cise Taxes and Tax RevenueThe government pays attention to elasticity of demand

Question

cise Taxes and Tax RevenueThe government pays attention to elasticity of demand when it selects goods and services on which to levy excise taxes (taxes levied on the production of a product or on the quantity fo the produc purchased). If a $1 tax is levied n a product and 10,000 units are sold, tax revenue will be $10,000 $1 X 10,000 units sold).If the government raises the tax to $1.50, but the higher prices that results reduces sales (quantity demanded) to 4000 because demand is elastic, tax revenue will decline to $6000 $1.50 X 4000 units sold). So a higher tax on a product that has an elastic demand will b ring in less tax revenue. In contrast, if demand is inelastic, the tax increase from $1 to $1.50 will boost tax revenue. For example, if sales fall from 10,000 to 9000, tax revenue will rise from $10,000 to $13,500 $1.50 X 9000 units). Little wonder that legislatures tend to seek out products such as liquor, gasoline, cigarettes, and phone services when levyingand raising taxes. Those taxes yield high tax revenues.

Question: Under what circumstance might a reduction of an excise tax actually produce more tax revenue?

Explanation / Answer

Answer:

When demand is elastic, then a reduction of excise tax might actually produce more tax revenue. For example; suppose initially excise tax was $1, price with exercise tax was $5 and quantity sold was 10000. And demand is elastic having value equal to -2. In this case, total revenue collected by government is $10000 (=1*10000).

Now suppose excise tax reduces to $0.8 which causes price of good to fall to $4.2.

So, % change in price = [(4.2-5)/5]*100 = - 16

We know price elasticity of demand = % change in quantity demanded/%change in price

This implies % change in quantity demanded = price elasticity of demand*%change in price

We are given % change in price = -16 and price elasticity of demand = -2

So, % change in quantity demanded = (-2)*(-16) = 32% i.e. quantity demanded will increase by

32%.

Given that initial quantity demanded was 10000, then with 32% increase, new quantity demanded would be equal to = 10000+10000*0.32 = 13200

So, new tax revenue (after decline in excise tax) = new tax rate*new quantity demanded = 0.8*13200 = $10560 (>$10000)

This implies that when demand is elastic, then a reduction of excise tax might actually produce more tax revenue.

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