Question

Suppose the market demand function for ice cream is Q^d = 10 - 2P and the market supply function for ice cream is Q^s = 4P - 2, both measured in millions of gallons of ice cream per year. Suppose the government imposes a $0.46 tax on each gallon of ice cream. The change in producer surplus due to the tax is: (Round to the nearest ten thousand and answer in millions. ex. 0.94 = 940,000)

Answer 1

Qd=10-2P
Qs=4P-2
At equilibrium Qs=Qd
10-2P=4P-2
12=6P
P=2
Q=10-2(2)=6

When Qs=0 P=0.5
PS=0.5*(2-0.5)*(6)=4.5

after tax the new supply will be
Qs=4(P-0.46)-2=4P-3.84
New equilibrium
4P-3.84=10-2P
4P+2P=10+3.84
6P=13.84
P=2.30
Q=10-2(2.30)=5.38

Price is 2.30
Initial price was 2 but the tax was for $0.46 This is only 2.30-2=0.30 increase
This means that buyes a\ay $0.30 of the tax
and sellers pay $0.16 of the tax and receive $1.84
New Producer Surplus=0.5*(Price producers receive-Price when supply is 0)*(new equilibrium quantity)
New Producer Surplus=0.5*(1.84-0.96)*(5.38)=2.36
Change=2.36-4.5=-2.14