Assume the elasticity of demand of good X is 1 and it is put on sale for 40 less this will lead to

Markets:  Elasticity

Price Elasticity of Demand

Elasticity is a tool for estimating responsiveness of some dependent variable to a change in an independent variable.

            Definition:  Elasticity:  The percentage change in a dependent variable brought about by a 1% change in an independent variable.

            Intuitively, elasticity may be regarded as a measure of sensitivity.  If people are sensitive or responsive, we will say that they are elastic.  If they are insensitive or not very responsive, we will regard them as inelastic.

Let's first focus on the Price Elasticity of Demand -- How responsive or sensitive are consumers of X to a change in the price of good X?

Price Elasticity of Demand:The percentage change in Quantity Demanded brought about by a 1% change in the price of a good, or

Algebraically:

ED = %

      %

Px             

Where

 ED =

Q/Q    = 

QP

P/P       

PQ

Remember:  Elasticity is always read as the absolute value.

Determinants of price elasticity of demand. 

            a) Availability of close substitutes: Demand is more elastic, the more substitutes that are available.

            b) Price relative to income or proportion of  total expenditures:  Demand is more inelastic, the smaller price is relative to income.

            c) Time: Demand is more elastic, the longer the time frame (because there are more available substitutes, information, etc.), ceteris paribus.

            d) Durability of the product

                    Possibility of postponing purchase

                    Possibility of repair

                    Used product market

Applications.  You should be able to make comparative statements about the elasticity of demand for various products:

a)  What is more elastic: the demand for automobiles in general, or the demand for VW Bug? (Assume there is no brand loyalty to Bugs).

            b) What is more elastic: Demand for salt, or the demand for an automobile?

c) What is more elastic: Your demand for pain pills at 3 a.m. at the 7-11, or your demand for pain pills in general for your medicine cabinet.   A clothes washer or other large appliance -- usually a large proportion of budget - so more elastic.  However:

d) With the clothes washer -- it might be more elastic because it might be repairable.  So as the price increases, people buy less because they decide to repair or buy a used machine instead.  So the more "durable" the machine is (see above), the more elastic demand will be with a price increase -- people will buy fewer machines because they postpone, repair or buy a used one.  Similar to "a" above.  (A price decrease might be less elastic).

Calculating Elasticity of Demand. There are three ways to calculate price elasticity of demand: arc price elasticity, point price elasticity, and direct percentage changes.  The method that is appropriate in any particular context depends on the information provided.

            a. Arc Price Elasticity. For example, consider the demand curve implied by the following table:

            P                      Q

            4                      40

            5                      10

Graph:

Notice the change in demand may be calculated as Q1-Q0, and

the change in price = P1-P0.

Then Price Elasticity of Demand =  (Q1-Q0)P/(P1-P0)Q

But it makes a big difference if you use (P0,Q0) as your divisor, or (P1,Q1).

For example:

                        (40-10)  (4)      =          30(4)                =  -3.00

                        (4-5)    (40)                  -1(40)

                        (40-10)  (5)      =          30(5)                =  -15.00

                        (4-5)    (10)                  -1(10)

Neither of these points is inherently more correct.  As a convention, we calculate the arc price elasticity of demand using the average of the distance between the 2 points:

             ED =  (Q1-Q0)(P1+P0/2)

                   (P1-P0)(Q1+Q0/2).

In this case

            =          (40-10)  (4+5/2)         =          30(4.5)             =  -5.4

                        (4-5)    (40+10/2)                  -1(25)

Arc Price elasticity is interpreted as follows: Over the range of prices between $4 and $5 on average, a 1% reduction in price increases quantity demanded by 5.4 %.

             b. Point price elasticity:  When you are given a slope, and a point.

 ED  = (slope)(P)/Q

 Example: Suppose a demand curve is

Qd = 30 - 10P

Then, if P = 2, then Q=10 and elasticity is

-10 (2)/10 = -2.

 Uses: Mostly when given a demand function.

Point Price elasticity is interpreted as follows: At a price of $2 a 1% reduction in price increases quantity demanded by 2 %.

            c. Implied Elasticity - Percentage changes.  For rough policy purposes - when you know the percentage changes.

             ED = %

                      %

Px     

Example.  Suppose that beer sales at Joe's Inn increased 20% in response to a �half price� (50% off night).  What is the implied elasticity of demand?

             20/-50 = -.4

Example:  Suppose that Joe sells 400 beers per day. What would be the effect of a 10% increase in beer prices on his sales?

            -.4 =  implies that for every 1% increase in price, Joe will sell .4% fewer beers.  So a 10% increase will lead to a 4% decrease (.4 x 10), or a decrease of .04(400) = 16 beers per day.

Due Practice Problems

A Graphical Interpretation of Price Elasticity. 

        Demand curves have points of elasticity, unitary elasticity and inelasticity (where the elasticity is greater than one, = one, and less than one).   Why?

