Chapter 3
Chapter 3
Chapter 3
Example 1: Suppose the demand function is p = 50 – 2q, and the supply function is p = 10 + 3q.
a) Find the equilibrium point
b) Sketch a graph
Solution to part a:
Answer to part a: the equilibrium point is at (8, 34). This means when the quantity is 8, the price is
$34.
Solution to part b:
40
20
10
2 4 6 8 10 12 14 16 18
Example 2: Suppose the demand function is p = 50 – 2q, and the supply function is p = 10 + 3q. (same
as the last example). What would be the effect of a $5 tax?
Solution: Let p = the new price, including the tax. The consumer pays p dollars for the product, but the
supplier receives only p – 5 dollars, since $5 goes to the government.
p = 50 – 2q
p = 15 + 3q
40
30
10
2 4 6 8 10 12 14 16 18
This is a general concept in economics. The effect of any tax on a product is to move the supply curve
upwards.
Here is one way to think about this: Let’s use the point (2, 16) from the original supply curve as an
example. Imagine a producer saying, “If the price is $16, I am willing to produce 2 units”
Now, with a $5 tax, the supply curve moves up $5, so imagine the producer saying “I used to be willing
to produce 2 items if the selling price was $16. But now, the price will have to be $21 for me to
produce 2 items. I still only get $16 and $5 goes to the government.”
Solution: Set the demand and supply functions equal to each other (but add $5 to the supply function)
50 – 2q = 15 +3q
35 – 2q = 3q
35 = 5q
7=q
The consumer pays $36. Out of this, $5 is the tax and the producer keeps $31.
Example 4: How much revenue does the government collect as a result of this $5 tax?
Solution: The government collects $5 per unit, and the quantity at the new equilibrium point is q = 7.
Therefore the tax revenue is:
The tax revenue can be represented in terms of area, using the diagram below:
The height of the rectangle is the tax (in this case, $5), and the width is q (in this case, 7). The area of
the rectangle is $35.
Notice that the producer surplus is less, because it is based on the price the supplier receives (in this
case, p – 5).
First, compute the revenue. However, it is not simply price times quantity, because the producer
receives p – 5 dollars.
To compute the area under the curve, use the q based on the tax, but use the original supply function
(without the tax), because the producer does not receive the tax:
Example 6: Suppose a demand function is p = 400q-0.5, and the supply function is p = 2q0.8. What is the
equilibrium point if there is a 9% sales tax on the product?
Solution: Just like the previous example, the demand function stays the same, while the supply
function moves upwards. How far does it move up? It moves up by 9%. This effectively means to
multiply the supply function by 1.09.
Example 7: What is the tax revenue, and what is the revenue for the producer?
Solution: First, we have to figure out the amount of the tax. Notice that we cannot simply multiply
53.88 by .09 to find the tax, because $53.88 is the price with the tax already included. We have to
multiply the original price (which is unknown) by 0.09. In this situation, we have to use a method
called back-taxing, to figure out the tax:
Since the tax is 9%, normally we multiply the original price by 1.09 to figure out the new price.
However, in this case, we don’t know the original price. Let’s call it p0.
Answer: the tax revenue is $245.24, and the producer’s revenue is $2,724.09
Practice Problems
Answers
1a) (425, $52.25). b) (406.25, $53.56). c) $1218 d) $20,527.36. e) $7,425.74 (for parts c, d and e,
quantity is rounded to the nearest whole number).
3a) (213.75, $11.70) b) (200.35, $12.24) c) price before tax: $11.55, tax: $0.69, tax revenue: $138.00
d) $2310 e) $4386.40 (for parts c, d and e, quantity is rounded to the nearest whole number).