Download The Price Expansion Path

Econ 11
Monique Romo
303-569-163
7c. Price Expansion Path
The price expansion path (also called the price expansion curve or the PEP) is a graph that shows what happens to
the optimal point as the price of a product is changed. To find the price expansion path, you find the consumer’s
optimum of each budget constraint. What’s important to note is that the budget constraints shift as the price of one
particular changes. You then draw a curve to connect the consumer’s optimum’s together. Figure 7.c.1 shows a
simple example of the price expansion path.
The budget constraint is a graph that represents a combination of goods that an individual can consume given the
prices of each good and their given income. The equation for the budget constraint is as follows:
X*Px + Y*Py = I
where x and y are the quantity being consumed and Px and Py are the prices of each product. Adding these will
make up your total income.
Points below the budget constraint line are affordable to a consumer, but not necessarily efficient. Points above the
budget constraint line are not accessible.
The consumer’s optimum is reached where the slope of the budget constraint equals the slope of the indifference
curve.
Figure 7.c.1
y
A
B
C
Price Expansion Path
(PEP)
Various Budget Constraints
(shift towards higher quantities of x as Px
decreases)
x
Figure 7.c.1 illustrates a simple example of the Price Expansion Path. The blue lines represent the various budget
constraints. In this case, as the price of good x decreases, a consumer is now able to consume more of x, which
shifts their budget constraint outwards away from the origin. In terms of y, the consumer’s consumption of y does
not change as the price of x decreases, which is why they all meet up at the same point on the y-axis. A, B, and C
represent a consumer’s optimal point on their different indifference curves that lie tangent to their respective budget
constraints. Connecting these points makes up the Price Expansion Path (PEP).
Econ 11
Monique Romo
303-569-163
The PEP can take on several forms, as long as the indifference curves do not cross. For example, Figure 7.c.2 below
shows this example.
y
Figure 7.c.2
NOT OK
A
PEP
C
B
BC
x
Figure 7.c.2 is NOT a possible PEP because a condition of IC’s is that they are not allowed to cross. In the graph,
the BC crosses the PEP at three different points, but when the IC’s are drawn, they cross. Therefore, this is not
possible.
PEP and Giffen Case
In other cases, the PEP could resemble something like Figure 7.c.3. This particular case is okay because after
drawing the budget constraints and allocating optimums and indifference curves, we see that they do not cross.
y
GIFFEN CASE
Figure 7.c.3
Px
PEP
X
B
OK
Slope = $1 = Px
C
BC
Slope = $2 = Px
A
x
30
45
Figure 7.c.3 represents a new PEP form and also illustrates the Giffen Case. In this example, the price of x
decreases, shifting the BC outwards. We would normally expect one’s consumption of x to increase as we jump
from C to B, but in this case, the quantity of x decreases from 45 to 30. This is known as a Giffen Good. A good if
a Giffen Good when the price of that good decreases, but consumers decide to consume less of it.
Econ 11
Monique Romo
303-569-163
PEP and Demand Curve
Just as the IEP and the Engel Curve are related, the curve that relates to the PEP is the Demand Curve. As the price
of x decreases, individuals decide to consume more of it, if they follow the law of Demand. Figures 7.c.4 and 7.c.5
will demonstrate how to derive the Demand curve from the PEP.
Figure 7.c.4
y
Slope = Px/Py = $3
Slope = Px/Py = $2
Slope = Px/Py = $1
PEP
C
A
B
x
10
43
25
Px
Figure 7.c.5
A'
3
B'
2
C'
1
Demand Curve
10
25
43
x
Figure 7.c.4 demonstrates the PEP we first saw. Just as before, as the price of x decreases, our budget constraint
shifts outward as we are able to consume more x. Bringing the price of x and the quantity consumed to a new graph,
we get Figure 7.c.5. Within this graph, we see how as the price of x goes down, the quantity consumed increases.
Point A in 7.c.4 becomes A’ in 7.c.5. Its shape and direction then becomes the Demand Curve.
Econ 11
Monique Romo
303-569-163
Study Questions
1. If the Price of good x decreases from $3 to $2 and our consumption increases respectfully from 10 to 11, the PEP
can be described as the following:
a)
b)
c)
d)
e)
downward sloping
horizontal
vertical
upward sloping
none of the above
2. As the price of a good decreases, how will our consumption change according to a simple PEP? How does our
budget constraint shift as a decrease in Px occurs?
3. What is the purpose of a PEP? What can we derive from it?
Answers
1. d) upward sloping
2. As the price of a good decreases, we will usually consume more of that good. If there is a decrease in Px, our
budget constraint shifts outward away from the origin.
3. A PEP shows what happens to the optimal point as the price of a product is changed. Connecting these optimal
points will give us a curve that traces the changes in such optimal points. We can then derive the Demand curve
from the PEP.