Economics: Chapter 7 - Taxes

Fundamental Principles and Mechanics of Excise Taxation

• Definition of an Excise Tax:

  • An excise tax is a per-unit tax levied on the purchase or sale of a specific good or service.

  • Rather than being assessed as a flat percentage on broad economic activities, it attaches to the physical volume or transaction units of a specified commodity.

• Statutory Examples in Canada:

  • Motor Vehicle Fuel (Gasoline): Subject to a federal excise tax of $10\,\text{cents per litre}$.

  • Fuel-Inefficient Vehicles: Vehicles consuming $16\,\text{litres}$ or more of fuel per $100\,\text{km}$ are assessed an excise tax of up to \\$4{,}000\,\text{per car}.

  • Ontario Gasoline Tax Stack (as of July 2010):

  • Federal excise tax: $10.0\,\text{cents per litre}$.

  • Provincial gasoline tax: $14.7\,\text{cents per litre}$.

  • Harmonized Sales Tax (HST): $13\%\,\text{applied on the subtotal}$.

  • Federal Carbon Tax Escalation (Ontario):

  • $2019\,\text{rate}$: $+4.4\,\text{cents per litre}$.

  • $2022\,\text{rate}$: $+11.1\,\text{cents per litre}$.

• Economic Effects of Excise Taxation:

  • Divergence of Market Prices: The tax drives a wedge between the price paid by consumers ($P_C$) and the price received by producers ($P_P$):     $\text{Tax Wedge} = P_C - P_P = T$

  • Buyer Price Increase: The price paid by purchasers rises above the pre-tax equilibrium price ($P_C > P_E$).

  • Seller Net Price Decrease: The net price retained by sellers falls below the pre-tax equilibrium price ($P_P < P_E$).

  • Quantity Contraction: Because buyers face a higher effective price and sellers receive a lower net price, the equilibrium quantity transacted contracts ($Q_T < Q_E$).

Market Equilibrium, Tax Incidence, and Statutory Equivalence

• Pre-Tax Baseline Market (Potterville Hotel Industry):

  • Pre-tax market equilibrium is established at point $E$ where the downward-sloping market demand curve ($D$) intersects the upward-sloping market supply curve ($S$).

  • Pre-tax Equilibrium Price ($P_E$): \\$80\,\text{per room per night}.

  • Pre-tax Equilibrium Quantity ($Q_E$): $10{,}000\,\text{rooms transacted per night}$.

• Excise Tax Imposed on Hotel Owners (T = \\$40\,\text{per room}):

  • Supply Curve Shift: Suppliers require an additional \\$40 at every output level to cover their marginal costs plus the tax liability. The supply curve shifts vertically upward by exactly the amount of the tax (\\$40) from $S_1$ to $S_2$.

  • New Equilibrium Outcome:

  • The new intersection between $S_2$ and $D$ occurs at point $A$.

  • Quantity Transacted ($Q_T$): Decreases from $10{,}000$ to $5{,}000\,\text{rooms}$.

  • Price Paid by Consumers ($P_C$): Rises from \\$80 to \\$100 (point $A$).

  • Price Received by Suppliers ($P_P$): Suppliers remit \\$40 to the government, keeping \\$60 per room (P_P = P_C - T = \\$100 - \\$40 = \\$60, represented by point $B$ on the original supply curve $S_1$).

• Excise Tax Imposed on Hotel Guests (T = \\$40\,\text{per room}):

  • Demand Curve Shift: Guests evaluate total willingness to pay inclusive of the tax. The demand curve shifts vertically downward by the exact amount of the tax (\\$40) from $D_1$ to $D_2$.

  • New Equilibrium Outcome:

  • The new intersection between $D_2$ and $S$ occurs at point $B$.

  • Quantity Transacted ($Q_T$): Decreases from $10{,}000$ to $5{,}000\,\text{rooms}$.

  • Price Received by Suppliers ($P_P$): Drops from \\$80 to \\$60 (point $B$).

  • Price Paid by Consumers ($P_C$): Consumers pay \\$60 to the hotel and an additional \\$40 directly in tax, totaling \\$100 (P_C = P_P + T = \\$60 + \\$40 = \\$100, represented by point $A$ on the original demand curve $D_1$).

• The Principle of Statutory Equivalence:

  • Economic Tax Incidence: The actual division of the tax burden between buyers and sellers in the form of higher prices paid and lower prices received.

  • Invariance Proposition: The economic incidence of an excise tax is identical regardless of whether it is statutorily collected from consumers or producers.

  • In both scenarios:

  • Consumer price burden: Increases by \\$20 (from \\$80 to \\$100).

