Suggested Answers for Mankiw, Chapter 8, “Other” Problems
Figure 3 illustrates the market for pizza. The equilibrium price is
equilibrium quantity is
, consumer surplus is area A + B + C, and
producer surplus is area D + E + F. There is no deadweight loss, as all the
potential gains from trade are realized; total surplus is the entire area
between the demand and supply curves: A + B + C + D + E + F.
With a $1 tax on each pizza sold, the price paid by buyers,
, is now
higher than the price received by sellers,
+ $1. The
quantity declines to
, consumer surplus is area A, producer surplus is
area F, government revenue is area B + D, and deadweight loss is area C +
E. Consumer surplus declines by B + C, producer surplus declines by D +
E, government revenue increases by B + D, and deadweight loss increases
by C + E.
If the tax were removed and consumers and producers voluntarily
transferred B + D to the government to make up for the lost tax revenue,
then everyone would be better off than without the tax. The equilibrium
quantity would be
, as in the case without the tax, and the equilibrium
price would be
. Consumer surplus would be A + C, because consumers
get surplus of A + B + C, then voluntarily transfer B to the government.
Producer surplus would be E + F, because producers get surplus of D + E
+ F, then voluntarily transfer D to the government. Both consumers and
producers are better off than the case when the tax was imposed. If
consumers and producers gave a little bit more than B + D to the
government, then all three parties, including the government, would be
better off. This illustrates the inefficiency of taxation.