𝑎𝑓𝑡𝑒𝑟 = 14
Let’s Calculate Sum of Tax, collected from market. 𝑃 𝑄 Supply Curve Demand Curve 𝑃𝑆 𝐵 = 5𝑄 𝑃 𝐷 = 120 − 3𝑄 𝑃𝑏𝑒𝑓𝑜𝑟𝑒 = 75 120 0 𝑃𝑆 𝐴 = 5𝑄 + 8 𝑃𝑎𝑓𝑡𝑒𝑟 = 78 𝑃𝑅𝐸𝐴𝐿 = 70 consumers really pay 𝑃𝑎𝑓𝑡𝑒𝑟 = 78 producers really get 𝑃𝑅𝐸𝐴𝐿 = 70 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 𝑄 𝑎𝑓𝑡𝑒𝑟 = 14
Compare before and after 𝑃 𝑄 Demand Curve 0 𝑄 𝑏𝑒𝑓𝑜𝑟𝑒𝑄 𝑎𝑓𝑡𝑒𝑟 𝑃 𝑄 CS PS 0 𝑃𝑏𝑒𝑓𝑜𝑟𝑒 before after 𝑄 𝑏𝑒𝑓𝑜𝑟𝑒
Dead Weight Loss 𝑃 𝑄 Demand Curve 0 𝑄 𝑏𝑒𝑓𝑜𝑟𝑒𝑄 𝑎𝑓𝑡𝑒𝑟 𝑃 𝑄 CS PS 0 𝑃𝑏𝑒𝑓𝑜𝑟𝑒 before after 𝑄 𝑏𝑒𝑓𝑜𝑟𝑒 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
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 𝑄 𝑄 12 6
Budget Constrain (make sure both axis is Q) - Pizza($16 each) and Movie($8 each) - Your weekly budget is $96 𝑀𝑜𝑣𝑖𝑒 𝑃𝑖𝑧𝑧𝑎 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? 𝑝𝑖𝑧𝑧𝑎 𝑄 𝑈𝑡𝑖𝑙𝑖𝑡𝑦 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 𝑈𝑡𝑖𝑙𝑖𝑡𝑦 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 𝑝𝑖𝑧𝑧𝑎 𝑄 𝑈𝑡𝑖𝑙𝑖𝑡𝑦 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 𝑀𝑜𝑣𝑖𝑒 𝑃𝑖𝑧𝑧𝑎 𝑄 𝑄 12 6
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 𝑎𝑛𝑑 3 𝑀𝑜𝑣𝑖𝑒 𝑃𝑖𝑧𝑧𝑎 𝑄 𝑄 12 4 2 2 4 93 𝑈 = 𝑄 𝑀 𝑄 𝑃 = 2
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 𝑎𝑛𝑑 3 𝑀𝑜𝑣𝑖𝑒 𝑃𝑖𝑧𝑧𝑎 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. 𝑀𝑜𝑣𝑖𝑒 𝑃𝑖𝑧𝑧𝑎 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] 𝑀𝑜𝑣𝑖𝑒 𝑃𝑖𝑧𝑧𝑎 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? 𝑝𝑖𝑧𝑧𝑎 𝑄 𝑈𝑡𝑖𝑙𝑖𝑡𝑦 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 𝑀𝑜𝑣𝑖𝑒 𝑃𝑖𝑧𝑧𝑎 𝑄 𝑄 12 4 2 2 4 93 𝑈 = 𝑄 𝑀 𝑄 𝑃 = 2 𝐴 𝐵 𝐶 𝑝𝑖𝑧𝑧𝑎 𝑄 𝑈𝑡𝑖𝑙𝑖𝑡𝑦 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. 𝑀𝑜𝑣𝑖𝑒 𝑃𝑖𝑧𝑧𝑎 𝑄 𝑄 12 4 2 2 4 93 𝑈 = 𝑄 𝑀 𝑄 𝑃 = 2 16𝑄 𝑝𝑖𝑧𝑧𝑎 + 8𝑄 𝑚𝑜𝑣𝑖𝑒 = $96
