Understanding Sales Taxes: Impact on Revenue and Market Burden

1. Sales Taxes, Revenue, and Burden

2. The effect of a sales tax collected from buyers is to • Shift the demand curve up by the amount of the tax. • Shift the supply curve down by the amount of the tax. • Shift the demand curve down by the amount of the tax. • Shift the supply curve up by the amount of the tax. • Shift both the demand and the supply curve, each by half the amount of the tax.

3. The demand curve has equation P=50-Q and the supply curve has equation P=10+Q where P is price and Q is quantity. The competitive equilibrium price and quantity are: • P= 30, Q=10 • P=30, Q=20 • P=20, Q=20 • P=10, Q=40 • P=40, Q=30

4. Why is that? • In equilibrium supply equals demand. • We have the demand curve with equation P=50-Q and the supply curve with equation P=10+Q. • The demand and supply curves cross where 50-Q=10+Q. Solve for Q and you find Q=20. Then P=50-Q=10+Q=30.

5. The demand curve has equation P=50-Q and the supply curve has equation P=10+Q where P is price in dollars and Q is quantity. If a sales tax of $10 per unit is collected from buyers, the new equilibrium price and quantity will be: • P= 35, Q=15 • P=35, Q=25 • P=25, Q=15 • P=10, Q=40 • P=30, Q=10

6. Why is that? • A sales tax collected from demanders shifts demand curve down by amount of the tax. • Old demand curve was P=50-Q. New one Must be P=40-Q. • The demand and supply curves cross where 40-Q=10+Q. Solve for Q and you find Q=15. Then P=40-Q=10+Q=25.

7. As in the previous question, the demand curve has equation P=50-Q and the supply curve has equation P=10+Q where P is price in dollars and Q is quantity. If a sales tax of $10 per unit is collected from buyers, how much revenue will the government raise with the tax? • $150 • $100 • $200 • $300 • $350

8. Why is that? With the tax, we found that the quantity sold is 15 units. The tax is $10 per unit. Tax revenue is tax per unit times quantity sold. $10x15=$150.

9. The Demand curve has equation Q=100-P. Supply curve has equation Q=10+2P. A sales tax of $15 is introduced. The after-tax price to demanders will • Rise by $5 • Rise by $7.50. • Rise by $15. • Rise by $10 • There is not enough information to tell.

10. Why is that? Let x be the rise in buyer’s after-tax price and y the fall in supplier’s after-tax price. We know that supply curve is twice as steep as the demand curve so y=2x. We also know that x+y=$15 is total amount of the tax. So x+2x=$15. Therefore x=$5.

11. Another Reflex Check • Enter the letter A on your clicker.

12. And on to our lecture…