Lecture 3: Taxes, Tariffs and Quota (Chapter 5)

1. Lecture 3: Taxes, Tariffs and Quota (Chapter 5) • Relation to “work horses” • Government and taxation • Taxes and quotas in general equilibrium • Welfare implications of taxes and tax reforms • Practices in applied modeling

2. Aim of lecture 3 • Highlighting welfare effects of different taxes • Illustrating implementation of taxes and quotas in general equilibrium

3. Mapping from theorems to “working horses”

4. Government and taxation • Direct taxes • Take away (give) a part of income and profits from (to) the agents. Can be used for redistribution purposes and to distribute the proceeds from: • Indirect taxes • Create a wedge between prices at various stages of supply and utilization of a commodity

5. Price wedges Production Consumption Indirect taxes Indirect taxes Intermediate demand Indirect taxes Market clearing Tariffs Tariffs Import Export

6. Government and taxation: tax on consumption • Recall from lecture 1 that a tax on consumption of goods implies that the relation between the market clearing price and the consumer price is given as: . • Types of consumption taxes: • Ad valorem tax: is fixed • Nominal tax: is fixed • Variable levy: is fixed, adjusts • Homogeneity of demand in market prices is preserved only under ad valorem tax

7. Example (continued) • Proceeds of indirect taxes • Public consumption • Indirect subsidies • Direct subsidies (lump-sum transfers) • Budget of the agent now reads: • All consumers (including government) take lump-sum transfers as given!

8. Taxes and quotas in general equilibrium: consumption tax • Optimization with given consumptions : (b) A feedback relation that sets by solving the consumer problem:

9. Taxes and quotas in general equilibrium: taxes on intermediate demand • Optimization with given consumptions : • Feedback on consumption as before and tax feedback relations:

10. Taxes and quotas in general equilibrium: tariffs in the international model • Under small country assumption, import and export prices are given and tariffs are included as: • Quota can be included as additional restrictions • With (the shadow prices) being the quota rents.

11. Taxes and quotas in general equilibrium: tariffs in the international model (continued) • International model can also be seen as set of national models linked through trade • World prices (import and export prices) are now endogenous and clear world markets • Tariffs now are the difference between clearing prices at world level and domestic clearing prices • We may assume that tariff revenue is distributed only among agents in the own country

12. Taxes and quotas in general equilibrium: tariffs in the international model (continued) • Optimization with given consumption • and feedback relations as before

13. Government activity: a summary • Government can be: • Social planner • Consumer (distortion, since public demand does not enter in private utility function, see Chapter 9) • Owner of resources (that can be used for transfers to private agents) • Activities and transactions in which government is involved include • Public consumption • Income from endowment and production and remittances from abroad • Redistributed income • Transfers to private consumers • Proceeds from indirect taxation and tariffs • Budget balancing • Trade balancing

14. Welfare implications: consumption tax • Shift to Negishi format • As in open economy format, taxes are represented in the objective • To recover consumer prices, an additional variable (total consumption) and an additional constraint (equating the sum of individual consumption to total consumption) are inserted • Feedback on welfare weights is adjusted to reflect tax-included budget constraint

15. Welfare implications: consumption tax (continued) With welfare weights set such that budget constraints hold: Note: homogeneity of the objective in welfare weights is lost for given !

16. How to reform? • Proposition 5.2 (welfare loss of a consumption tax) “removing taxes cannot reduce total welfare”. No gain if: • All commodities are taxed in the same way and • redistribution of tax gains is such that every consumer receives a lump-sum transfer equal to the amount of taxation paid • Proposition 5.3 (welfare gains from reform) • Recall from lecture 1 that in general, subsidies, tariffs, monopoly premiums and wage subsidies can be represented by separate agent terms in objective with a weight factor. • Consumer welfare rises as weight factor is reduced • Proposition 5.4 (eventual welfare gains from reducing taxes) • If indirect taxes are close to zero, there can be no welfare loss from reduction of taxes