  • Producer price burden: Decreases by \\$20 (from \\$80 to \\$60).

  • Transaction volume: Contracts by $5{,}000\,\text{rooms}$.

  • Total tax wedge: Exactly \\$40.

Determinants of Tax Incidence: The Decisive Role of Elasticity

• Core Axioms of Tax Incidence:

  • The statutory assignment of a tax contains no economic content regarding who bears the real burden.

  • Tax incidence depends strictly on the price elasticities of supply and demand.

• Case 1: Inelastic Demand Relative to Supply ($E_S > E_D$):

  • When buyers have few readily available substitutes and cannot adjust quantities easily, demand is relatively steep.

  • When producers have high responsiveness to price shifts, supply is relatively flat.

  • Incidence Distribution: Sellers pass almost the entire tax forward to consumers.

  • Gasoline Market Demonstration:

  • Pre-tax price: P_E = \\$1.00\,\text{per litre}.

  • Excise tax: T = \\$0.25\,\text{per litre}.

  • Post-tax consumer price: $P_C = \\$1.20\,\text{to}\,\\$1.25\,\text{per litre}$.

  • Post-tax producer net price: Decreases only marginally below $P_E$.

  • Consumers absorb the overwhelming majority of the tax wedge.

• Case 2: Elastic Demand Relative to Supply ($E_D > E_S$):

  • When buyers have ample substitutes or discretionary demand, demand is relatively flat.

  • When producers face fixed capacities or severe constraints in alternate resource allocation, supply is relatively steep.

  • Incidence Distribution: Producers are unable to pass the tax forward without experiencing a complete loss of market volume; therefore, they absorb the tax.

  • Downtown Parking Space Demonstration:

  • Pre-tax price: P_E = \\$6.00\,\text{per parking space}.

  • Excise tax: T = \\$5.00\,\text{per parking space}.

  • Post-tax consumer price: P_C = \\$6.50\,\text{per space} (+\\$0.50 burden).

  • Post-tax producer net price: P_P = \\$1.50\,\text{per space} (-\\$4.50 burden).

  • Producers absorb $90\%$ of the tax burden because physical parking facilities cannot easily adjust to alternative uses in the short term.

• General Rule of Relative Elasticity:   $\frac{\Delta P_C}{|\Delta P_P|} = \frac{E_S}{|E_D|}$

  • The party with the smaller price elasticity (the less responsive, more captive side of the market) bears the larger share of the tax burden.

• Application: The Incidence of Canadian Payroll Taxes:

  • Program Components: Canada Pension Plan (CPP) and Employment Insurance (EI).

  • Statutory Rules (2013):

  • Employees pay approximately $6.83\%$ on their first \\$50{,}000 of earnings.

  • Employers match employee CPP contributions dollar-for-dollar ($1.0 \times$) and contribute $1.4 \times$ the employee EI contribution.

  • Incidence Reality:

  • The price elasticity of labor demand by firms is relatively high (employers can substitute labor with capital, restructure operations, or shift investments).

  • The price elasticity of labor supply by primary wage-earners is extremely low (aggregate hours worked changes very little in response to wage variations).

  • Consequently, workers bear almost the entire burden of payroll taxes in the form of lower net wages rather than employers bearing it in lower profits.

Tax Revenue Dynamics, Rate Adjustments, and the Laffer Curve

• Calculation of Excise Tax Revenue:

  • Tax revenue ($TR$) equals the per-unit tax rate ($T$) multiplied by the total units transacted under the tax ($Q_T$):     $\text{Tax Revenue} = T \times Q_T$

  • Geometric Interpretation: On a supply-and-demand graph, tax revenue corresponds to the area of a rectangle:

  • Height of rectangle: Tax wedge ($P_C - P_P = T$

  • Width of rectangle: Transacted quantity under the tax ($Q_T$)

  • Potterville Hotel Example:     $\text{Tax Revenue} = \\$40\,\text{per room} \times 5{,}000\,\text{rooms} = \\$200{,}000$

• The Non-Linear Relationship Between Tax Rates and Revenue:

  • Doubling the excise tax rate will rarely double government tax revenue because the higher tax rate reduces the transaction base ($Q_T$).

