Suppose demand and supply are given by:

Qdx=14−0.5PxQxd=14−0.5Px and

Qsx=0.25Px−1Qxs=0.25Px−1.

a) Determine the equilibrium price and quantity.

b) Suppose a $12 excise tax is imposed on the good. Determine the new equilibrium price and quantity.

c) How much tax revenue does the government earn with the $12 tax?

a) Determine the equilibrium price and quantity.

Equate the demand and supply equations to solve for equilibrium price and quantity, we get:

• 14−0.5P=0.25P−115=0.75PP∗=20Q∗=414−0.5P=0.25P−115=0.75PP∗=20Q∗=4

b) Suppose a $12 excise tax is imposed on the good. Determine the new equilibrium price and quantity.

Rewrite the demand and supply equation as a function of P, we get:

• PST=4+4QPST=4+4Q and PDT=28−2QPDT=28−2Q

The effect of tax will be the same whether it is imposed on producers or consumers. Suppose government imposes $12 tax on producers, the supply curve after tax is given by: PST=4+4Q+12=16+4QPST=4+4Q+12=16+4Q

Then the new equilibrium quantity after tax can be found from equating PDT=28−2QPDT=28−2Q and PST=16+4QPST=16+4Q, which gives QT=2QT=2 and PT=24PT=24

c) How much tax revenue does the government earn with the $12 tax?

The revenue that government obtained from tax is given by:

• TR=Tax×QTTR=12×2=24