17. How to reform? (continued) • Proposition 5.2 suggest that all indirect taxes should be removed in one reform • Since this is rarely feasible, it is important to look at effects of gradual reforms • Phasing of reform, starting from a situation with high indirect taxes • Proposition 5.3 tells us that all wedges should first be decreased simultaneously and proportional • If taxes are decreased to low levels, then Proposition 5.4 tells us that reform could be stepwise: no tax should be raised, but some can be set to zero in a series of piecemeal reforms • Throughout the process, compensating transfers should be given • Agents should not be able to anticipate the reform process

18. How to reform? Why compensation is important • (Weakly) Pareto-superior tax reforms can be designed, if they are supported by compensating transfers • However, if there is no compensation, even full elimination of taxes may lead to welfare losses: • Closed economy, 2 consumers, 1 commodity, no production • Consumer 1 owns all endowments • 100% tax on consumption • Tax receipts given to consumer 2 • Consumers have identical, strictly concave, increasing, continuously differentiable utility functions • It follows that both have the same income • It also follows that they have the same welfare weight

19. How to reform? Why compensation is important • Abolishing tax with no compensation leads to zero income for consumer 2, and by strict concavity this implies:

20. Practices in application: taxes and tariffs in CGE • Introduction of tariffs and taxes does not change commodity balances, but only budgets and price formation • Special price equations: • Trade: tariff-ridden import prices are exogenous: • Trade: exports are assumed not to be perfect substitutes in the rest of the world, so prices are endogenous, and the price adjusts according to: . This price then enters the export demand function and the balance of payments • Budget equations: • Export demand • Tax functions, household budgets, government budget

21. Practices in application:Specification of wedges in CGE • Tax wedges can be fixed, observed parameters, which may be varied in scenario analyses • Tax wedges may be specified as explicit functions of endogenous variables, the parameters of which can be estimated. • Tax wedges can be specified as variable levy, to maintain relative prices with certain range (e.g. relation domestic price and world market price) • Tax wedges may be fully endogenous and result from social welfare optimization • Taxes may be used to stabilize quantities: tariff quota, with voluntary export restraint as special case where tariff revenue accrues to the exporter

22. Practices in applications: a SAM

23. Practices in applications:properties of income tax schedule • Income tax schedule should satisfy following properties • Continuity • Homogeneity of degree 1 in • Adding up: , with equality whenever • Positiveness: • There exists a constant such that if all consumers are taxed at the same proportional rate so that for all i, for

24. Practices in applications: Tax functions • Tax functions can be specified in an ad-hoc manner, where properties of the tax schedule should be satisfied • However, optimal taxation schedules may theoretically be derived from maximization of social welfare, according to some social welfare function that is agreed upon by society

25. Practices in applications: Tax functions (continued) • Consider social welfare optimization program for an exchange economy: With being strictly concave increasing

26. Practices in applications: Tax functions (continued) Substituting leads to a composite mapping W. Note that we have to assume concavity of the individual utility functions to preserve concavity of the sum of these functions, and thus concavity of W in x (see proposition A.1.4) Which equivalent to the previous problem for This can be decomposed as a two-level problem: • Optimal expenditure allocation • Consumer i’s utility maximization

27. Practices in applications: Tax functions (continued) Level 1 maximization: Individual maximization: , where his expenditure is obtained from (1) From this, we can obtain expenditure allocation functions and derive direct tax functions

28. Practices in applications: Tax functions (continued) • The optimal allocation that follows is unique • This implies that tax schedules are not only useful to reach specific distributional goals, but also to stabilize the economy • This also holds if there are distortions already in the economy that must be taken as given by the modeler

29. Individual optimization Concave utility function Increasing in all commodities Slutsky equation Preferences over known goods Social welfare optimization Concave composite social welfare function Increasing in all utilities “Slutsky equation” Anonymity Practices in applications: Tax functions (continued)

30. Practices in applications: Tax functions (continued) • We did not impose restrictions on transfers that relate to property rights of individuals. • If all endowments are divided over individuals and all rights need to be respected, then we seem to be back in the Negishi format, where there is no room from redistribution and uniqueness is lost • However, even under full respect of rights tax revenue needed for redistribution can be mobilized without creating distortions: • VAT: given tax rate that does not differentiate between commodities. This simply raises the overall price level and does not affect relative prices • Profits of state-owned companies can be used • Government could establish markets for commodities that went unpriced before (Pigouvian taxes; double dividend discussion)