**4. Optimal commodity taxes: Ramsey rule**

as the starting point. Within this scope, balance between the goals of justice (equality) in taxation and economic efficiency is tried to be redressed. On the other hand, trade-off between

Existence of the relevant trade-off depends on the existence and influence of distortionary taxes. In today's conditions, in which the state has asymmetrical information about the individual's social and economic characteristics, the goal of income redistribution can be possible through the use of distortionary taxes. The state can assure income justice by using distortionary taxes only by conceding economic efficiency. Because of this reason, optimal taxation lays emphasis on tax subject, tax rate, and tax base, which will minimize efficiency loss in securing

In general terms, distortionary taxes can be defined as taxes that will influence or change economic decisions of taxpayers. The main reason for distortionary taxation on the other hand is to assure redistribution of revenue, which is one of the fundamental functions of the state and thus to achieve a society structure more egalitarian than the one that could have been

The state, which has a social aim of distributing the tax burden in a fair and balanced way within the scope of fiscal policy, needs distortionary taxes in order to realize this aim. State's complete and absolute knowledge about the characteristics of each individual in the society underlies this need. In this context, use of distortionary taxes is a consequence of the aim to redistribute revenue in a world, where the state knows characteristics of individuals only incompetently [9]. Within this scope, in the assurance of justice (equality), individuals having the same ability to pay will be assumed to be in equal conditions, and same amount of taxes

When different abilities to pay are at stake, the state redistributes revenue in a way to load a greater amount of public expenditures to higher income groups. Different societies may have different preferences on equality and efficiency. These differences bring along different tax systems in practice. Discussions on how progressive tax structure should be in order to enable equality are a result of value judgments about equality. In this context, inequality reduced through progressive tax structure can only be possible by the acceptance of a certain amount of efficiency loss. According to Diamond and Mirrless [11], administratively, it is not possible for the state to realize its revenue distributer goal on the grounds of social justice and revenue creator goal on the grounds of public finance, through lump-sum taxes. Since lump-sum tax is not appropriate, optimal taxation will only be a taxation that will not impair the efficiency of production. This on the other hand is only possible if the taxation on the final production can be diversi-

In the light of these explanations, optimal tax structure is defined as the tax structure, which reflects the preferences of the society between the balance of efficiency loss and equality and

these goals created different approaches to the topic.

**3. Distortionary taxes and efficiency loss**

achieved via a uniform lump-sum tax [9].

will be taken from them [10].

fied between products at no cost [12].

a certain amount of tax revenue.

126 Taxes and Taxation Trends

The main topic of discussion in the literature regarding optimal commodity taxes, which are approached under the heading of optimal taxation, is about the proportional structure of the taxes in question. In this context, literature searches which tax rates, single rate or varying, will create optimal results in the construction of optimal commodity taxes. Within this scope, while on one side, there is the view arguing that a single rate tax will not damage market forces and will be synonymous with a fixed rate tax on income [14]; on the other side, optimal commodity taxes within the context of Ramsey and varying rates take place.

Ramsey rule involves taxing commodity and zero capital taxes in the long run [15] for minimizing the deadweight loss. For public choice theory, equilibrium taxes and feasible tax structure apart from Ramsey analysis are important subjects because tax system can cause rent seeking when it is used as an income distribution tool [16, 17].

Optimal commodity taxation, which was proposed in 1927 by Ramsey and whose theoretical structure has developed through today's modern approaches, is based on the inverse elasticity rule, which claims goods with low demand elasticity to be taxed at a higher rate will reduce efficiency loss, and Corlett-Hauge Rule, which claims leisure complement goods that will change the preferences of consumers between working and leisure on behalf of working need to be taxed at a higher rate.

As seen in **Figure 1**, tax application may cause a decrease in social wealth by changing price before and after tax. The reason behind this is the decline of production under the amount before tax because of the change in price. Minimization of this efficiency loss, which is also called excess tax burden or deadweight loss (DWL), is the purpose of the tax systems.

Under the assumption that characteristics of individuals can only be known deficiently and thus lump-sum taxes are not applicable, Ramsey searched the tax structure that will minimize efficiency loss (deadweight loss) associated to the collection of a specific amount of tax revenue. Excess tax burden is caused by the reduction in equilibrium quantity because individuals change their behaviors and consume taxed product less. Decrease in the quantity of the product depends on demand elasticity. According to Ramsey rule, tax rate imposed on the good with high elasticity should be lower than the tax rate imposed on the good with low elasticity [18]. In this way, as seen in **Figure 1**, decrease in the equilibrium quantity of goods would be minimized.