Budget constrain and MRS 1. How to calculate tangent of Budget constrain? 𝑀𝑜𝑣𝑖𝑒 𝑃𝑖𝑧𝑧𝑎 𝑄 𝑚𝑜𝑣𝑖𝑒 𝑄 𝑝𝑖𝑧𝑧𝑎 12 4 2 2 4 93 16𝑄 𝑝𝑖𝑧𝑧𝑎 + 8𝑄 𝑚𝑜𝑣𝑖𝑒 = $96 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] 𝑀𝑜𝑣𝑖𝑒 𝑃𝑖𝑧𝑧𝑎 𝑄 𝑄 12 4 2 2 4 93 𝑈 = 𝑄 𝑀 𝑄 𝑃 16𝑄 𝑝𝑖𝑧𝑧𝑎 + 8𝑄 𝑚𝑜𝑣𝑖𝑒 = $96 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] 𝑀𝑜𝑣𝑖𝑒 𝑃𝑖𝑧𝑧𝑎 𝑄 𝑄 12 4 2 2 4 93 𝑈 = 𝑄 𝑀 𝑄 𝑃 16𝑄 𝑝𝑖𝑧𝑧𝑎 + 8𝑄 𝑚𝑜𝑣𝑖𝑒 = $96 2. How to calculate MRS 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) 𝑀𝑜𝑣𝑖𝑒 𝑃𝑖𝑧𝑧𝑎 𝑄 𝑄 12 4 2 2 4 93 𝑈 = 𝑄 𝑀 𝑄 𝑃 2. How to calculate MRS 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
Let us think in Qualitative first. 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
Let us think in Qualitative first. 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 𝑀𝑜𝑣𝑖𝑒 𝑃𝑖𝑧𝑧𝑎 𝑄 𝑚𝑜𝑣𝑖𝑒 𝑄 𝑝𝑖𝑧𝑧𝑎 12 4 2 2 4 93 16𝑄 𝑝𝑖𝑧𝑧𝑎 + 8𝑄 𝑚𝑜𝑣𝑖𝑒 = $96 6 - 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? 16
Remember Budget constrain 𝑀𝑜𝑣𝑖𝑒 𝑃𝑖𝑧𝑧𝑎 𝑄 𝑝𝑖𝑧𝑧𝑎 12 4 2 2 4 93 6 It become like this. So what? 16 𝑄 𝑚𝑜𝑣𝑖𝑒 16𝑄 𝑝𝑖𝑧𝑧𝑎 + 6𝑄 𝑚𝑜𝑣𝑖𝑒 = $96
Remember Budget constrain 𝑀𝑜𝑣𝑖𝑒 𝑃𝑖𝑧𝑧𝑎 𝑄 𝑝𝑖𝑧𝑧𝑎 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 𝑄 𝑚𝑜𝑣𝑖𝑒 16𝑄 𝑝𝑖𝑧𝑧𝑎 + 6𝑄 𝑚𝑜𝑣𝑖𝑒 = $96𝐴 𝐵
Move the new Budget constrain to tangent of Indifference curve. 𝑀𝑜𝑣𝑖𝑒 𝑃𝑖𝑧𝑧𝑎 𝑄 𝑝𝑖𝑧𝑧𝑎 12 4 2 2 4 93 6 16 𝑄 𝑚𝑜𝑣𝑖𝑒 16𝑄 𝑝𝑖𝑧𝑧𝑎 + 6𝑄 𝑚𝑜𝑣𝑖𝑒 = $96 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
Move the new Budget constrain to tangent of Indifference curve. 𝑀𝑜𝑣𝑖𝑒 𝑃𝑖𝑧𝑧𝑎 𝑄 𝑝𝑖𝑧𝑧𝑎 12 4 2 2 4 93 6 16 𝑄 𝑚𝑜𝑣𝑖𝑒 16𝑄 𝑝𝑖𝑧𝑧𝑎 + 6𝑄 𝑚𝑜𝑣𝑖𝑒 = $96 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.
Move the new Budget constrain to tangent of Indifference curve. 𝑀𝑜𝑣𝑖𝑒 𝑃𝑖𝑧𝑧𝑎 𝑄 𝑝𝑖𝑧𝑧𝑎 12 4 2 2 4 93 6 16 𝑄 𝑚𝑜𝑣𝑖𝑒 16𝑄 𝑝𝑖𝑧𝑧𝑎 + 6𝑄 𝑚𝑜𝑣𝑖𝑒 = $96 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.
