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
Consumers' surplus is the area under the demand curve and
price. Draw the demand curve and supply curve and use the
area of a right triangle to find this area before and after
is introduced. The demand curve intersects the vertical
$P=60. With no taxes, price is 16 and quantity is
880. The area of the consumers' surplus triangle is therefore
With the tax, the price rises to $20 and quantity is
800. The area of the consumers' surplus triangle is now
With no tax, the price is $16 and the area of the profits
$(16-5)x880/2)=$4840. The after tax price for suppliers
$15. The area of the profits triangle is
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