  • Comparison Across Three Tax Rates in Potterville:

  • Tax Rate of \\$20\,\text{per room}:

    • Consumer price: P_C = \\$90

    • Producer price: P_P = \\$70

    • Quantity transacted: $Q_T = 7{,}500\,\text{rooms}$

    • Revenue: $\\$20 \times 7{,}500 = \\$150{,}000$

  • Tax Rate of \\$40\,\text{per room}:

    • Consumer price: P_C = \\$100

    • Producer price: P_P = \\$60

    • Quantity transacted: $Q_T = 5{,}000\,\text{rooms}$

    • Revenue: $\\$40 \times 5{,}000 = \\$200{,}000$

  • Tax Rate of \\$60\,\text{per room}:

    • Consumer price: P_C = \\$110

    • Producer price: P_P = \\$50

    • Quantity transacted: $Q_T = 2{,}500\,\text{rooms}$

    • Revenue: $\\$60 \times 2{,}500 = \\$150{,}000$

• The Laffer Curve Hypothesis:

  • Theoretical Postulate: Plotting tax revenue as a function of the tax rate yields an inverted U-shaped curve.

  • At a $0\%$ tax rate, revenue is zero.

  • Initial increases in the rate expand revenue because the rate increase outweighs the reduction in quantity.

  • Beyond a peak threshold, further increases in the tax rate shrink the tax base so severely that total revenue drops toward zero.

  • Historical Application (Reagan Administration, 1981):

  • Used by Ronald Reagan to claim that cutting high marginal income tax rates would spur economic activity sufficiently to expand total tax receipts.

  • Empirical Reality:

  • Economic consensus confirms that Reagan's tax cuts did not increase revenue.

  • Real-world taxation regimes operate almost universally on the upward-sloping side of the Laffer curve, making cases where rate cuts expand revenue exceptionally rare.

Welfare Analysis: Surplus Destruction and Deadweight Loss

• Destruction of Consumer and Producer Surplus:

  • Consumer Surplus Loss: Consumers face a price rise from $P_E$ to $P_C$. The loss in consumer surplus is represented geometrically by the trapezoid bounded by $P_C$, $P_E$, and the demand curve (Area $A + B$).

  • Producer Surplus Loss: Producers experience a price drop from $P_E$ to $P_P$. The loss in producer surplus is represented by the trapezoid bounded by $P_E$, $P_P$, and the supply curve (Area $C + F$).

  • Total Surplus Lost by Market Participants:     $\Delta \text{Total Surplus} = -(\text{Area } A + B + C + F)$

• Government Revenue Gain:

  • The government claims revenue equal to $T \times Q_T$, corresponding to rectangle Area $A + C$.

  • This revenue represents a direct transfer of wealth from consumers and producers to the public treasury.

• Deadweight Loss ($DWL$):

  • The portion of surplus lost by consumers and producers that is not recouped as government revenue represents a net deadweight loss to society:     $\text{Deadweight Loss} = (\text{Loss in CS} + \text{Loss in PS}) - \text{Government Revenue} = \text{Area } B + F$

  • Geometric Nature: Forms a triangle (Harberger's triangle) pointing toward the pre-tax equilibrium point $E$:

  • Base of triangle: Tax wedge ($T = P_C - P_P$

  • Height of triangle: Lost volume of mutually beneficial trade ($Q_E - Q_T$     $\text{Deadweight Loss} = \frac{1}{2} \times T \times (Q_E - Q_T)$

  • Economic Cause: Deadweight loss arises because the tax prevents mutually beneficial trades where marginal consumer willingness to pay exceeds marginal producer cost ($P_C > P_P$) between output levels $Q_T$ and $Q_E$.

• Administrative Costs and Total Economic Inefficiency:

  • Administrative Costs: The real resources consumed in administering the tax system, including costs incurred by the government to audit, enforce, and collect the tax, and costs borne by taxpayers to comply, keep records, hire accountants, or evade the tax.

  • Total Economic Inefficiency:     $\text{Total Inefficiency} = \text{Deadweight Loss} + \text{Administrative Costs}$

  • Optimal tax design seeks to raise necessary public revenues while minimizing this combined measure of inefficiency.

Efficiency Implications: Deadweight Loss and Relative Elasticities

• Impact of Elasticities on Deadweight Loss:

  • Deadweight loss is directly proportional to how much market volume contracts ($Q_E - Q_T$).

  • The more responsive buyers and sellers are to price changes, the greater the quantity reduction for any given tax wedge $T$, leading to larger deadweight losses.

• Demand Elasticity and Deadweight Loss:

  • Elastic Demand: When buyers are price-sensitive, an excise tax triggers a sharp drop in consumption, resulting in a large deadweight loss triangle.

  • Inelastic Demand: When buyers cannot substitute the good easily, consumption declines minimally, resulting in a narrow, small deadweight loss triangle.

• Supply Elasticity and Deadweight Loss:

  • Elastic Supply: When producers easily exit or reassign resources elsewhere, quantity supplied contracts sharply, causing large deadweight losses.

  • Inelastic Supply: When producers have fixed capacities or no outside options, production remains nearly unchanged, minimizing deadweight losses.

