Elasticity
Elasticity refers to the responsiveness
of demand or supply to changes in price or income. The usual meaning is
the price elasticity of demand, or the responsiveness of the
quantity demanded to price. We speak of an elastic demand 
one which is very responsive to price, and which would result in a relatively
flat demand curve; and of an inelastic
demand  one not very responsive to price.
The language is a bit awkward. When we say inelastic, we mean
the responsiveness is small not nonexistent. The terminology perfectly inelastic
is sometimes used for a demand which is not at all responsive to price.
The coefficient of elasticity or COE for short is the measure of elasticity.
It is defined as the percentage change in the quantity demanded divided by the percentage change in price.
There are two things to note about this definition.
 It is in terms of percentage changes, not just "changes". An increase of a dollar is a big percentage change for a newspaper, and will lose them many customers; a dollar increase in the price of a car will not
lose many buyers  yet the newspaper and car demand curves could have the
same elasticity. Percentage change calculations are further discussed
in the link on the midpoint formula .
 There is a close connection between the elasticity of demand and the
revenue change resulting from a price change. If the
COE is greater than 1, it means the percentage change in quantity is greater than the percentage change in price. For example, if the COE is 3, a 10 percent increase in price will lead to a ____ percent decrease in
quantity demanded, or to a ____ loss in revenue. (If you can't fill in the
blanks, click here for a discussion of percentage change algebra
Extended elasticity concepts
As well as the price elasticity of demand  by far the
most frequently used elasticity concept  we can also speak of:
 the income elasticity of demand
defined as the percentage change in quantity demanded divided by the
percentage change in income. Income elasticity can be
either positive or negative, so the associated sign is important.
Goods with a negative income elasticity are inferior
goods  as income rises, the quantity of potatoes purchased may fall, so
that potatoes would be inferior goods.
Goods with a positive income elasticity are normal goods;
if the income elasticity is not simply positive but is greater than
one the good is classified as a luxury good.
This terminology makes the economist's definition of inferior and luxury
goods depend on observable economic data rather than a subjective
judgement.
 the crossprice elasticity of demand is defined as
the percentage change in the quantity of one good when the price of
another good changes. Again, the sign can be either
positive or negative. If positive, the two goods are
substitutes  when the price of coffee goes up, the
quantity of tea also goes up. If negative, the two goods are
complements  when the price of gas goes up, the
number of automobiles purchased goes down.
 the price elasticity of supply is defined as the
percentage change in the quantity supplied divided by the percentage change
in the price of the good. Normally, the longrun
elasticity of supply is greater than the shortrun
elasticity of supply  that is, the supply curve will be
flatter in the long run than in the short run.
Elasticity problems
 Given the following demand schedule:
Demand
PRICE  QUANTITY  REVENUE 

15  10  ____ 
10  55  ____ 
5  100  ____ 
 Fill in the revenue column; without doing any further computations,
is the demand curve elastic or inelastic?
Why?
 Compute the coefficient of elasticity between a price of $5 and of $15 using the midpoint formula. If you have
forgotten the midpoint formula, review the hypertext link here
 Answer the above questions for the following demand schedule:
Demand schedule
PRICE  QUANTITY  REVENUE 

100  100   
300  90   
500  80   

Given the demand curve Q = 200  4P
 Graph the demand curve, showing exactly where it cuts the axes.
 How much is demanded at a price of 10 dollars? 11 dollars?
9 dollars?
 Use the above information to find the elasticity of the curve at a price of $10, that is between prices of $9
and $11. (Note: given a demand curve in algebraic form, we can find the
elasticity at a point by raising and lowering the price
by a dollar. We then construct a table similiar to the tables in the first
two probems and compute the elasticity between the points defined by
the given price plus or minus one dollar.)

Using the same demand curve, Q = 200 4P
 How much is demanded at a price of 40 dollars? at a price of 39 dollars?at a price of 41 dollars?
 What is the coefficient of elasticity at a price of
40 dollars?
 How does this compare with the coefficient of elasticity found in the
previous problem? Is elasticity the same anywhere along a straight line
demand curve? How does it vary with price?

Given the demand curve Q = 100  1/2 P

Can we say it is less elastic than the previous demand curve?

Is it less elastic than the previous demand curve at a price of
30 dollars?

Is it less elastic than the previous demand curve at a price of one dollar?
 Does elasticity vary along this demand curve? Explain how  does
elasticity increase or decrease with price? Is this the same as the
previous curve?
Answers to elasticity problems.
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