Question

Compare one poor person with an income of $10,000 per year with a relatively wealthy person who has an income of $60,000 per year. Imagine that the person drinks 15 bottles of wine per year at a price of $10 per bottle while the wealthy person drinks 50 bottles of wine per year at an average price of $20 per bottle. If a tax of $1 per bottle is imposed on wine, who pays more on taxes? Who pays the greater amount as a percentage of income? If a tax equal to 10% of the wine is imposed, who pays more in taxes? Who pays more as a greater percentage of income?

Answer 1

(a) Tax = $1 per bottle (Specific tax)

Total expenditure of poor person before tax = 15 x $10 = $150

Assuming tax increases price by $1,

Total expenditure of poor person after tax = 15 x $(10 + 1) = 15 x $11 = $165

Tax paid = $165 - $150 = $15

Tax as % of income = $15 / $10,000 = 0.0015 = 0.15%

Total expenditure of wealthy person before tax = 50 x $20 = $1,000

Assuming tax increases price by $1,

Total expenditure of wealthy person before tax = 50 x $(20 + 1) = 50 x $21 = $1,050

Tax paid = $1,050 - $1,000 = $50

Tax as % of income = $50 / $60,000 = 0.0008 = 0.8%

Therefore, wealthy person pays more in taxes, but poor person pays more as % of his income.

(b) When tax = 10% of price of wine (Ad-valorem tax)

Total expenditure of poor person before tax = 15 x $10 = $150

Tax increases price by ($10 x 10%) = $1 (to $11).

Total expenditure of poor person after tax = 15 x $11 = $165

Tax paid = $165 - $150 = $15

Tax as % of income = $15 / $10,000 = 0.0015 = 0.15%

Total expenditure of wealthy person before tax = 50 x $20 = $1,000

Tax increases price by ($20 x 10%) = $2 (to $22).

Total expenditure of wealthy person before tax = 50 x $22 = $1,100

Tax paid = $1,100 - $1,000 = $100

Tax as % of income = $100 / $60,000 = 0.0017 = 0.17%

Therefore, wealthy person pays more in taxes, and wealthy person pays more as % of his income.