**Figure 1.** Deadweight loss of taxation. Source: Ref. [44].

Under the assumption that people resemble each other, Ramsey taxes are expressed as the sum of the inverses of supply and demand elasticity.

$$\frac{t}{\overline{p}} = \text{\tiny k \{1/n\_{\mu}^d + 1/n^s\}}\tag{1}$$

However, according to Corlett-Hague Rule, varying tax rates, in which leisure complementary goods that will change the preferences of consumers between working and leisure in favor of working will be taxed at higher rates, serve for the assurance of optimality in commodity taxes. In this context, Diamond [11] proposed leisure complementary goods to be

Optimal Taxation of Consumption in the Scope of Changing Elasticities of Demand...

http://dx.doi.org/10.5772/intechopen.74378

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(iii) Tax rates are expected to be inversely proportional with uncompensated own-price elas-

The most important criticism toward the Ramsey rule composed of above-mentioned hypotheses is caused by the fact that necessity goods devoted to meet basic needs to have low price elasticity of demand and luxury goods to have high price elasticity. Under the assumption that consumers resemble each other, taxation of luxury goods at a lower rate compared to

Ramsey taxes, which were pointed out in the above section in detail, are criticized because of

At this point, first main criticism to Ramsey analysis is the assumption that all individuals resemble each other. The fundamental reason for the state to use distortionary taxes instead of lump-sum taxes is to have redistribution goals, which are not possible to attain in another way. In case this assumption is valid, there are no causes of the state for not imposing lump-

Nevertheless, when taxes are imposed within the context of inverse elasticity rule, an equal amount of decrease in demand in all goods will be caused by collecting lower rates of taxes from goods with a high possibility of change in demand amount and at higher rates from goods with a low possibility of change in demand amount; and thus, efficiency loss will be minimized. According to this approach, taxation of necessity goods, which have low compensated demand elasticity and have a large share in the consumer's budget, at a higher rate than luxury

Generally, price elasticity of demand for good, which are consumed with the purpose of meeting basic needs, is low, while price elasticity of demand for luxury goods is high. Based on this rule, tax rate to be imposed on basic necessity goods will be high, and tax rate to be imposed on luxury goods will be low. What needs attention here is the assumption that consumers are alike. However, since income distribution and demand for different products will vary, such a rule will create negative results in terms of tax equity especially in developing

Ramsey defended this rule by placing economic efficiency to forefront. Therefore, although theoretically consistent, this analysis becomes contradictive in practice with the influence of

its current assumptions and negativity they might create in income distribution.

taxed at relatively higher rates intended to the efficiency purpose.

necessity goods is claimed to influence justice of taxation negatively.

**5. Redistribution and Ramsey taxes**

ticity of demand.

sum taxes.

countries.

goods comes to the fore [9].

socio-political reasons [20].

In this equation, *t* represents tax rate per unit, *p* represents price after tax, *nu d* represents compensated elasticity of demand, and *n<sup>s</sup>* represents supply elasticity [9].

In the inverse elasticity rule suggested by Ramsey, under the assumption that supply curve is finite or, in other words, a horizontal supply curve exists, tax is stated to be inversely proportional to compensated demand elasticity. Accordingly, all goods to be affected equally from taxes are aimed by collecting lower rates of taxes from goods with high price elasticity of demand and higher rates of taxes from goods with low price elasticity of demand.

Within the framework of this purpose, Sandmo [19] expresses that Ramsey rule can be based on the following three hypotheses:


Elasticity of substitution between goods and leisure lies behind the fact that single rate tax, which does not change the relative prices of goods and will not be different from the lumpsum tax that will be imposed on labor income, is not optimal [14].

However, according to Corlett-Hague Rule, varying tax rates, in which leisure complementary goods that will change the preferences of consumers between working and leisure in favor of working will be taxed at higher rates, serve for the assurance of optimality in commodity taxes. In this context, Diamond [11] proposed leisure complementary goods to be taxed at relatively higher rates intended to the efficiency purpose.

(iii) Tax rates are expected to be inversely proportional with uncompensated own-price elasticity of demand.

The most important criticism toward the Ramsey rule composed of above-mentioned hypotheses is caused by the fact that necessity goods devoted to meet basic needs to have low price elasticity of demand and luxury goods to have high price elasticity. Under the assumption that consumers resemble each other, taxation of luxury goods at a lower rate compared to necessity goods is claimed to influence justice of taxation negatively.