Remember Budget constrain 𝑀𝑜𝑣𝑖𝑒 𝑃𝑖𝑧𝑧𝑎 𝑄 𝑝𝑖𝑧𝑧𝑎 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 𝑄 𝑚𝑜𝑣𝑖𝑒 16𝑄 𝑝𝑖𝑧𝑧𝑎 + 6𝑄 𝑚𝑜𝑣𝑖𝑒 = $96
Summary of Income Effect and substitution effect 𝑀𝑜𝑣𝑖𝑒 𝑃𝑖𝑧𝑧𝑎 𝑄 𝑝𝑖𝑧𝑧𝑎 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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170902 entrepreneurial economics1

  • 1. Entrepreneurial Economics A supplemental lecture on BMA5001 Organized by NUS MBA Entrepreneurship Club 2nd September, 2017 1
  • 2. About author Ryosuke ISHII (RYO) • MIT Microeconomics graded 93% (on edX, 3 months online course)
  • 3. 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
  • 4. 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
  • 6. Elasticity is Sensitivity. Price Elasticity means how sensitive to price they are? I change the price Market reacts. Elasticity
  • 7. Elasticity So, the dividend(denominator) should be Price 𝑒 = 𝑄𝑢𝑎𝑛𝑡𝑖𝑡𝑦 𝐶ℎ𝑎𝑛𝑔𝑒 𝑃𝑟𝑖𝑐𝑒 𝐶ℎ𝑎𝑛𝑔𝑒
  • 8. Elasticity 𝑒 = 𝑄𝑢𝑎𝑛𝑡𝑖𝑡𝑦 𝐶ℎ𝑎𝑛𝑔𝑒 𝑃𝑟𝑖𝑐𝑒 𝐶ℎ𝑎𝑛𝑔𝑒 𝑃 𝑄 𝑃 𝑄 Larger 𝑒 means Very sensitive Smaller 𝑒 means Little sensitive
  • 9. 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 = % 𝑄𝑢𝑎𝑛𝑡𝑖𝑡𝑦 𝐶ℎ𝑎𝑛𝑔𝑒 % 𝑃𝑟𝑖𝑐𝑒 𝐶ℎ𝑎𝑛𝑔𝑒 = ( 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
  • 10. Elasticity 𝑃 𝑄 𝑃 = 100 𝑃𝑎𝑓𝑡𝑒𝑟 = 80 Δ𝑃 = −20 𝑄 = 100 𝑄 𝑎𝑓𝑡𝑒𝑟 = 400 Δ𝑄 = 300 Actually, its not just change, its % of Change. 𝑒 = % 𝑄𝑢𝑎𝑛𝑡𝑖𝑡𝑦 𝐶ℎ𝑎𝑛𝑔𝑒 % 𝑃𝑟𝑖𝑐𝑒 𝐶ℎ𝑎𝑛𝑔𝑒 , but how to measure “% of Change”? Mesuring 1: Point Elasticity % 𝑄𝑢𝑎𝑛𝑡𝑖𝑡𝑦 𝐶ℎ𝑎𝑛𝑔𝑒 = Δ𝑄 𝑄 = | 𝑄 𝑎𝑓𝑡𝑒𝑟 − 𝑄 𝑄 | = 300 100 % 𝑃𝑟𝑖𝑐𝑒 𝐶ℎ𝑎𝑛𝑔𝑒 = Δ𝑃 𝑃 = | 𝑃𝑎𝑓𝑡𝑒𝑟 − 𝑃 𝑃 | = | −20 100 | So, 𝑒 = % 𝑄𝑢𝑎𝑛𝑡𝑖𝑡𝑦 𝐶ℎ𝑎𝑛𝑔𝑒 % 𝑃𝑟𝑖𝑐𝑒 𝐶ℎ𝑎𝑛𝑔𝑒 = | (3) ( −1 5 ) | = 15 ≥ 1 (it can be done because the Curve is Linear Function)
