**For a given price change,
how responsive is the decline in quantity? For a
given per centage change in P,**

**how large will be the per
centage change in Q?**

**Price Elasticity of
Demand: The percentage change in
Quantity Demanded that results from a 1% change in Price.**

**In other words, the percentage
change in Quantity Demanded caused by a percentage change in P.**

**There are two basic ways to
measure elasticity. We can use a Point Elasticity measure, or an
Arc Elasticity Measure:**

**Point Elasticity Measure:**

** | DQ/Q| = | P * DQ | = e**

**| (Q _{2}-Q_{1})/[Q_{1}+Q_{2}]
| = e**

**Total Revenue:
Dollars earned by suppliers**

** in the
market per period by the sale of**

** quantity of
a good at a given price.**

**TR = P x Q**

**Dollars per period =
[$/unit] *[# of units sold]**

**
per period**

**Suppose we have the
following demand curve, P = 100-Q/2 with the accompanying graph.**

**There are three points
marked on the graph:**

** Point A:
P = 80, Q = 40 , Total Revenue = $3200**

** Point M: P =
50, Q = 100, Total Revenue = $5000**

** Point B:
P = 20, Q = 160, Total Revenue = $3200**

**We can graph Total Revenue
as an area on the graph of the demand curve, or, we**

**can graph Total Revenue
against quantity per period directly, and get the following**

**graph.
Note the 'upside-down bowl' shape of the TR curve. Note, too, that**

**TR reaches it maximum at the
midpoint of the demand cureve, where the price**

**elasticity of demand equals 1.**

**Point Elasticity at Point
M: P = 50, Q = 100:**

**At (100,50):**

** e
= | 50/100 * -50 | = 1 At the midpoint, e = 1. This is a Unit Elastic point.**

**Point elasticity at
Point A: P = 80,Q = 40:**

**e
= | 80/40 * -2 | = 4 Curve is elastic
at (40,80), since e>1.**

**Point elasticity at Point
B: P = 20, Q =160:**

**e =
| 20/160 * -2 | = 1/4 Curve is inelastic at
(160,20), since e<1.**

**Using the Arc Elasticity
Measure, or Mid-Point Formula:**

*Midpoint forumula:
Calculate the elasticity on the arc*

*from Point A to Point M,
starting at Point A:*

**Let (Q _{1},P_{1})
= (40,80) = Point A**

**Let (Q _{2},P_{2})
= (100,50) = Point M**

**Q _{2}-Q_{1}
= 100-40 = 60 (Q_{2}+Q_{1})/2 = 140/2
= 70**

**P _{2}-P_{1}
= 50-80 = -30 (P_{2}+P_{1})/2 = 130/2
= 65**

**e
= [60/70]/[-30/65] = [130/70] = 1.86**

**NOTE: The arc
elasticity equals the point elasticity at the midpoint**

**of the arc. That is why
the arc elasticity formula is sometimes**

**called the midpoint formula.**

**For this problem, at
the point P = 65, Q = 70, the point elasticity would**

**be:**

**e =
| 65/70 * -2 | = [130/70] = 1.86**

**Price elasticity of demand
measures the availability of**

**substitutes for a good.**

**1. A more elastic
curve => there are more available**

**substitutes for the good.**

**2. The more narrowly
defined is a good, the more**

**elastic is its demand.
Demand for food, for example,**

**is less elastic than demand
for a**

**type of food, hamburgers, for
instance.**

**3. Over time, we expect
elasticity to grow, as more**

**substitutes are made available.**

**Demand for gasoline today is
less elastic than**

**demand for gasoline per month,
or per year, others things equal.**

**See the accompanying graph.**

**Steeper demand curve:
P = 100 - Q/2**

**At C, the point price
elasticity of demand is**

**
|40/120*-2| = 2/3**

**Flatter demand curve:
P = 50 - Q/4**

**At câ, the point
price elasticity of demand is**

** |20/120*-4| =
2/3**

**Yet, we would call the
ãflatterä demand curve more**

**elastic than the
ãsteeperä one.**

**Assume we have the supply
curve: P = 10+Q/2**

**Equilibrium with P =
100-Q/2:**

**
100-Q/2 = 10+Q/2**

**
90 = Q**

**
55 = P Call this point E.**

**Equilibrium with P = 50-Q/4**

**
50-Q/4 = 10+Q/2**

**
40 = 3Q/4**

**
53.3 = Q**

**
36.65 = P Call this point F.**

*Point Elasticity at
Point E:*

** P/Q = 55/90**

** DQ/DP =
-2 Point elasticity =
[55/90]*2 = 110/90**

**
= 1.22**

*Point Elasticity at
Point F:*

**P/Q = 36.65/53.3**

**DQ/DP =
-4
Point elasticity = [36.65/53.3]*4**

**
= 2.75**

**For a given supply curve,
then, the equilibrium point on the steeper demand**

**curve is less elastic than the
equilibrium point on the flatter demand curve.**

**Price Elasticity of Supply**

Price elasticity of supply is very similar in concept to price elasticity of demand. In each case, we are measuring the responsiveness of a quantity to a change in price.

**Price Elasticity of Supply: **The
percentage change in Quantity Supplied that results from a 1% change in
Price.

In other words, the percentage
change in Quantity Supplied caused by a percentage change in P.

**The equation used to
calcuate the price elasticity of supply is the same as that used for
the price elasticity of demand:**

**Point Elasticity Measure:**

** | DQ/Q| = | P * DQ | = e**

**Arc Elasticity Measure:**

**| (Q _{2}-Q_{1})/[Q_{1}+Q_{2}]
| = e**

A linear supply curve that has a
positive intercept on the vertical or Price axis is **elastic** at every point: For every
point on the curve, **e>1**
at every point, and e approaches 1 as Q rises
from 0.

A linear supply curve that has a
negative intercept on the vertical or Price axis, is inelastic at every point: For every
point on the curve, **e<1**at
every point, and e approaches 1 as Q rises from 0.

A linear supply curve that has an
intercept of 0, i.e., goes through the origin, is **unit elastic** at every point: For every
point on

the curve, **e
= 1.**