Question

According to studies undertaken by the US Department of Agriculture, the price elasticity of demand for cigarettes is between – 0.3 and – 0.4 and the income elasticity is about + 0.5.
Suppose Congress, influenced by studies linking cigarette smoking to cancer, plans to raise the excise tax on cigarettes so the price rises by 10%. Estimate the effect that the price increase will have on cigarette consumption and consumer spending on cigarettes (in percentage terms).

Answer 1

The price elasticity of demand for cigarettes is between – 0.3 and – 0.4

The income elasticity is about + 0.5

Now due to taxes price rises by 10%.

We know that price elasticity of demand for cigarettes = % change in Q / % change in P

-0.3 = % change in Q / 10% or -0.4 = % change in Q / 10%

% change in Q = -0.3*10% = -3% or -4%

Hence quantity demanded declines by 3% to 4%

Consumer spending on cigarettes = price of cigarettes * quantity of cigarettes

% change in spending on cigarettes = % change in price of cigarettes + % change in quantity of cigarettes

= +10% + (-3%) or +10% + (-4%)

Hence Consumer spending on cigarettes rises by 6% to 7%.