Taxes and Subsidies - Chapter 6 Review

University of Missouri: Chapter 6 - Taxes and Subsidies

Key Concepts of Taxes and Subsidies

• Tax Wedge: Both taxes and subsidies create a "tax wedge," which is the difference between the price buyers pay and the price sellers receive.

• Tax Incidence:

  • Who ultimately pays a tax depends on the elasticity of supply and demand, not on how tax laws are written or who physically sends the check to the government.

  • This principle is summarized as "Elasticity equals escape." The side of the market (buyers or sellers) with the relatively more elastic curve will bear less of the tax burden, as they can more easily "escape" the market or adjust their behavior.

  • Conversely, the side with the relatively less elastic curve will pay more of the tax.

  • This debunks the economic myth that businesses simply "pass on" taxes to customers. In all but extreme cases, any commodity tax will be shared between consumers and businesses, with the exact fraction depending on relative elasticities.

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• Deadweight Loss:

  • Taxes and subsidies both create deadweight losses, also known as the "value of wasted resources" (VWR).

  • The size of the deadweight loss is also determined by the elasticity of supply and demand.

  • This is metaphorically described as "The bucket leaks," meaning that the government raises revenue at a greater cost to overall welfare.

Types of Taxes

• Per-Unit Tax: A fixed dollar amount applied to each unit traded.

  • Example: $1 per pound of tofu, gasoline, cigarettes, alcohol.</p></li></ul></li><li><p><strong>Sales Taxes:</strong> Typically a percentage of the price.</p><ul><li><p>Example: 5$168,600), Medicare (2.9% total).

  • These create large "tax wedges" in labor markets.

• Property Taxes: Not directly tied to a transaction; based on the value of an asset (like a house), regardless of whether it is bought or sold.

• Income Taxes: Levied on individual or corporate income.

  • Example: Federal income tax (e.g., highest marginal rate of 37%), State income tax (e.g., 4.8% in Missouri).

Understanding the Tax Wedge

• When a tax is imposed, it creates a wedge between the price buyers pay and the price sellers receive.

• Impact on Quantity: This wedge leads to a reduction in the quantity traded compared to the market equilibrium without the tax.

• Tax Revenue Calculation: Total tax revenues are calculated as the tax per unit multiplied by the final quantity traded after the tax is implemented ($Tax imes Q_{after-tax}$).

