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MIT 15 010 - Consumer and Producer Surplus

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OUTLINE OF TODAY’S RECITATIONConsumer Surplus1.1 Consumer Surplus2.1 Tax2.1 Tax3.1 DWL with a Taxby the consumer Es - Ed4.1 Gasoline at Market Equilibrium and with a Tax4.2.5 Deadweight loss due to Maximum Price PolicyEs - EdSloan School of Management 15.010/15.011 Massachusetts Institute of Technology RECITATION NOTES #2 Surplus Analysis with Government Intervention Friday - September 17, 2004 OUTLINE OF TODAY’S RECITATION 1. Review of Consumer and Producer Surplus: brief review from last recitation 2. Government Intervention: how can the Government intervene and what is the effect 3. Deadweight Loss: what it is, why it is important and how it is calculated 4. Numeric Examples: Two exercises to understand how all concepts work together 1. REVIEW OF CONSUMER AND PRODUCER SURPLUS 1.1 Consumer Surplus 1.2 Producer Surplus 1.1 Consumer Surplus P QDS Q* P* CS Consumer’s surplus is the difference between what the consumer is willing to pay, and what he actually pays. Intuitively, it is “the amount left in the hands of the consumer”. If a consumer has a demand curve D, like the one shown in the chart, and the Equilibrium is reached for a price P*, then he will buy Q* and will be left with a surplus equal to the shaded triangle. 11.2 Producer Surplus P QDS Q* P* PS Producer’s surplus is the difference between the amount that the producer is paid and the amount he was willing to accept. Intuitively, it is “the amount left in the hands of the producer”. If a producer has a supply curve S and the Equilibrium is reached for a price P*, then he will sell Q* and will be left with a surplus equal to the shaded triangle. 2. GOVERNMENT INTERVENTION 2.1 Tax 2.2 Subsidy 2.3 Quota 2.4 Tariff 2.1 Tax When a government applies a tax (t) to a good, the price that consumers pay (Pd) is higher than the price that suppliers receive for the good (Ps): PQDSQ* PDt PS PD = PS + t The total amount of tax the Government will collect (Government’s Surplus) is equal to the area: t * Q* = (PD - PS) * Q* 2.2 Subsidy When a government applies a subsidy (s) to a good, the price that consumers pay for the good (Pd) is lower than the price that suppliers receive for the good (Ps): PQDSQ* PS s PDPD = PS - s (NOTE: a subsidy is a negative tax!) The total amount of subsidy the Government will have to pay is equal to the area: s * Q* = (PS – PD) * Q* This is the Government’s loss of surplus. (In the examples section you can see what 2happens if the Government sets a maximum price for the goods instead of a subsidy) 2.3 Tariff Without government intervention, at world price (Pw), domestic producers supply Q and foreign producers supply Q*-Q. P QDSdomestic Q* Q Pw Imports When a government applies a tariff to a good, it is setting a tax on the quantities of good that foreign producers sell in the country. In effect, it is raising the price of foreign goods from Pw to Pd: Pd = Pw + tariff P QDSdomestic Q* Q Pw ImportsPd Qi Qi* } Tariff Domestic producers will produce up to a level Qi, while foreign producers will produce (Qi* - Qi) The total demanded amount will be: Qi* = Qi + imports The total amount of tariff the Government will collect is equal to the area: imports * tariff = (Qi*- Qi) * (PD- Pw) This is the Government’s surplus. 2.4 Quota 3When a government applies a quota to a good, it is setting the maximum level of quantity that foreign producers can sell in the country. Domestic producers will produce up to a level Qi, while foreign producers will produce (Qi* - Qi). The total demanded amount will be: Qi* = Qi + quota P QDSQ* Q Pw Quota Pd Qi Qi* NOTE: in a quota the Government does not collect any money! In the quota case the foreign producers receive the surplus, whereas in the tariff case the government does This above graphic representation of a quota is equivalent to the one done in the lecture, where the market supply curve is derived more intuitively, as shown below. The only difference is that the supply curve for domestic producers is shifted, but the areas and quantities remain the same. P QDSPw Quota Q Q1 Q2 Q* Amounts produced: Local producers: Q + (Q2-Q1) Foreign producers: (Q1-Q) 43. DEADWEIGHT LOSS 3.1 DWL with a Tax 3.2 DWL with a Tariff or a Quota 3.3 Pass through formula 3.1 DWL with a Tax When the Government intervenes with a tax the total surplus available in an economy is smaller than the total surplus available when there is no intervention: W/Tax(CS + PS + Gov S) < W/o Tax(CS + PS) The amount of surplus lost in the economy is called Deadweight Loss (DWL) and is represented by the shaded area in the chart. PQDSCS PDt PS Q* DWL PS Gov S 3.2 DWL with a Quota or Tariff When the Government intervenes with a Tariff or a Quota the total surplus available in an economy is smaller than the total surplus available when there is no intervention: ∆ Consumer Surplus = -(A+B+D+C) ∆ Producer Surplus = A Quota: Gain to Foreign Producers = D Tariff: Gain to Government = D DWL = -(B+C) The amount of surplus lost in the economy is called Deadweight Loss (DWL) and is represented by the sum of the two triangles B and C. C B D P QDS Q* Pw Quota PdQi Qi* }Tariff A 3.3 Pass through formula When a tax is applied, it generally affects both producers and consumers and not necessarily in the same way. We can graphically demonstrate that if the demand for a good is very elastic, producers will bear most of the tax burden. Instead, if the demand is very inelastic, the consumers will bear most of the tax burden. In order to calculate the percentage of a tax that will be paid by the consumer, we can use the pass-through formula: 5% of tax paid = Es . by the consumer Es - Ed where Es is the price elasticity of supply, and Ed is the price elasticity of demand. 4. NUMERIC EXAMPLES 4.1 Gasoline at Market Equilibrium and with a Tax 4.2 Dynamic Changes in Market Equilibrium in the Gasoline Market 4.3 Government sets a Maximum Price 4.1 Gasoline at Market Equilibrium with a Tax 4.1.1 Available Information Let’s assume that: Demand curve for Gasoline: Qd = 105.5 – 5.5. P (P in $/gallon, Q in Bn gallons) Supply curve for Gasoline: Qs = 20 + 80 P C B A S D Po = 19.18 P* = 1.00 Qo = 20 Q* = 100 Q (billion gallons) 4.1.2 Determine the Equilibrium In order to do so, we


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