  • 11. Elasticity 𝑃 𝑄 𝑃 = 100 𝑃𝑎𝑓𝑡𝑒𝑟 = 80 Δ𝑃 = −20 𝑄 = 100 𝑄 𝑎𝑓𝑡𝑒𝑟 = 400 Δ𝑄 = 300 𝑒 = % 𝑄𝑢𝑎𝑛𝑡𝑖𝑡𝑦 𝐶ℎ𝑎𝑛𝑔𝑒 % 𝑃𝑟𝑖𝑐𝑒 𝐶ℎ𝑎𝑛𝑔𝑒 , 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
  • 12. Elasticity 𝑒 = % 𝑄𝑢𝑎𝑛𝑡𝑖𝑡𝑦 𝐶ℎ𝑎𝑛𝑔𝑒 % 𝑃𝑟𝑖𝑐𝑒 𝐶ℎ𝑎𝑛𝑔𝑒 , 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. % 𝑄𝑢𝑎𝑛𝑡𝑖𝑡𝑦 𝐶ℎ𝑎𝑛𝑔𝑒 = Δ𝑄 𝑄 = 𝑄 𝑎𝑓𝑡𝑒𝑟 − 𝑄 𝐴𝑣𝑒𝑟𝑎𝑔𝑒(𝑄) % 𝑃𝑟𝑖𝑐𝑒 𝐶ℎ𝑎𝑛𝑔𝑒 = Δ𝑃 𝑃 = 𝑃𝑎𝑓𝑡𝑒𝑟 − 𝑃 𝐴𝑣𝑒𝑟𝑎𝑔𝑒(𝑃) So, 𝑒 = % 𝑄𝑢𝑎𝑛𝑡𝑖𝑡𝑦 𝐶ℎ𝑎𝑛𝑔𝑒 % 𝑃𝑟𝑖𝑐𝑒 𝐶ℎ𝑎𝑛𝑔𝑒 = ( 𝑄 𝑎𝑓𝑡𝑒𝑟 − 𝑄 𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑄 ) ( 𝑃𝑎𝑓𝑡𝑒𝑟 − 𝑃 𝐴𝑣𝑒𝑟𝑎𝑔𝑒(𝑃) ) 𝑃 𝑄 𝑃 = 100 𝑃𝑎𝑓𝑡𝑒𝑟 = 80 Δ𝑃 = −20 𝑄 = 100 𝑄 𝑎𝑓𝑡𝑒𝑟 = 400 Δ𝑄 = 300 𝑎𝑣𝑒𝑟𝑎𝑔𝑒(𝑄) 𝑎𝑣𝑒𝑟𝑎𝑔𝑒(𝑃) 𝐿𝑒𝑡′ 𝑠 𝑐𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑒 𝑒! 𝐴 𝐵
  • 13. Elasticity Actually, its not just change, its % of Change. 𝑒 = % 𝑄𝑢𝑎𝑛𝑡𝑖𝑡𝑦 𝐶ℎ𝑎𝑛𝑔𝑒 % 𝑃𝑟𝑖𝑐𝑒 𝐶ℎ𝑎𝑛𝑔𝑒 , but how to measure “% of Change”? Mesuring 2: Arc Elasticity % 𝑄𝑢𝑎𝑛𝑡𝑖𝑡𝑦 𝐶ℎ𝑎𝑛𝑔𝑒 = Δ𝑄 𝑄 = 𝑄 𝑎𝑓𝑡𝑒𝑟 − 𝑄 𝐴𝑣𝑒𝑟𝑎𝑔𝑒(𝑄) = 300 250 % 𝑃𝑟𝑖𝑐𝑒 𝐶ℎ𝑎𝑛𝑔𝑒 = Δ𝑃 𝑃 = 𝑃𝑎𝑓𝑡𝑒𝑟 − 𝑃 𝐴𝑣𝑒𝑟𝑎𝑔𝑒(𝑃) = −20 90 So, 𝑒 = % 𝑄𝑢𝑎𝑛𝑡𝑖𝑡𝑦 𝐶ℎ𝑎𝑛𝑔𝑒 % 𝑃𝑟𝑖𝑐𝑒 𝐶ℎ𝑎𝑛𝑔𝑒 = ( 𝑄 𝑎𝑓𝑡𝑒𝑟 − 𝑄 𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑄 ) ( 𝑃𝑎𝑓𝑡𝑒𝑟 − 𝑃 𝐴𝑣𝑒𝑟𝑎𝑔𝑒(𝑃) ) = | 1.2 ∗ 9 −2 | = 5.4 𝑃 𝑄 𝑃 = 100 𝑃𝑎𝑓𝑡𝑒𝑟 = 80 Δ𝑃 = −20 𝑄 = 100 𝑄 𝑎𝑓𝑡𝑒𝑟 = 400 Δ𝑄 = 300 𝑎𝑣𝑒𝑟𝑎𝑔𝑒(𝑃) 𝑎𝑣𝑒𝑟𝑎𝑔𝑒(𝑄)
  • 14. Elasticity Why “%” important? Think about the Case: 𝑃 𝑄 𝑃 = 100 𝑃𝑎𝑓𝑡𝑒𝑟 = 80 Δ𝑃 = −20 𝑄 = 100 𝑄 𝑎𝑓𝑡𝑒𝑟 = 125 (𝑄, 𝑃) = 100,100 (𝑄 𝑎𝑓𝑡𝑒𝑟, 𝑃𝑎𝑓𝑡𝑒𝑟) = 125,80 (1)What is arc 𝑒 = % 𝑄𝑢𝑎𝑛𝑡𝑖𝑡𝑦 𝐶ℎ𝑎𝑛𝑔𝑒 % 𝑃𝑟𝑖𝑐𝑒 𝐶ℎ𝑎𝑛𝑔𝑒 ? (2)What is the Revenue before and after?
  • 15. Elasticity Why “%” important? Think about the Case: 𝑃 𝑄 𝑃 = 100 𝑃𝑎𝑓𝑡𝑒𝑟 = 80 Δ𝑃 = −20 𝑄 = 100 𝑄 𝑎𝑓𝑡𝑒𝑟 = 125 (𝑄, 𝑃) = 100,100 (𝑄 𝑎𝑓𝑡𝑒𝑟, 𝑃𝑎𝑓𝑡𝑒𝑟) = 125,80 (1)What is arc 𝑒 = % 𝑄𝑢𝑎𝑛𝑡𝑖𝑡𝑦 𝐶ℎ𝑎𝑛𝑔𝑒 % 𝑃𝑟𝑖𝑐𝑒 𝐶ℎ𝑎𝑛𝑔𝑒 ? 𝑒 = −20/90 25/112.5 = | − 1| (2)What is the Revenue before and 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.
