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..