Answers for West Headland

1).  Set supply equal to demand:  1200-20P=80P-400 and solve for P.  This gives the competitive price of  P=$16.
Then the quantity must be 880.  (Substitute P=16 into either the demand or supply equation. )

2)  Where P is the price paid by demanders, suppliers get an after tax price of only P-5.  The new supply equation  is Q=80(P-5)-400=80P-800.  Supply equals demand when 1200-20P=80P-800.  Solve this for P. You will find that the after tax price is P=$20.    Quantity is now 800.  So barbers can pass on 4/5 of the tax.
 After the tax is imposed, 800 haircuts are sold.  With a $5 tax on each haircut, the government's tax revenue totals  $4000.

3) Total loss in profits of buyers and sellers is $(19360+4840)-(16,000+4000)=$4200.  Government revenue is
$4000, so excess burden is $200.

4)  Where P is the price paid by demanders, barbers get an after subsidy payment of P+5 for each haircut.  The new supply equation is Q=80(P+5)-400=80P.   Supply equals demand when 1200-P=80P.  That is, where P=$12.
Then the number of haircuts sold is 960.  The cost to the government is $5x960=$4800.

5)  Cost to government is $4800.  Increase in profits to buyers and sellers is $(23040+$5760)-(19360+4840)=$4600.   Excess cost is $4800-4600=$200.

Finding total consumers' surplus and profits:

 Consumers' surplus is the area under the demand curve and above the price.  Draw the  demand curve and supply curve and use the formula for area of a  right triangle  to find this area before and after the tax is introduced.   The demand curve intersects the vertical axis at $P=60.  With no taxes, price is  16 and quantity is 880.  The area of the consumers' surplus triangle is therefore $(60-16)x880/2 =19,360.
With the tax, the price rises to $20 and quantity is 800. The area of the  consumers' surplus triangle  is now $(60-20)x800/2=$16000.  

With no tax,  the price is $16 and  the area of the profits triangle is $(16-5)x880/2)=$4840.    The after tax price for suppliers is  $20-5= $15.   The area of the profits triangle is $(15-5)x800/2=$4000.

To find profits with the surplus, again draw the appropriate triangles and find their areas.
  With the subsidy, the price is $16 and quantity is 960.  The area of the consumers' surplus triangle is (60-12)x960/2=$23,040.
 The profits of sellers with the subsidy are $(17-5)x960/2=$5760..