  • 16. Elasticity 𝑃 𝑄 𝑃 = 100 𝑃𝑎𝑓𝑡𝑒𝑟 = 80 Δ𝑃 = −20 𝑄 = 100 𝑄 𝑎𝑓𝑡𝑒𝑟 = 125 (𝑄, 𝑃) = 100,100 (𝑄 𝑎𝑓𝑡𝑒𝑟, 𝑃𝑎𝑓𝑡𝑒𝑟) = 125,80 (1)What is arc 𝑒 = % 𝑄𝑢𝑎𝑛𝑡𝑖𝑡𝑦 𝐶ℎ𝑎𝑛𝑔𝑒 % 𝑃𝑟𝑖𝑐𝑒 𝐶ℎ𝑎𝑛𝑔𝑒 ? 𝑒 = −20/90 25/112.5 = | − 1| (2)What is the Revenue before and 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. 𝑃𝑄 Why “%” important? Think about the Case:
  • 17. Elasticity 𝑃 𝑄 𝑃 = 100 𝑃𝑎𝑓𝑡𝑒𝑟 = 80 Δ𝑃 = −20 𝑄 = 100 (𝑄, 𝑃) = 100,100 (1) If we think 𝑒 = 5.4 ≫ 1 case. (2)What is the Revenue before and after? 𝑄 𝑎𝑓𝑡𝑒𝑟 = 400 Why “%” important? Think about the Case:
  • 18. Elasticity Why “%” important? Think about the Case: 𝑃 𝑄 𝑃 = 100 𝑃𝑎𝑓𝑡𝑒𝑟 = 80 Δ𝑃 = −20 𝑄 = 100 (𝑄, 𝑃) = 100,100 (1) If we think 𝑒 = 5.4 ≫ 1 case. (2)What is the Revenue before and after? 𝑅𝑒𝑣 𝑏𝑒𝑓𝑜𝑟𝑒 = 𝑃𝑄 = 10,000 𝑅𝑒𝑣 𝑎𝑓𝑡𝑒𝑟 = 𝑃𝑎𝑓𝑡𝑒𝑟 𝑄 𝑎𝑓𝑡𝑒𝑟 = 32,000 So, if e > 1, - Price down gain Revenue - Price Up lose Revenue 𝑄 𝑎𝑓𝑡𝑒𝑟 = 400
  • 19. 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↓
  • 20. 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
  • 22. 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?
  • 23. 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.
  • 24. 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
  • 25. 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
  • 26. 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
  • 27. 𝑃 𝑄 CS This is because the CS can be calculated by the Area on the graph.
  • 28. Producer Surplus(PS) can be calculated same way. 𝑃 𝑄 PS
  • 29. 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
  • 30. 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
  • 31. 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
  • 32. 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
  • 33. So, Welfare can be calculate: 𝑃 𝑄 Consumer Surplus(CS) + Producer Surplus(PS) CS PS
  • 34. How tax change D/S curves and the Dead Weight Loss See also; Lecture notes 2 Part B
  • 35. 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.
  • 36. 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
  • 37. 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
  • 38. 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: 𝑃𝑅𝐸𝐴𝐿 − 𝑃𝑏𝑒𝑓𝑜𝑟𝑒 = 𝑡𝑎𝑥 𝑐𝑜𝑛𝑠𝑢𝑚𝑒𝑟 𝑃𝑏𝑒𝑓𝑜𝑟𝑒 − 𝑃𝑎𝑓𝑡𝑒𝑟 = 𝑡𝑎𝑥 𝑝𝑟𝑜𝑑𝑢𝑐𝑒𝑟 𝑃𝑏𝑒𝑓𝑜𝑟𝑒 𝑃𝑎𝑓𝑡𝑒𝑟 𝑃 𝐷 𝑏 = 120 − 3𝑄
  • 39. Let’s calculate for this example! 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 𝑃𝑏𝑒𝑓𝑜𝑟𝑒 𝑃𝑎𝑓𝑡𝑒𝑟 𝑃𝑅𝐸𝐴𝐿 𝑃 𝐷 𝑏 = 120 − 3𝑄
