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Week 4 – Elasticity, Tax Incidence and Tax Burden Note: first midterm – Friday Oct 26 at 3 p.m. Elasticity = sensitivity or reponsiveness Changes in one variable as another variable changes How sensitive is the quantity demanded to changes in the price of the product? Answer is given by elasticity of demand. How sensitive is the quantity of tomatoes supplied by businesses to changes in the price of tomatoes in Ontario? Answer is given by the elasticity of supply of tomatoes in Ontario. Elasticity of Demand ED = dQ/dP x P/Q ED = percentage change in quantity demanded percentage change in price ….how consumers respond to a change in market price Elasticity of Supply ES = dQ/dP x P/Q ES = percentage change in quantity supplied percentage change in price …how producers respond to a change in market price If demand is P = 100 – Q, what is the elasticity of demand at Q = 80? At Q = 80, P = $20 ED = dQ/dP x P/Q = 1/(-1) x 20/80 = ¼ What does it mean to say that the elasticity of demand at this point is ¼? It means that if P = $20 and the price changes by 4%, we expect that the quantity demanded will change by about 1%. (Why “about”?) Terminology: Demand is elastic if ED > 1 Demand is inelastic if ED < 1 Demand is unit(ary) elastic if ED = 1 Ripley’s Believe-it-or-not Strange, but true, fact Elasticity is different at every different point along a linear demand curve P A B C Demand Curve Q Is a linear demand curve realistic? Thinking about different goods, some have more elastic demands; others have less elastic demands. What affects elasticity of demand? Availability of close substitutes is key Also amount spent on this good by the consumer How are elasticity of demand and changes in revenue related? See it on a graph (when demand is elastic): P A B C Demand Curve Q When demand is inelastic P A B C Demand Curve Q When demand is unit elastic P A B C Demand Curve Q When demand is elastic, a fall in price will raise total revenue When demand is elastic, a rise in price will lower total revenue When demand is inelastic, a fall in price will lower total revenue When demand is inelastic, a rise in price will raise total revenue When demand is unit elastic, a fall or a rise in price will have no effect on total revenue P A B C Demand Curve P Elasticity and Taxation An illustration of the use of “elasticity” Think about the tax on one particular product (not a general tax on many products) – e.g., gasoline, liquor, cigarettes This is called an “excise” tax Could be a “flat-rate” tax e.g., $5 per bottle of liquor, $0.30 per litre of gasoline, $10 per carton of cigarettes Could be an “ad-valorem” tax e.g., 10% of the price on a bottle of liquor, 25% on a litre of gasoline, 30% on a carton of cigarettes. To keep it simple, we look only at flat-rate excise tax. Two interesting questions (and elasticity comes into both!): 1. Who really pays an excise tax, and what does this depend on? 2. How does taxation affect the allocation of society’s economic resources and economic well-being? In economics language: 1. What is the incidence of an excise tax (who bears the burden of an excise tax)? 2. How much is the excess burden of an excise tax (also known as the deadweight loss due to the tax)? Incidence of an excise tax Political Science – Government decides who will bear the tax by levying it on the consumers (buyers) or on the producers (sellers). Economics – Statutory incidence ≠ Economic Incidence The market decides who will bear the tax – depends on how consumers and producers react to the tax. In other words: incidence of the tax depends on the elasticity of demand and the elasticity of supply. Economic analysis: A tax drives a “wedge” between buyers and sellers. Buyers pay one price (including the tax), but sellers receive another price. We can show this on graph by: If the tax is levied on consumers, we will have two demand curves. One represents the amount buyers pay, the other represents the amount sellers receive. Imagine a tax of $10 per sheet on plywood sheets… Price $60 $50 $40 Tax (per unit amount) $25 Original Demand (D) $15 Net-of-tax Demand (D-T) 0 100,000 350,000 Market for 4’ x 8’ sheets of ¾” plywood Quantity Per month Demand was: D: P = 60 - .0001Q This is now the “gross-of-tax” demand curve New “net-of-tax” demand curve is: D-T: P = 50 - .0001Q If, instead, the tax is levied on sellers… If the tax is levied on producers, we will have two supply curves. The original supply curve represents the net amount sellers receive (not including the tax) for supplying different numbers of units of the good. The S+T curve represents the amount buyers will pay for the same numbers of units of the good (including the tax). Imagine again a tax of $10 per sheet on plywood sheets, this time levied on sellers… Price (S+T) Gross amount paid by buyers to suppliers (including tax) $35 $25 Original Supply (S) net-of-tax Tax (T) $21 $15 $11 0 100,000 350,000 Market for 4’ x 8’ sheets of ¾” plywood Quantity Per month Supply was: S: P = 11 + .00004Q This is now the “net-of-tax” supply curve The gross-of-tax supply curve (the amount buyers will have to pay to suppliers – including the tax) is: S+T: P = 21 + .00004Q Analyzing the economic incidence of a tax on consumers/buyers: Price $60 Supply $25 Demand $11 0 350,000 Market for 4’ x 8’ sheets of ¾” plywood Quantity Per month Analyzing the economic incidence of a tax on producers/sellers: Price $60 Supply $25 Demand $11 0 350,000 Market for 4’ x 8’ sheets of ¾” plywood Quantity Per month Buyers’ share of tax = P1 – P0 Sellers’ share of tax = P0 – PS Note that statutory incidence ≠ economic incidence Tax is levied by governments on either consumers or producers. However, tax is generally shared between buyers and sellers. Amount that buyers pay vs. amount sellers pay depends on elasticity of demand and elasticity of supply according to this formula: BS/SS = ES/ED The math of a tax on buyers: The math of a tax on sellers: Compare the results: Does our elasticity formula work? Incidence of an excise tax with extreme elasticities: Excess Burden of an Excise Tax When a tax is levied, it changes the behaviour of buyers and sellers. Because the gross price is higher, consumers want to consume less. Because the net price is lower, suppliers want to supply less. Therefore, less output is produced and consumed in this industry (i.e., economic resources are reallocated to other industries and away from this industry) How much well-being is lost as a result of the tax? Well-being can be measured as the sum of consumer surplus + producer surplus Consumer surplus is the surplus of consumer utility over the amount paid for the good (measured in dollars). Producer surplus is the surplus of revenues to producers over the amount necessary to get them to supply the good (measured in dollars) Identify consumer surplus and producer surplus on this graph: Price $60 Supply $25 Demand $11 0 350,000 Market for 4’ x 8’ sheets of ¾” plywood Quantity Per month Now, look at the effects on consumer surplus and producer surplus of a tax on consumers: Price $60 Supply $25 Demand $11 0 350,000 Market for 4’ x 8’ sheets of ¾” plywood Quantity Per month Now look at the effects on consumer surplus and producer surplus of a tax on sellers: Price $60 Supply $25 Demand $11 0 350,000 Market for 4’ x 8’ sheets of ¾” plywood Quantity Per month Identify on the graphs: Amount of tax revenue Amount of tax revenue “paid” by consumers (buyers’ share of total tax paid) Amount of tax revenue “paid” by suppliers (suppliers’ share of total tax paid) Loss of consumer surplus Loss of producer surplus Deadweight Loss (Excess Burden) How is excess burden affected by elasticity? Let’s look at some examples. The math of excess burden (tax on buyers): The math of excess burden (tax on suppliers): Remember, taxes bring benefits too. We have only been looking at the costs of taxation.