• Tax Policy Rule for Efficiency:

  • To minimize the efficiency costs of taxation, governments should tax goods and services with relatively inelastic demand, relatively inelastic supply, or both.

  • In these markets, the tax does not significantly alter consumer and producer behavior.

• The Zero Deadweight Loss Extremes:

  • Perfectly Inelastic Demand ($E_D = 0$, vertical curve): Quantity transacted remains unchanged ($Q_T = Q_E$); deadweight loss is exactly zero. Consumers pay the entire tax.

  • Perfectly Inelastic Supply ($E_S = 0$, vertical curve): Quantity transacted remains unchanged ($Q_T = Q_E$); deadweight loss is exactly zero. Producers pay the entire tax.

Equity versus Efficiency: Principles of Tax Design

• Principles of Tax Equity:

  • The Benefits Principle: Individuals who derive direct benefits from public spending should finance the taxes that support that spending.

  • Canadian Example 1: The Gas Tax Fund earmarks revenues from fuel taxes directly to improve municipal highway and public transit infrastructure.

  • Canadian Example 2: The Air Travellers Security Charge (ATSC) is levied directly on airline passengers to fund airport passenger screening and air travel security.

  • The Ability-to-Pay Principle: Those with greater economic resources and financial capacity should contribute a greater amount of taxes than those with lesser means.

• Lump-Sum Taxes (Poll Taxes):

  • Definition: A fixed-amount tax levied equally on every individual regardless of their income, assets, or consumption choices.

  • Efficiency Profile: A lump-sum tax introduces zero deadweight loss ($DWL = 0$) because it does not alter marginal incentives or distort economic choices.

  • Equity Failure: Lump-sum taxes impose severe financial burdens on low-income earners, making them regressive and socially contentious.

  • Historical Backlash:

  • The Great English Peasant Rebellion of 1381 (instigated by third-tier poll taxes).

  • The British Poll Tax Riots of 1989–1990 under Margaret Thatcher, which triggered widespread civic unrest and the subsequent repeal of the Community Charge.

• The Trade-Off Between Equity and Efficiency:

  • Taxes that best satisfy equity criteria (such as progressive income taxes) create marginal disincentives for labor supply, capital investment, and saving, thereby generating economic inefficiency.

  • Taxes that maximize economic efficiency (such as lump-sum taxes) are often regressive and fail equity standards.

  • Consequently, tax policy entails a fundamental trade-off: an increase in equity typically incurs an efficiency cost, and gains in efficiency often require compromises in fairness.

Empirical Overview of Taxation: Canadian Structures and Global Benchmarks

• Foundations of Tax Architecture:

  • Tax Base: The defined measure or economic value upon which a tax is levied.

  • Tax Structure: The schedule specifying how tax liabilities vary across different levels of the tax base.

• Primary Tax Bases and Common Taxes:

  • Income Tax: Tax base is total personal or family earnings from wages, investments, and capital.

  • Payroll Tax: Tax base is the employer's wage payments to employees.

  • Sales Tax: Tax base is the gross value of retail goods and services sold.

  • Profits Tax (Corporate Income Tax): Tax base is the accounting net profit of corporations.

  • Property Tax: Tax base is the assessed market value of real estate.

  • Wealth Tax: Tax base is the accumulated net worth of an individual or household.

• Tax Structure Categories:

  • Proportional Tax (Flat Tax): The tax rate is identical across all income or asset brackets; every taxpayer remits the same constant proportion of their base.

  • Progressive Tax: The average tax rate rises as income increases; higher-income individuals pay a greater share of their total income than lower-income earners.

  • Regressive Tax: The average tax rate falls as income increases; lower-income individuals pay a greater share of their total income than higher-income earners.

  • Marginal Tax Rate: The proportion of each additional dollar of income that is collected in taxes:     $\text{Marginal Tax Rate} = \frac{\Delta \text{Tax Paid}}{\Delta \text{Taxable Income}}$

• Comparative Model: Proportional versus Progressive Systems (Taxmania):

• Income Redistribution in Canada (Table 7-2, 2011 Data):

  • Federal personal income tax reflects the ability-to-pay principle, complemented by progressive social transfers (acting as a negative income tax for lower-income households):

• Structure of Canadian Government Tax Revenues (Table 7-4, 2012 Data):

• International Comparison of Overall Tax Burdens (2009 Taxes as a Percent of GDP):

  • United States: $24.0\%$

  • Korea: $25.6\%$

  • Canada: $31.1\%$

  • Israel: $31.4\%$

  • Britain: $34.3\%$

  • France: $41.9\%$

  • Sweden: $46.4\%$