cost of taxation

Chapter Six Overview

  • Concepts Discussed:

    • Price yields

    • Price floors

    • Taxation (Primary focus)

Taxation Fundamentals

  • Definition of Tax:

    • A tax creates a wedge between the price that buyers pay and the price that sellers receive.

    • After tax, buyers pay a higher price, and sellers receive a lower price.

    • Taxes decrease the number of units that are bought and sold in the market.

Tax Imposition

  • Imposition of Tax:

    • The effects of a tax appear the same regardless of whether imposed on buyers or sellers.

    • Discussion will not specify the side of imposition to simplify visual analysis (using the "tax toothpick" method).

Goals for Today

  • Understand and determine:

    • Consumer surplus

    • Producer surplus

    • Tax revenue

    • Total surplus with and without tax for comparison.

Tax Revenue

  • Assumption on Tax Revenue:

    • Tax revenue can fund beneficial services (e.g., education, roads, police) and is included in total surplus.

    • Despite potential losses in administrative inefficiency, this is considered in this theoretical analysis as a "best case scenario".

  • Definition of Total Surplus with Tax:

    • Total surplus = Consumer Surplus + Producer Surplus + Tax Revenue.

  • Total Surplus without Tax:

    • Total surplus is simply the sum of consumer surplus and producer surplus (no tax revenue).

Graphical Representation

  • No-Tax Equilibrium:

    • Intersection of demand and supply curves indicates equilibrium.

  • Introduction of Tax:

    • A tax of t dollars is introduced, forming a tax wedge.

    • The tax wedge visually illustrates the difference between prices paid by buyers and received by sellers.

    • The height of the tax wedge equals the size of the tax.

  • Tax Graph:

    • Prices Identified:

    • Price buyers pay: At the demand curve touched by the tax wedge.

    • Price sellers receive: At the supply curve touched by the tax wedge.

    • Number of units sold under tax: Found where the tax wedge fits snugly.

Tax Impact Analysis

  • Tax Revenue Generation:

    • Government raises revenue through the tax.

    • Tax revenue = Tax size (t) × Number of units sold (QT) under tax.

    • Tax revenue visually represented as a green shaded rectangle in the graph (area = QT × t).

Surplus Analysis

  • Consumer Surplus Without Tax:

    • Defined as the area below the demand curve and above the equilibrium price from 0 to QE.

    • Corresponds to areas A + B + C (whole upper triangle).

  • Producer Surplus Without Tax:

    • Defined as the area below the price and above the supply curve from 0 to QB.

    • Results in the area of D, E, F (the lower triangle).

  • Total Surplus Without Tax:

    • Total Surplus = Areas A + B + C + D + E + F (no tax revenue).

Comparative Analysis

  • Introducing Tax Effects:

    • New equilibrium introduces complexity with two prices:

    • The buyer price and seller price both need to be considered for surplus calculations.

  • Consumer Surplus With Tax:

    • Calculated using the price that buyers pay.

    • Now the relevant area where units are sold is identified up to QT, resulting in a new consumer surplus (shape a).

  • Producer Surplus With Tax:

    • Defined using the price sellers receive.

    • Calculated as area f within the bounds of QT.

  • Tax Revenue:

    • Tax revenue area is defined as the area encompassing b + d (the green rectangle).

    • This revenue funding is integrated into total surplus, now calculated as:

    • Total Surplus = Consumer Surplus + Producer Surplus + Tax Revenue = A + B + D + F.

Observations on Taxation

  • Welfare Reduction:

    • Tax causes a reduction in total surplus labeled as deadweight loss (regions C + E), which highlights lost surplus due to reduced trading efficiency.

    • Deadweight Loss Definition:

    • The lost surplus due to market distortion (tax) preventing mutually beneficial trades.

  • Mutually Beneficial Trades Implication:

    • Units between QT (taxed quantity) and QE (original equilibrium quantity) are effectively lost.

    • Potential gains for buyers exceeding costs for sellers in this range remain unexploited.

Further Implications

  • Factors Influencing Deadweight Loss:

    • Deadweight loss correlates with the reduction of traded quantity.

    • Elasticities of supply and demand play a role: more elastic curves result in larger deadweight losses.

  • Deadweight Loss Formula:

    • DWL = \frac{1}{2} \times T \times (QE - QT)

    • T represents the size of the tax.

    • DWL triangle formed between original equilibrium and new tax quantity sold.

  • Conclusion and Future Discussions:

    • Importance of understanding implications for tax policy and efficiency considerations discussed in the next chapter.