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Commodity Taxation (Deadweight Loss (Background:
Assume that the economy…
Commodity Taxation
Deadweight Loss
Background:
- Assume that the economy is in a first-best equilibrium.
- When the government introduces commodity taxes, individuals respond by changing their consumption
- Tax-induced responses move economy away from first-best and are associated with efficiency costs or deadweight loss (DWL)
Marginal Deadweight Loss
- Marginal deadweight loss can be decomposed into a mechanical effect and a behavioural effect
- Mechanical effect on revenue: Revenue increases due to imposed taxation
- Behavioural effect on revenue: Revenue decreases as people undercosume the good
Formulation:
x = qty consumed, t = tax per unit, p = producer price, P = p + t = consumer price
- dDWL = -tdx (tax x change in qty)
Ramsey Tax Model
Without Equity Concerns
Assumptions:
- No income effects (uncompensated demand = compensated demand)
- Independent markets (no cross-price effects)
With independent markets, DWL from taxing good is independent of the taxation of all other goods
Optimisation Problem:
- Choose t1...tn to minimise total DWL s.t. revenue require R = t1x1...tnxn greater than or equal to R-bar
- By FOC, (dDWL/dt)/(dR/dt) = mu
- Marginal DWL per dollar of tax revenue must be the same for all commodities
- Intuitively, if the marginal DWL per dollar raised for good i is higher than for good j, we can shift $1 of tax from i to j so as to collect the same revenue at a lower total DWL
Inverse Elasticity Rule: We should tax inelastic goods at higher rates than elastic goods. This is because behavioural response will be less, thus reducing DWL.
Set-up:
- 1 consumer (no equity concerns)
- Consumer gets utility for leisure L and goods x1...xn
- Govt faces an exogenous revenue requirement
- Lump-sum taxation is ruled out
With Equity Concerns
Set-up:
- Allow for heterogeneity in income
- Govt wants to redistribute from high-income to low-income consumers
Inverse Elasticity Rule with Equity Concerns: (1/elasticity)*equity weight
- Equity weight is high for goods weighing more heavily in the budget of high-income consumers (e.g. luxuries) and low for goods weighing more heavily in the budget of low-income consumers (necessities)
Equity-Efficiency Trade-off
- Higher taxes on luxuries than necessities improve equity
- Luxuries are likely to be more elastic than necessities, thus lower taxes on luxuries than on necessities to improve efficiency
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Reasons:
- Satisfy a revenue requirement for financing public goods (Ramsey taxation)
- Redistribution from rich to poor (Ramsey taxation with equity concerns)
- Correction of externalities and other market failures (Pigouvian taxation)
- Correction of internalities due to behavioural/psychological aspects (Paternalistic taxation)