# Elasticity and Taxes

5 Jul

Let the following figure represent the market price of an good before and after alplying a tax. Let this good be a CD. Pre-tax equilibrium price of an CD is 6\$ and equilibrium quantity is 1 million. So, if goverment levies an tax of an dollar per each CD, who is actually pays it?

Since this price is applied for sellers, it is taken as addition to marginal cost of our CD. Now sellers must get 1\$ for each CD to get the same revenue as they got before. While sellers want to offer,for example, ½ million of CDs for 4\$, they will have to set the price to 5\$ (since 1\$ is the tax), to offer the same ½ million of CDs. The tax shift the supply curve  upward. After tax equilibrium price is 6.50\$ , whereas the before tax price was 6\$. So in our case ½ dollar is paid by suppliers and the same amount of money is paid by demanders.

Also abserve that the equilibrium quantity decreases after the tax was levied and the higher price is imposed to consumers.

Elasticities

If elasticities of demand and supply are different then the tax applied to consumers is also different.  Two ideas should be understood. First, with a constant supply, the more inelastic is demand for the product, the biggest portion of tax should be paid by consumers. To verify this assumption let’s sketch the effect of tax on elastic and inelastic demand (In a perfectly inelastic demand all tax is paid by buyers, but in a perfectly elastic demand all tax is paid by seller).

In the first figure from above, where is shown an elastic demand, a small portion of tax (Pe-P1) is shifted to consumers and most of the tax (P1-Pa) is paid by suppliers. However, in second figure where the demand tends to be more inelastic the biggest part of the tax (Pi-P1) is paid by consumers and less of it (P1-Pb) is shifted to producers.

Observe that in both figures there is a decline in equilibrium quantity and this decline is less when demand more inelastic, this fact is used by government when levy great taxes on cigarettes, liquor, automobile tires, telephone services and other products which demand is thought to be inelastic. Since demand isn’t so elastic, this tax doesn’t reduce sales too much, so the tax revenue remains high.

Second, with a constant demand, the more inelastic is supply, the larger tax is shifted to producers. Like in the following first figure most of the tax (Pe-P1) is shifted to consumers and only a small part (P1-Pa) is going to be paid by suppliers.  But when the supply is inelastic (second figure) major part of the tax (P1-Pb) falls on sellers and just a small part (Pi-P1) is shifted to demanders.