Perfectly Elastic Demand
In the case of perfectly elastic demand, the burden of the tax is entirely borne by the producer of the good or service. Perfectly elastic demand means that consumer is willing to pay the same price for infinite quantity demanded. When the tax is imposed in this condition, the producer borne it by cutting its supply, while price of the good remains same. The consumer pays price ‘p’ while the producer gets ‘p`’, the quantity demanded falls from ‘q’ to ‘q`’. The highlighted portion is the tax burden borne by the producer (p-p`). Graphically it could be shown as below:
Perfectly inelastic demand
This and the above are the two extreme cases of demand conditions, and are very rarely found in real world. In this case the burden of the tax is completely borne by the consumer. Perfectly inelastic demand means that the consumer is willing to pay any price for the same quantity demanded (q). This could be a necessity good or service, for example water service. People need specific amount of water every month in order to survive and therefore will pay any amount for their minimum water consumption. In real life, this may not be possible as it will create havoc in the country, and consumer groups may take action against the government. Price of the good will rise by the amount of tax while the same quantity will be demanded. The consumer will pay price ‘p`’ while the producer will get price ‘p’ and therefore the whole tax burden is borne by the consumer. Graphically it could be shown as below:
Unit elastic demand
In the case of unit elasticity of demand, the burden of the tax is borne equally by both consumer and producer. When the tax is introduced, the price rises from ‘p’ to ‘p`’, quantity demanded fall from ‘q’ to ‘q`’. In this case, in addition to consumer and producer bearing the burden, a portion of quantity demanded is wasted as a dead-weight loss or society loss. The dead weight loss is in the form of underproduction of good or service, while the burden on consumer and producer is in monetary form. Graphically it could be shown as:
After analysing the above conditions, we can conclude that, as the price elasticity of demand increases, more of the tax burden is borne by the producer of the goods and results in lower tax revenue and vice-versa. If the price elasticity of demand is between ‘unit elastic’ and ‘perfect elastic’, producer bears more burden than consumer, and on the other hand, when the price elasticity of demand is between, ‘perfectly inelastic’ and ‘unit elastic’, consumer bears more tax burden than the producers. Now we should look at the different supply conditions and how they affect on the bearing of the burden of unit tax imposed by the government.
Perfectly elastic and perfectly inelastic supply
In the first case, the burden of the tax is completely borne by the consumer. The price will rise from ‘p’ to ‘p`’, while the quantity demanded will fall from ‘q’ to ‘q`’. This is represented by diagram ‘a’. On the other hand, when the supply is perfectly inelastic, the burden of the tax is completely borne by the producer of the good. In this case the price of the product and the quantity demanded remains same, but the tax is paid entirely out of producers pockets. This is represented by the diagram ‘b’.
For supply conditions, we can now conclude that as the elasticity of supply increases, more tax burden will be borne by the consumer and results in lower tax revenue and vice-versa. If the elasticity of supply is between ‘unit elastic’ and ‘perfectly elastic’, consumer bear more tax burden than the producer, on the other hand, when the elasticity of supply is between ‘perfectly inelastic’ and ‘unit elastic’, producer of the good bear more burden than the consumer. Therefore if we analyse both demand and supply situations, we find that both behave in the opposite direction.
When the government imposes a tax on a good, sometimes it results in a social cost. The cost to the society is the dead-weight loss in the terms of under-production of a good due to tax. This could be found when a good or service has either price elasticity for demand or supply between ‘unit elastic’ and ‘perfectly elastic’. The new equilibrium is not socially efficient as there is a distortion. Quantity supplied is less than socially-efficient quantity. The dark triangle are represents the dead-weight loss to the society in the diagram below.
It is true that tax distorts the socially efficient quantity levels and produces a waste to the society, but similarly tax could be justifiable in the case where no distortion occurs or when in order to remove negative externality in the society.
When government taxes a good or a service whose price elasticity for demand and supply is either inelastic or perfectly inelastic, either there is very little distortion or no distortion at all. In the case earlier seen of perfectly inelastic demand and supply, the quantity level remain unchanged and therefore the society does not bears the waste from under-production of good. Socially efficient quantity is still traded and therefore tax in these cases may be justifiable.
Government must raise money through tax revenue for many purposes, therefore it would be better to tax goods which are inelastic in demand or supply, in order for the waste to the society to be minimal. In UK alcohol and tobacco have inelastic demand and therefore the government taxes it very heavily with a minimal distortion and waste to the society.
On the other hand, the taxes can also be justified in the case of any negative externality arising from the good or service. For instance, Cigarettes pollute the environment and causes diseases and deaths. In order to offset the negative externality, the government may tax the good in order to reduce the quantity demanded, hence removing the negative externality, as the market will clear at socially efficient output which is less than the original equilibrium output. The need for distortion in the output for the cigarettes is now done through putting a tax on it.
The current equilibrium is not socially efficient due to the negative externality from the cigarettes pollution. D* is the marginal social benefit and due to negative externality it is below the original demand curve. The society would be efficient at the output q*, as there will be less pollution. At q* the marginal social benefit (d*) and the marginal social cost (s) are equal and therefore no negative externality will be produced. Now the government steps in and impose a tax on cigarettes.
The government imposes a tax of amount ‘e`-e*’ and therefore the equilibrium quantity is reduced to q* which in fact is the required socially efficient output for cigarettes. The distortion by the tax is offset by the society wanting to have less output due to environmental reasons. In this case, society will be better off when there is reduction in the output rather than being worse off. Therefore tax in these situations may be justifiable. This is an another reason apart from the minimal waste to society through tax as discussed above, that the alcohol and tobacco are heavily taxed in UK.
References:
Begg et al 2003, Economics seventh edition , McGraw Hill UK.
Sloman et al 2003, Economics fifth edition , Financial times management.
Griffiths et al 2001, Applied Economics, Pearson Education Singapore.
