More questions on the effects of a sales tax.

1) The town of West Headland has many barbershops and they price competitively.  The  demand for haircuts  is given by the equation Q=1200-20P.  Nobody is willing to supply a haircut for less than $5.   The supply  curve has the equation Q=80P-400 for all P>$5
 What is the equilibrium price for a haircut?  What is the equilibrium number of haircuts?

2)  Suppose that the town imposes a $5 sales tax on haircuts.  The tax is collected from barbers.    What is the new equilibrium price that buyers must pay for a haircut? the new equilibrium quantitty?
How much revenue is raised?

3)    It can be shown that total consumers' surplus (buyers' profits) were $19,360 before the tax was imposed and $16,000 afterwards.  It can also be shown that total profits of sellers were $4840 before the tax was imposed and $4000 after the tax was imposed.  How much is the excess burden of the tax?    (For extra credit--Can you show that buyers and sellers profits before and after were what is claimed here?)

3)  As part of a city beautification program, the town government decides that instead of taxing, they will  subsidize  haircuts, by paying barbers $5 for every haircut that they give.
What is the new equilbirium price paid by buyers for a haircut?  the new equilibrium quantity? How much does the subsidy cost the
town government?

4)   Total profits  of buyers, with the subsidy can be shown tobe $23,040. Total profits of sellers with
the subsidy can be shown to be $5760. 
How much is the excess cost  of the subsidy?  (For extra credit--Show that the total profits are as claimed here.)

Answers available here.