Question

The demand and supply curves are given by q=130−3p and q=2p−60, respectively; the equilibrium price is $38 and the equilibrium quantity is 16 units. A sales tax of 2% is imposed on the consumer. (a) Find the equation of the new demand and supply curves. b) Find the new equilibrium price and quantity. (c) How much is paid in taxes on each unit? How much of this is paid by the consumer and how much by the producer? (d) How much tax does the government collect?

Answer 1

The demand and supply curves are given by q=130−3p and q=2p−60, respectively; the equilibrium price is $38 and the equilibrium quantity is 16 units. A sales tax of 2% is imposed on the consumer.

(a) Since tax is imposed on consumers, demand function changes to q = 130 – 3(p + 2%*p) or

q = 130 – 3.06p and supply function remains unchanged at q = 2p – 60.

b) The new equilibrium price and quantity are determined by

130 – 3.06p = 2p – 60

p = 37.55

Price received by sellers = 37.55

Price paid by consumers = 37.55*1.02 = 38.30

Quantity = 2*37.55 – 60 = 15.10 units

(c) A total of 0.75 is paid in taxes on each unit. Of this, 0.30 is paid by the consumer and 0.45 is paid by producers.

(d) Government collects 0.75 as tax per unit and a total of 11.325