  • 40. 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)
  • 41. 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
  • 42. Supply Side Taxation: 3 steps thinking: 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 𝑡𝑎𝑥 𝑐𝑜𝑛𝑠𝑢𝑚𝑒𝑟 + 𝑡𝑎𝑥 𝑝𝑟𝑜𝑑𝑢𝑐𝑒𝑟 = 𝑡𝑎𝑥 𝑃𝑏𝑒𝑓𝑜𝑟𝑒 𝑃𝑎𝑓𝑡𝑒𝑟 𝑃𝑅𝐸𝐴𝐿
  • 43. Let’s calculate for this example! 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: 𝑃𝑅𝐸𝐴𝐿 − 𝑃𝑏𝑒𝑓𝑜𝑟𝑒 = 𝑡𝑎𝑥 𝑐𝑜𝑛𝑠𝑢𝑚𝑒𝑟 𝑃𝑏𝑒𝑓𝑜𝑟𝑒 − 𝑃𝑎𝑓𝑡𝑒𝑟 = 𝑡𝑎𝑥 𝑝𝑟𝑜𝑑𝑢𝑐𝑒𝑟 𝑃𝑏𝑒𝑓𝑜𝑟𝑒 𝑃𝑎𝑓𝑡𝑒𝑟 𝑃 𝐷 𝑏 = 120 − 3𝑄
  • 44. Supply Side Taxation: 3 steps thinking: 𝑃 𝑄 Supply Curve Demand Curve 𝑃𝑏𝑒𝑓𝑜𝑟𝑒 𝑃𝑎𝑓𝑡𝑒𝑟 𝑃𝑅𝐸𝐴𝐿 𝑃𝑆 𝐵 = 5𝑄 𝑃 𝐷 = 120 − 3𝑄 𝑃𝑆 𝐴 = 5𝑄 + 8 Calculate before Equilibrium, 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 𝑡𝑎𝑥 𝑐𝑜𝑛𝑠𝑢𝑚𝑒𝑟 + 𝑡𝑎𝑥 𝑝𝑟𝑜𝑑𝑢𝑐𝑒𝑟 = 𝑡𝑎𝑥
  • 46. Let’s Calculate CS and PS before tax 𝑃 𝑄 Supply Curve Demand Curve 𝑃𝑏𝑒𝑓𝑜𝑟𝑒 𝑃𝑎𝑓𝑡𝑒𝑟 𝑃𝑅𝐸𝐴𝐿 𝑃𝑆 𝐵 = 5𝑄 𝑃 𝐷 = 120 − 3𝑄 CS PS
  • 47. Let’s Calculate CS and PS before tax 𝑃 𝑄 Supply Curve Demand Curve 𝑃𝑆 𝐵 = 5𝑄 𝑃 𝐷 = 120 − 3𝑄 CS PS Calculate before Equilibrium, 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
  • 48. 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 𝑃𝑏𝑒𝑓𝑜𝑟𝑒 = 75 120 0 𝑃𝑆 𝐴 = 5𝑄 + 8 𝑃𝑎𝑓𝑡𝑒𝑟 = 78 𝑃𝑅𝐸𝐴𝐿 = 70 𝑄 𝑎𝑓𝑡𝑒𝑟 = 14
  • 49. Let’s Calculate CS and PS after tax $8 (for producer) 𝑃 𝑄 Supply Curve Demand Curve 𝑃𝑆 𝐵 = 5𝑄 𝑃 𝐷 = 120 − 3𝑄 𝑃𝑏𝑒𝑓𝑜𝑟𝑒 = 75 120 0 𝑃𝑆 𝐴 = 5𝑄 + 8 𝑃𝑎𝑓𝑡𝑒𝑟 = 78 𝑃𝑅𝐸𝐴𝐿 = 70 CS PS The Welfare should be calculated based on - What consumer really pay - What producer really get So, for consumers they really pay 𝑃𝑎𝑓𝑡𝑒𝑟 = 78 for producers they really get 𝑃𝑅𝐸𝐴𝐿 = 70 Yes, taxation makes price difference Between consumers and producers.𝑄 𝑏𝑒𝑓𝑜𝑟𝑒 = 15 𝑄 𝑎𝑓𝑡𝑒𝑟 = 14
  • 50. Let’s Calculate CS and PS after tax $8 (for producer) 𝑃 𝑄 Supply Curve Demand Curve 𝑃𝑆 𝐵 = 5𝑄 𝑃 𝐷 = 120 − 3𝑄 𝑃𝑏𝑒𝑓𝑜𝑟𝑒 = 75 120 0 𝑃𝑆 𝐴 = 5𝑄 + 8 𝑃𝑎𝑓𝑡𝑒𝑟 = 78 𝑃𝑅𝐸𝐴𝐿 = 70 𝐶𝑆 𝑎𝑓𝑡𝑒𝑟 𝑃𝑆 𝑎𝑓𝑡𝑒𝑟 𝐶𝑆 𝑎𝑓𝑡𝑒𝑟 = (120 − 78) × 14 2 = 294 𝑃𝑆 𝑎𝑓𝑡𝑒𝑟 = (70 − 0) × 14 2 = 490 𝑄 𝑏𝑒𝑓𝑜𝑟𝑒 = 15 𝑄 𝑎𝑓𝑡𝑒𝑟 = 14
  • 51. Let’s Calculate Sum of Tax, collected from market. 𝑃 𝑄 Supply Curve Demand Curve 𝑃𝑆 𝐵 = 5𝑄 𝑃 𝐷 = 120 − 3𝑄 𝑃𝑏𝑒𝑓𝑜𝑟𝑒 = 75 120 0 𝑃𝑆 𝐴 = 5𝑄 + 8 𝑃𝑎𝑓𝑡𝑒𝑟 = 78 𝑃𝑅𝐸𝐴𝐿 = 70 Where is tax and why? 𝑄 𝑏𝑒𝑓𝑜𝑟𝑒 = 15 𝑄 𝑎𝑓𝑡𝑒𝑟 = 14
  • 52. Let’s Calculate Sum of Tax, collected from market. 𝑃 𝑄 Supply Curve Demand Curve 𝑃𝑆 𝐵 = 5𝑄 𝑃 𝐷 = 120 − 3𝑄 𝑃𝑏𝑒𝑓𝑜𝑟𝑒 = 75 120 0 𝑃𝑆 𝐴 = 5𝑄 + 8 𝑃𝑎𝑓𝑡𝑒𝑟 = 78 𝑃𝑅𝐸𝐴𝐿 = 70 consumers really pay 𝑃𝑎𝑓𝑡𝑒𝑟 = 78 producers really get 𝑃𝑅𝐸𝐴𝐿 = 70 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 𝑄 𝑎𝑓𝑡𝑒𝑟 = 14