  • Example: If a $1/lb tax on tofu reduces quantity traded to$Q2$, then tax revenues are$1 imes Q2$.</p></li><li><p>The buyer's share of tax revenue = Buyer's portion of tax per unit$ imes Q2$.</p></li><li><p>The seller's share of tax revenue = Seller's portion of tax per unit$ imes Q2$.</p></li></ul></li></ul><h4 id="0a118731-0428-4de0-a763-ae7d3b480619" data-toc-id="0a118731-0428-4de0-a763-ae7d3b480619" collapsed="false" seolevelmigrated="true">Tax Incidence: Who Pays the Tax?</h4><ul><li><p><strong>Definition:</strong> Tax incidence is the ultimate economic burden of a tax, regardless of who is legally required to send the tax payment to the government.</p></li><li><p><strong>Graphical Representation:</strong></p><ul><li><p>When a tax is placed on <strong>suppliers</strong>, the supply curve shifts upward by the amount of the tax. The new equilibrium results in a higher price paid by buyers and a lower price received by sellers.</p></li><li><p>When a tax is placed on <strong>buyers</strong>, the demand curve shifts downward by the amount of the tax. The new equilibrium results in a lower price received by sellers, while buyers effectively pay more per unit (price + tax).</p></li><li><p><strong>Crucially, the final prices paid by buyers and received by sellers, and thus the tax incidence, are the same regardless of whether the tax is legally levied on buyers or sellers.</strong> What matters is the tax wedge itself.</p></li></ul></li><li><p><strong>Effect of Elasticity on Incidence:</strong></p><ul><li><p><strong>Demand more elastic than supply:</strong> Sellers bear more of the tax burden.</p></li><li><p><strong>Supply more elastic than demand:</strong> Buyers bear more of the tax burden.</p></li></ul></li></ul><h5 id="dbd02299-9a0d-4ea2-8c82-d0687b813542" data-toc-id="dbd02299-9a0d-4ea2-8c82-d0687b813542" collapsed="false" seolevelmigrated="true">Polar Cases for Tax Incidence (Perfect Elasticity)</h5><ul><li><p><strong>Perfectly Elastic Demand:</strong> If demand is perfectly elastic (horizontal demand curve), buyers can perfectly escape the tax. The entire tax burden falls on the <strong>sellers</strong>.</p></li><li><p><strong>Perfectly Elastic Supply:</strong> If supply is perfectly elastic (horizontal supply curve), sellers can perfectly escape the tax. The entire tax burden falls on the <strong>buyers</strong>.</p></li><li><p><strong>Perfectly Inelastic Demand:</strong> If demand is perfectly inelastic (vertical demand curve), buyers have no escape. The entire tax burden falls on the <strong>buyers</strong>, and the quantity traded does not change.</p></li><li><p><strong>Perfectly Inelastic Supply:</strong> If supply is perfectly inelastic (vertical supply curve), sellers have no escape. The entire tax burden falls on the <strong>sellers</strong>, and the quantity traded does not change.</p><ul><li><p><strong>Historical Footnote:</strong> This concept led 19th-century social reformers like Henry George to advocate for taxes on land, as land is largely inelastically supplied, ensuring the burden falls on landowners.</p></li></ul></li></ul><h5 id="5e01c5ac-8511-471a-ac4e-4cb92d6e909f" data-toc-id="5e01c5ac-8511-471a-ac4e-4cb92d6e909f" collapsed="false" seolevelmigrated="true">Practical Applications of Tax Incidence</h5><ul><li><p><strong>Cigarette Taxes:</strong> If cigarette manufacturers can easily move production or avoid state taxes, a larger portion of the tax will fall on smokers. High state taxes may also lead to consumers purchasing cigarettes in other states, reducing the effectiveness of the tax as a smoking deterrent within that state.</p></li><li><p><strong>Health Insurance Mandates:</strong> Mandates requiring employers to provide health insurance effectively act as a tax on labor. This will tend to reduce wages, with the share of the cost borne by employees depending on the relative elasticities of labor supply and demand. Firms may also have incentives to replace workers with machines.</p></li><li><p><strong>Analogy:</strong> In a long-distance relationship, the partner who is more committed (less elastic in their willingness to endure travel) will do more of the driving, bearing a larger "tax" of travel costs.</p></li></ul><h4 id="7fce9f3f-0625-4842-89f9-a69fac4d4e6a" data-toc-id="7fce9f3f-0625-4842-89f9-a69fac4d4e6a" collapsed="false" seolevelmigrated="true">Deadweight Loss of Taxes</h4><ul><li><p><strong>Definition:</strong> Deadweight loss (DWL) occurs because a tax distorts market incentives, leading to a reduction in the quantity traded below the efficient level. It represents the loss in total surplus (consumer surplus + producer surplus) that is not offset by government revenue.</p></li><li><p><strong>Graphical Explanation:</strong></p><ul><li><p><strong>Without Tax:</strong> Consumer surplus (CS) and producer surplus (PS) are maximized.</p></li><li><p><strong>With Tax:</strong> The market shrinks. CS and PS both decrease. Part of this loss is captured by the government as tax revenue. However, a portion (the DWL) is simply lost welfare. These are trades that would have been mutually beneficial but no longer occur due to the tax.</p></li><li><p>For example, in a diagram where initial CS =$A+B+C$and PS =$D+E+F$, after a tax, CS =$A$, PS =$F$, and Tax Revenues =$B+D$. The areas$C+E$represent the deadweight loss.</p></li></ul></li><li><p><strong>Relationship with Elasticity:</strong></p><ul><li><p>Deadweight losses are <strong>larger</strong> when demand and/or supply curves are more elastic, because the quantity traded is more sensitive to the price change caused by the tax, resulting in a larger reduction in trades.