Direction of Change versus Sensitivity A summary of the all of
the determinants of demand and supply are given in their respective
functions. These functions assist in distinguishing between a
movement from a shift of a curve AND the direction of change for
each of the determinants. To increase the explanatory power of the
demand and supply model, and to make it more interesting, we need
to not only know the direction of change but how much each of the
determinants affects demand and supply. This concept of
responsiveness is called elasticity.
Slide 3
Measuring Responsiveness or Sensitivity The initial candidate
for measuring sensitivity is the concept of slope. Slope tells us
the change in the quantity demanded or demand from a change in one
of its determinants (i.e. Q d /P in the case of prices) The
problems with slope are: Slope is unit dependent. If the units in
which the currency (dollars to pesos) or quantity changes (boxes of
apples to individual apples) it will change the slope. For example,
the change from dollars to pesos will decrease the slope. Slope
gives no indication of the beginning point. It also doesnt tell us
where we started (e.g. a stock goes up by a $1. A large increase if
the purchases price was $1 a small increase if the purchase price
was $1,000) Therefore, we use percentage changes. Percentages are
not unit dependent. If the measure of quantity is changed from
boxes to individual apples the percentage change will remain the
same. Percentages always refer to a starting point. Since
percentage are always taken from a starting point, the base, they
better measure the extent of change. We will return to this point
shortly when we calculate elasticities along a straight-line
(constant slope) demand curve.
Slide 4
Various Elasticities Ep = Price elasticity of demand = %change
in quantity demanded/% change in price Ey = Income elasticity of
demand = %change in demand/% change in income Ex =Cross-price
elasticity of demand = %change in demand/% change in the price of a
related good Or, any other elasticity is simply the %change in
something/% change in something else
Slide 5
An Intuitive Approach to Elasticity Since price elasticity of
demand (Ep) is always negative (law of demand) we ignore the
negative sign and take the absolute value of price elasticity. %Q d
= Output Effect and %P = Price Effect E p > 1 or Elastic %Q d
> %P a given %P creates a larger %Q d or Output Effect >
Price Effect Quantity demanded is sensitive to price. If price
falls slightly, quantity demanded will increase by a large amount,
or vice versa. E p < 1 or Inelastic %Q d < %P a given %P
creates a smaller %Q d or Output Effect < Price Effect Quantity
demanded is not sensitive to price. If price falls significantly,
quantity demanded will increase slightly, or vice versa. E p = 1 or
Unit Elastic %Q d = %P a given %P creates an equal %Q d or Output
Effect = Price Effect If price falls, quantity demanded will
increase by the same relative amount, or vice versa. Note, in the
above descriptions percentages are a easier and clearer way of
explaining sensitivity.
Slide 6
Using Elasticity: The Relationship between P, Q and TR As P the
law of demand tells us that Q . What happens to TR is not clear (P
x Q = TR ?) The increase in price, the price effect, increases TR,
ceteris paribus, but the decrease in quantity demanded, the output
effect, ceteris paribus, would increase would TR. So, change in TR
hinge about the relative strength of the price and output effects.
Elasticity provides the key because it tells us the size of the
price and output effect. The strength of the price effect is
measured by the %P and that of the output effect by the %Q d. For
example, if the %P = 5% and the %Qd =10%, the output effect is
larger that the price effect. So if P the Q will strong enough to
cause TR . Second example, For example, if the %P = 10% and the %Qd
=5%, the price effect is larger that the output effect. So, the P
will be stronger than the Q and TR .
Slide 7
Summary of P, Q and TR E p > 1 Responsive or elastic %Q d
> %P or Output Effect > Price Effect - if P goes down (up)
total revenue goes up (down) E p < 1 Not responsive or inelastic
%Q d < %P Output Effect < Price Effect - if P goes down (up)
total revenue goes down (up) E p = 1 unit elastic %Q d = %P Output
Effect = Price Effect - if P goes down (up) total revenue stays the
same
Slide 8
Price and Output Effects So, far we have defined the output and
price effects using percentage changes. The Price Elasticity is
simply the ratio of the OE and the PE in percentage terms. We can
also define the price and output effects in absolute or dollar
terms. If P falls, Output Effect = Pnew x Q = Pnew x (Qnew-Qold)
this is extra revenue you get from selling additional units at the
new price. If P falls, Price Effect = P x Qold = (Pnew-Pold) x Qold
this is the revenue you lose from selling the old units at a new
lower price. If P increases: Output Effect = Pold x Q = Pold x
(Qnew-Qold) Price Effect = P x Qnew = (Pnew-Pold) x Qnew Change in
TR = OE +PE
Slide 9
Figure 2 Total Revenue Copyright2003 Southwestern/Thomson
Learning Demand Quantity Q P 0 Price P Q = $400 (revenue) $4
100
The Mid-point Formula: Calculating Price Elasticity Economists,
when calculating elasticity, using the midpoints between the new (P
1 and Q 1 ) and old (P 0 and Q 0 ) prices and quantities, rather
than the old price and quantity that others typically use. E p = %Q
d / %P = (Q 1 - Q 0 )/[(Q Q + Q 1 )/2] (P 1 - P 0 )/[(P 0 + P 1
)/2]
Slide 12
Calculating Price Elasticity the Price Elasticity of Demand
Demand is price elastic $5 4 Demand Quantity 100050 Price
Slide 13
Linear Demand Curve:Elasticity
Slide 14
E>1 E=1 E
Other Demand Elasticities Income Elasticity of Demand - Sign is
important: Normal Good E Y >0 Inferior Good E Y 1 Income-elastic
and a luxury good because as Y the % of Y spend on the good (TE/Y)
E Y 0 (P R Q R Q ) Complement Ex
Elasticity and Tax Incidence A tax drives a wedge between the
price the buyer pays and the seller receives. Before Tax: P e =P B
=P S After Tax: P B >P S by the amount of the tax. Example: Per
unit tax of $1. If the buyer pays $6 for one unit of the good, the
seller receives $5 and $1 goes to the government in tax. P B MC to
buyers Q D Tax Wedge P S MB to sellers Q S Taxes can be imposed on
the buyer or the seller, but the government usually imposes them on
the seller for ease of collection. Tax imposition determines who
nominally pays the tax, but who really pays the tax depends on
elasticities of demand and supply (and doesnt depend upon whether
the buyers or the seller pays the tax!). Who really pays the tax,
the tax incidence or burden, depends upon how buyers and sellers
respond to price changes. If the buyers can respond relatively more
to price changes more than suppliers, suppliers pay more of the
tax. If the suppliers can respond relatively more than the buyers,
then the buyers pay more of the tax. Remember the water fight
example!
Slide 31
Graphing Tax Incidence If the buyer pays the tax, a new demand
curve is created to reflect the fact that sellers receive lower
prices. If the seller pays the tax, a new supply curve is created
to reflect the fact that buyers pay higher prices. In either case,
the higher price to buyers causes buyers to decrease their quantity
demanded and the sellers to decrease their quantity supplied. Thus
both the buyers and the sellers will likely both pay part of the
tax. The tax incidence or burden is related to how each responds to
price changes or their price elastiticies. If E D >E S then
buyers pay less of the tax and sellers more of the tax. If E D<
E S then buyers pay more of the tax and sellers less of the tax.
Note that the tax incidence or burden does NOT depend upon who pays
the tax to the government!
Applications Getting to Mr./Ms. Rich: Luxury Tax on Yachts Case
study The payroll tax: Federal Insurance Contribution Act (FICA)
for Social Security and Medicare