Question

Suppose supply and demand curves are:QD=28−2P;QS=−4+2P. If a tax of $2 is imposed on buyers. What is the tax revenue collected by the government

Answer 1

demand; Q= 28-2P

suppply; Q= -4+2P

Equilibrium: demand = supply

that  is, 28-2P=-4+2P

32 = 4P

P=8

This implies Q= 12

So, equlibrium price and quantity are {8,12}

Now, a tax of $2 is imposed on buyers.So, buyers will demand the same quantity at a price $2 lower.

demand; Q=28-2P

equivalent to P= 14-Q/2

now demand equation changes to P= 14-(Q/2)-2

that is, P=12-Q/2

equivalent to

Q=24-2P

NEW equilibrium

demand equals supply

that is, 24-2P = -4+2P

28=4P

P= 7 (this the price received by sellers)

implies Q= 10

price paid by buyers will be $2 higher than price received by sellers.(This $2 is collected by government). So, buyers price is $9.

So after tax, 10 units of quantity are traded in the market on which government collects a tax of $2 per unit.

so, total revenue is $2*10= $20

Tax revenue collected by government is $20.