</p></li><li><p>If demand and/or supply curves are inelastic, a tax will deter fewer trades, leading to a <strong>smaller</strong> deadweight loss.</p></li></ul></li><li><p><strong>The "Bucket Leaks" Metaphor:</strong> This implies that for every dollar of tax revenue raised, the reduction in overall welfare (consumer and producer surplus) is greater than one dollar.</p></li></ul><h5 id="224ea8a1-6a3d-4ec4-8412-ae7f26e36f9d" data-toc-id="224ea8a1-6a3d-4ec4-8412-ae7f26e36f9d" collapsed="false" seolevelmigrated="true">When a Tax Causes No Deadweight Loss</h5><ul><li><p>A tax will not cause a deadweight loss if either the supply curve or the demand curve is <strong>perfectly inelastic</strong> (vertical).</p></li><li><p><strong>Reason:</strong> When supply or demand is perfectly inelastic, the quantity traded does not change in response to the tax. While buyers and/or sellers still bear the tax burden, no efficient trades are prevented, thus no deadweight loss occurs.</p></li><li><p>This provides another argument for a Georgian-style land tax, as land is considered to have perfectly inelastic supply.</p></li></ul><h5 id="5e645f39-59b6-4778-aa48-bb07e242b6e3" data-toc-id="5e645f39-59b6-4778-aa48-bb07e242b6e3" collapsed="false" seolevelmigrated="true">Deadweight Loss and Zero Tax Revenue</h5><ul><li><p>It is <strong>false</strong> that if a tax raises no revenue, it will produce no deadweight loss.</p></li><li><p>A sufficiently high tax can reduce the quantity traded to <strong>zero</strong>, resulting in$0$tax revenue ($Tax imes 0 = 0$).</p></li><li><p>However, a significant deadweight loss will still exist because all the potentially beneficial trades that <em>would have occurred</em> in the absence of the tax are now prevented.</p></li></ul><h5 id="6d914187-e096-45d3-b1aa-28cf63c155b3" data-toc-id="6d914187-e096-45d3-b1aa-28cf63c155b3" collapsed="false" seolevelmigrated="true">Other Implications of High Taxes</h5><ul><li><p>Sufficiently high taxes can lead to the emergence of <strong>illegal or black markets</strong> to avoid the tax.</p><ul><li><p>Example: Discrepancies in cigarette taxes between states (e.g., Missouri:$0.17/pack vs. New York: $5.35/pack) can incentivize smuggling or sales of single cigarettes ("loosies"). This also presents differential impacts on law enforcement.</p></li></ul></li></ul><h4 id="fbafc92c-1e4d-4194-a544-9420313957c8" data-toc-id="fbafc92c-1e4d-4194-a544-9420313957c8" collapsed="false" seolevelmigrated="true">Subsidies</h4><ul><li><p><strong>Definition:</strong> A subsidy is essentially a reverse tax, where the government directly gives money to consumers or producers for each unit traded.</p><ul><li><p>Subsidy =$Price{received by sellers} - Price{paid by buyers}$.</p></li></ul></li><li><p><strong>Impact of Subsidies:</strong></p><ul><li><p>Similar to taxes, who ultimately benefits from a subsidy (or bears its cost) does not depend on who receives the check from the government.</p></li><li><p>Who benefits depends on the <strong>relative elasticities of demand and supply</strong>.</p></li><li><p>Subsidies increase the quantity traded beyond the efficient level (the quantity that would be traded without government intervention).</p></li><li><p>Subsidies must be paid for by taxpayers.</p></li></ul></li><li><p><strong>Deadweight Loss of Subsidies:</strong></p><ul><li><p>Despite benefits to producers and consumers through increased quantity and more favorable prices, subsidies also create a <strong>deadweight loss</strong>.</p></li><li><p>This is because the government incurs a cost greater than the combined increase in consumer and producer surplus.</p></li><li><p><strong>Graphical Explanation:</strong> The cost to the government is the total subsidy amount ($Subsidy imes Q_{after-subsidy}$). The gains in consumer surplus and producer surplus are less than this total cost, with the difference being the deadweight loss.</p></li></ul></li></ul><h5 id="54ffb421-a376-4bd7-81d1-82904d5f1a6c" data-toc-id="54ffb421-a376-4bd7-81d1-82904d5f1a6c" collapsed="false" seolevelmigrated="true">Applications of Subsidies</h5><ul><li><p><strong>Agricultural Water Subsidies (e.g., California's Central Valley):</strong> Farmers often pay significantly less for water than its actual cost ($20-$30/acre-foot vs. 200-$500/acre-foot). If the demand for California cotton is more elastic than the supply of cotton from farmers (meaning farmers' ability to adjust their production in response to price changes for water is limited), the benefit of these water subsidies largely accrues to the cotton sellers (farmers).

  • Economics of "Free" Goods:

    • Making it Illegal to Charge: This typically leads to shortages.

    • Large Subsidies: A subsidy large enough to drive the price to consumers down to 0$$ will result in a significant increase in quantity traded, but also lead to large deadweight losses because the cost to taxpayers for each unit is high, exceeding the value placed on those units by society.

  Reasons for Government Intervention (Taxes and Subsidies)

  • From an economic perspective, taxes and subsidies are often used to address market failures.

  • This includes situations involving public goods and externalities, which will be explored in later chapters. These interventions aim to correct inefficiencies by altering prices and quantities to align private incentives with social welfare. However, as demonstrated, these interventions come with inherent deadweight losses.

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