  • 53. Compare before and after 𝑃 𝑄 Demand Curve 0 𝑄 𝑏𝑒𝑓𝑜𝑟𝑒𝑄 𝑎𝑓𝑡𝑒𝑟 𝑃 𝑄 CS PS 0 𝑃𝑏𝑒𝑓𝑜𝑟𝑒 before after 𝑄 𝑏𝑒𝑓𝑜𝑟𝑒
  • 54. Dead Weight Loss 𝑃 𝑄 Demand Curve 0 𝑄 𝑏𝑒𝑓𝑜𝑟𝑒𝑄 𝑎𝑓𝑡𝑒𝑟 𝑃 𝑄 CS PS 0 𝑃𝑏𝑒𝑓𝑜𝑟𝑒 before after 𝑄 𝑏𝑒𝑓𝑜𝑟𝑒 This is Dead Weight Loss This is a Social Welfare Loss that caused by tax
  • 55. 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
  • 57. 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
  • 58. 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
  • 59. 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
  • 60. Budget Constrain (make sure both axis is Q) - Pizza($16 each) and Movie($8 each) - Your weekly budget is $96 𝑀𝑜𝑣𝑖𝑒 𝑃𝑖𝑧𝑧𝑎 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
  • 61. 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.
  • 62. 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
  • 63. 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? 𝑝𝑖𝑧𝑧𝑎 𝑄 𝑈𝑡𝑖𝑙𝑖𝑡𝑦 12 2 4 5 5
  • 64. 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 𝑈𝑡𝑖𝑙𝑖𝑡𝑦 12 2 4 5 5
  • 65. 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 𝑝𝑖𝑧𝑧𝑎 𝑄 𝑈𝑡𝑖𝑙𝑖𝑡𝑦 12 2 4 5 5
  • 66. 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 𝑀𝑜𝑣𝑖𝑒 𝑃𝑖𝑧𝑧𝑎 𝑄 𝑄 12 6
  • 67. 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 𝑎𝑛𝑑 3 𝑀𝑜𝑣𝑖𝑒 𝑃𝑖𝑧𝑧𝑎 𝑄 𝑄 12 4 2 2 4 93 𝑈 = 𝑄 𝑀 𝑄 𝑃 = 2
  • 68. 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 𝑎𝑛𝑑 3 𝑀𝑜𝑣𝑖𝑒 𝑃𝑖𝑧𝑧𝑎 𝑄 𝑄 12 4 2 2 4 93 𝑈 = 𝑄 𝑀 𝑄 𝑃 = 3
  • 69. MRS(Marginal Rates of Substitute) on Indifference curve Think about 𝑈 = 2 = 𝑄 𝑀 𝑄 𝑃. 𝑀𝑜𝑣𝑖𝑒 𝑃𝑖𝑧𝑧𝑎 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
  • 70. MRS(Marginal Rates of Substitute) and Marginal Utility [advance] 𝑀𝑜𝑣𝑖𝑒 𝑃𝑖𝑧𝑧𝑎 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? 𝑝𝑖𝑧𝑧𝑎 𝑄 𝑈𝑡𝑖𝑙𝑖𝑡𝑦 12 2 4 5 5
  • 71. 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 𝑀𝑜𝑣𝑖𝑒 𝑃𝑖𝑧𝑧𝑎 𝑄 𝑄 12 4 2 2 4 93 𝑈 = 𝑄 𝑀 𝑄 𝑃 = 2 𝐴 𝐵 𝐶 𝑝𝑖𝑧𝑧𝑎 𝑄 𝑈𝑡𝑖𝑙𝑖𝑡𝑦 12 2 4 5 5
  • 72. 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. 𝑀𝑜𝑣𝑖𝑒 𝑃𝑖𝑧𝑧𝑎 𝑄 𝑄 12 4 2 2 4 93 𝑈 = 𝑄 𝑀 𝑄 𝑃 = 2 16𝑄 𝑝𝑖𝑧𝑧𝑎 + 8𝑄 𝑚𝑜𝑣𝑖𝑒 = $96
  • 73. Budget constrain and MRS 1. How to calculate tangent of Budget constrain? 𝑀𝑜𝑣𝑖𝑒 𝑃𝑖𝑧𝑧𝑎 𝑄 𝑚𝑜𝑣𝑖𝑒 𝑄 𝑝𝑖𝑧𝑧𝑎 12 4 2 2 4 93 16𝑄 𝑝𝑖𝑧𝑧𝑎 + 8𝑄 𝑚𝑜𝑣𝑖𝑒 = $96 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
