Question

In an effort to reduce alcohol consumption, the government of economy XYZ is considering $1 tax on each gallon of liquor sold (the tax is levied on producers). Suppose that the demand curve is QD = 500,000- 20000P (where QD is the number of gallons of liquor demanded and P is the price per gallon), and the supply curve for liquor is Qs = 30000P (where Qs is the number of gallons supplied).

a. Calculate the before tax equilibrium price and quantity

b. Calculate the after tax equilibrium price and quantity   

c. How much revenue does the tax raise for the government?   

d. How much of the revenue comes from consumers, and how much from producers?   

e. Suppose that the demand for liquor is more elastic for younger drinkers than for older drinkers. Will the liquor tax be more, less, or equally effective at reducing liquor consumption among young drinkers? Explain   

Answer 1

Solution:

a) Calculation of before tax equilibrium price and quantity

QD=Qs

500,000- 20000P=30000P

P=500,000/50,000

=$10

QD=500,000-20000*10

=300,000

Thus before tax equilbrium price is $10 and quantity is 300,000gallon

b)Calculation of after tax equilibrium price and quantity

QD=Qs

500000-20,000P=30000(P-1)

P=10.6

QD=500000-20,000*10.6

=288,000

c)Tax revenue for the government

$1*288,000=$288,000

d)Consumer pay=$10.60

Producer received=$9.60

Tax amount=$1

Consumer pay=($10.60-10)*288000=$172,800

Producer pay=($10-9.60)*288000=115,200