Question
.12) In the effort to reduce alcohol consumption, the
government is considering a $1 tax on each gallon of liquor sold. The legal incidence of the tax
will be on producers. Suppose the demand for alcohol is described by Q
D
= 500,000 – 20,000*P
where Q
D
is quantity and P is price per gallon (NOTE: the
inverse
demand curve would be P = 25
– 0.00005*Q
D
). The supply curve is described at Q
S
= 30,000*P (NOTE: This would make the MC
curve MC = (1/30,000)*Q
S
).
a.
Draw the supply and demand curves before the tax is imposed. Calculate the
equilibrium price and quantity.
b.
Add the tax to the supply curve. Calculate the new price per gallon consumers pay, the
price per gallon producers receive, and the new equilibrium quantity.
c.
Calculate the amount of revenue the tax generates. How much of the tax is paid by
consumers? How much of the tax is paid by producers?
d.
Calculate the elasticity of demand at the original equilibrium price. Calculate the
elasticity of supply at the original equilibrium price.
e.
Calculate the deadweight loss of the tax.
f.
Suppose that if you were to disaggregate the market demand into young drinkers and
old drinkers you would find that the demand for alcohol is more elastic among young
drinkers than old drinkers. Which group of drinkers will change their behavior more?
Which group of drinkers will bear the bigger burden of the proportion of the tax that
falls on consumers? Expla
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