Graph:

        Some demand curves could have a range of prices where demand is perfectly inelastic - what does this mean?  (The elasticity coefficient would = 0).  And . . .

Graph:

        Would a demand curve be perfectly elastic?  The elasticity coefficient would = infinity!  And . . .

Usually we think of ranges of price as being relatively inelastic or relatively elastic.  An individual demand curve could be perfectly inelastic for a range of prices but a market demand curve usually would not be - why?

Graphs:

Price Elasticity and TR, AR, MR                       

What can we say about the price a firm is charging for its good, given limited information. (Say, only information about the demand schedule, and perhaps MC information.  Some important inferences can be drawn only from information about elasticity.

           Total Revenue (TR) is Price x Quantity

            So Average Revenue (AR) is shown along the demand curve.  TR/Q = Price.

            Marginal Revenue (MR) is the change in TR given a change in Q

If the demand curve is downward sloping, such that the price (AR) is falling, the MR must be below it.  Explain.

So Graphically:

When MR is positive, TR must be increasing as price is dropping.  Price elasticity of demand will be greater than one.  A drop in price of 1% will lead to a greater than 1% increase in demand.  So although selling for a lower price, still increase TR due to volume increase.

When MR is zero, TR is not changing.  Price elasticity of demand will equal one (unitary).  A drop in price of 1% will lead to 1% increase in demand.  The lower price and increase in volume just offset each other - no change in TR.

When MR becomes negative, TR is falling.  Price elasticity of demand is less than one.  A drop in price of 1% will lead to a lower than 1% increase in demand.  So the lower price is not made up for in volume sales and TR declines.

Graphs:

             Thus:  TR is maximized when MR = 0.

Question:  if your marginal cost of producing something is zero -- with respect to elasticity, where should you set your price?  Why?

    Recall that profit = TR - TC

Question:  The elasticity of demand at Jones Co. is -.5.  They are considering a sale.  What can you say about the rationality of a price cut?  Price increase?

Let's sum up what we have learned with some questions:

Question:  Suppose that auto-seller Jim Ford at Ford city lowers the price of the popular Focus by $2,000 in honor of Spring.  Suppose that in response, weekly sales increase from 4 per week to 8.  If the normal price of a new Focus is $10,000 what is the arc price elasticity of demand?

                            =      (4-8)(10,000 + 8,000/2))/(10,000-8,000)(4 + 8/2) = -36,000/12,000 =

                           =       -3.

- Over the current price range, is Marginal Revenue positive or negative?          

- Could Jim Ford expect to increase revenues by further lowering price?  Would such a move be profitable?

- What would you expect to be the response of customers to a similar percentage mark-down on all cars in the Ford city lot?.

- Suppose all U.S. domestic auto sales increase over last year by 5% in response to a 10% price decrease.  What is the implied price elasticity?

                 = 5/-10  = -.5          

Question:  Consider a firm selling plastic 3-sided rulers (inches, centimeters, and thumbs).  Suppose that price elasticity was -.2.  What can you say about the firms' pricing decision?  

Elasticity of Derived Demand - Demand Elasticity with respect to Inputs

What is derived demand?

Here are Alfred Marshall's four principles of governing the elasticity of derived demand:

1. The more essential is the component in question.

2. The more inelastic is the demand curve for the final product.

3. The smaller is the fraction of total cost going to this component.

4. The more inelastic is the supply curve of cooperating factors. 

        Cooperating factors:  other factors that are used along with the one in question to produce the final good.  Supply elasticity -- the percentage change in the supply/the percentage change in the price of the factor -- so if this is inelastic -- meaning that as the price of the factor increases or decreases, the factors are still supplied.

Consider the derived demand for a construction worker (electrician) that builds houses.  Houses - the final product.

1.  You cannot build a house without an electrician.  So if wages went up, derived demand would be pretty inelastic here.

2.   Assume the demand for housing is somewhat inelastic (obviously depends on the market, etc. but let's go with it for now) -- so if the price of houses went up -- demand would not change much.  Therefore, the derived demand for electricians would also be relatively inelastic.

3. The cost of electrical work is probably a relatively small percentage of the entire cost of the house.  So if wages went up, derived demand would be pretty inelastic here too.

4.  And also assuming that the supply elasticity of cooperating factors ( i.e., other crafts employed on the project) is rather low - then again, the derived demand for electricians would be pretty inelastic.  The other factors would not change their supply much -- so therefore, the demand for electricians would stay about the same.  If, for example, the cement guys were very supply elastic -- and their wage decreased -- they would not supply the cement work -- so the electricians would be out of work as well!!

What happens when elasticity of demand is 1?

When price elasticity of demand for a good is less than 1 it means the good has a low responsiveness to changes in?

When elasticity of demand of good A is less than 1 demand for good A is elastic?

What does it mean if a good has a price elasticity equal to 1?