Price Elasticity of Demand and Supply
The slope of a line tells us its steepness; it is a relationship between price changes and quantity changes on
a demand curve, for example.  It that case, it is always a negative relationship.

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
         | DP/P |     | Q   DP |
Arc Elasticity Measure:

|     (Q2-Q1)/[Q1+Q2]    |  = e
|                          2           |
|      (P2-P1)/[P1+P2       |
                        2

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.
       |                25 |

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 (Q1,P1) = (40,80) = Point A

Let (Q2,P2) = (100,50) = Point M

Q2-Q1 = 100-40 = 60    (Q2+Q1)/2 = 140/2 = 70

P2-P1 = 50-80 = -30    (P2+P1)/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
         | DP/P |     | Q   DP |

Arc Elasticity Measure:

|     (Q2-Q1)/[Q1+Q2]    |  = e
|                          2           |
|      (P2-P1)/[P1+P2       |
                        2

    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<1at 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.