Linear demand and supply functions: calculating the effects of
specific (excise) taxes on markets and community welfare
1: Suppose we are given the following demand and supply functions:
Qd = 60 – 2P
Qs = -4 + 2P
(a) Solve for the equilibrium price and quantity.
(b) Plot the two curves on a coordinate map.
Suppose the government imposes an indirect (excise) tax on the
product of $6 per unit. This means that the supply curve will shift
upwards by $6 for each level of output.
The new supply curve S2 (S1 + tax) lies above the initial supply curve
S1. Just count $6 up along the vertical axis from the y-intercept of 2.
We find that the new y-intercept of S2 is 8. Now draw a line parallel
to S1 – this gives you the new supply curve.
2: How to find the new price paid by consumers, the price received
by producers and the quantity bought and sold following the
imposition of a tax.
To get accurate values, we must find the new post-tax supply
function, solve for Pc and Qt and then use Pp = Pc – tax per unit to
find Pp.
Given a supply function of the general form Qs = c + dP,
whenever there is an upward shift of the function by t units,
where t = tax per unit, we replace P by P –t. The new supply
function becomes Qs = c + d (P – t)
We can now use this rule to find the new supply function. Our initial
supply function was Qs = -4 + 2P. With a tax of $6 per unit, this
function shifts upwards by $6, so that t =6. Therefore the new supply
function becomes:
Qs = -4 + 2(P-6)
Simplify to find the new supply function.
Plot the new supply function on the diagram
3: Now use the original demand function and new supply function to
solve for equilibrium price and quantity
Qd = 60 – 2P
Qs =
4: Using the data in the table below:
Price
1
2
3
4
5
Quantity Demanded
20
16
12
8
4
Quantity Supplied
2
6
10
14
18
(a) Find the equations of the supply and demand curves and graph
your results
(b) Now suppose that a $1 per unit sales tax is imposed. Find the S +
T equation and determine how much equilibrium price rises. Graph
your results
5: Impact of a Unit Sales Tax
Suppose that a $2 per unit sales tax is implemented (Column 4).
Column 1
Price
1
2
3
4
5
6
7
8
9
10
Column 2
Quantity
Demanded
40
36
32
28
24
20
16
12
8
4
Column 3
Quantity
Supplied
3
6
9
12
15
18
21
24
27
30
Column 4
QS if tax = $2
The firm, of course, will treat the tax as an additional cost and will try
to pass it on to the buyer. Notice that with no tax (Column 3) the firm
would offer 9 units at a price of $3. Once the tax is imposed, the firm
will offer 9 units only at a price of $5.
(a)
(b)
(c)
(d)
(e)
(f)
(g)
Calculate the original linear demand and supply functions.
Plot these functions on a diagram
Determine the equilibrium price and quantity. Verify that
your calculations and positioning (diagram) are the same
values.
If a $2 specific tax is imposed on the product, determine the
values for Column 4
Using the values in Column 4 calculate the new linear supply
function.
Taking the original linear demand and the new linear supply
function calculate the new equilibrium price and quantity.
Plot the new linear supply function on the diagram
Calculate the area of
 Tax revenue
 Consumer Surplus
 Producer Surplus
 Economic/Total/Community Surplus