  • 74. Budget constrain and MRS[advance] 𝑀𝑜𝑣𝑖𝑒 𝑃𝑖𝑧𝑧𝑎 𝑄 𝑄 12 4 2 2 4 93 𝑈 = 𝑄 𝑀 𝑄 𝑃 16𝑄 𝑝𝑖𝑧𝑧𝑎 + 8𝑄 𝑚𝑜𝑣𝑖𝑒 = $96 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…
  • 75. Budget constrain and MRS[advance] 𝑀𝑜𝑣𝑖𝑒 𝑃𝑖𝑧𝑧𝑎 𝑄 𝑄 12 4 2 2 4 93 𝑈 = 𝑄 𝑀 𝑄 𝑃 16𝑄 𝑝𝑖𝑧𝑧𝑎 + 8𝑄 𝑚𝑜𝑣𝑖𝑒 = $96 2. How to calculate MRS 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
  • 76. So, where is the optimal? (Max U under the badget) 𝑀𝑜𝑣𝑖𝑒 𝑃𝑖𝑧𝑧𝑎 𝑄 𝑄 12 4 2 2 4 93 𝑈 = 𝑄 𝑀 𝑄 𝑃 2. How to calculate MRS 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
  • 79. 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
  • 80. Let us think in Qualitative first. 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
  • 81. Let us think in Qualitative first. 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
  • 82. Remember Budget constrain 𝑀𝑜𝑣𝑖𝑒 𝑃𝑖𝑧𝑧𝑎 𝑄 𝑚𝑜𝑣𝑖𝑒 𝑄 𝑝𝑖𝑧𝑧𝑎 12 4 2 2 4 93 16𝑄 𝑝𝑖𝑧𝑧𝑎 + 8𝑄 𝑚𝑜𝑣𝑖𝑒 = $96 6 - 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? 16
  • 83. Remember Budget constrain 𝑀𝑜𝑣𝑖𝑒 𝑃𝑖𝑧𝑧𝑎 𝑄 𝑝𝑖𝑧𝑧𝑎 12 4 2 2 4 93 6 It become like this. So what? 16 𝑄 𝑚𝑜𝑣𝑖𝑒 16𝑄 𝑝𝑖𝑧𝑧𝑎 + 6𝑄 𝑚𝑜𝑣𝑖𝑒 = $96
  • 84. Remember Budget constrain 𝑀𝑜𝑣𝑖𝑒 𝑃𝑖𝑧𝑧𝑎 𝑄 𝑝𝑖𝑧𝑧𝑎 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 𝑄 𝑚𝑜𝑣𝑖𝑒 16𝑄 𝑝𝑖𝑧𝑧𝑎 + 6𝑄 𝑚𝑜𝑣𝑖𝑒 = $96𝐴 𝐵
  • 85. Move the new Budget constrain to tangent of Indifference curve. 𝑀𝑜𝑣𝑖𝑒 𝑃𝑖𝑧𝑧𝑎 𝑄 𝑝𝑖𝑧𝑧𝑎 12 4 2 2 4 93 6 16 𝑄 𝑚𝑜𝑣𝑖𝑒 16𝑄 𝑝𝑖𝑧𝑧𝑎 + 6𝑄 𝑚𝑜𝑣𝑖𝑒 = $96 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
  • 86. Move the new Budget constrain to tangent of Indifference curve. 𝑀𝑜𝑣𝑖𝑒 𝑃𝑖𝑧𝑧𝑎 𝑄 𝑝𝑖𝑧𝑧𝑎 12 4 2 2 4 93 6 16 𝑄 𝑚𝑜𝑣𝑖𝑒 16𝑄 𝑝𝑖𝑧𝑧𝑎 + 6𝑄 𝑚𝑜𝑣𝑖𝑒 = $96 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.
  • 87. Move the new Budget constrain to tangent of Indifference curve. 𝑀𝑜𝑣𝑖𝑒 𝑃𝑖𝑧𝑧𝑎 𝑄 𝑝𝑖𝑧𝑧𝑎 12 4 2 2 4 93 6 16 𝑄 𝑚𝑜𝑣𝑖𝑒 16𝑄 𝑝𝑖𝑧𝑧𝑎 + 6𝑄 𝑚𝑜𝑣𝑖𝑒 = $96 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.
  • 88. Remember Budget constrain 𝑀𝑜𝑣𝑖𝑒 𝑃𝑖𝑧𝑧𝑎 𝑄 𝑝𝑖𝑧𝑧𝑎 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 𝑄 𝑚𝑜𝑣𝑖𝑒 16𝑄 𝑝𝑖𝑧𝑧𝑎 + 6𝑄 𝑚𝑜𝑣𝑖𝑒 = $96
  • 89. Summary of Income Effect and substitution effect 𝑀𝑜𝑣𝑖𝑒 𝑃𝑖𝑧𝑧𝑎 𝑄 𝑝𝑖𝑧𝑧𝑎 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.
  • 90. Want to learn more? • See Entrepreneurial Economics #2! • https://www.slideshare.net/ryouen/170925-entrepreneurial- economics2
  • 91. 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