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 ©1989 & 2002 John Petroff. 

 

CHAPTER 2:

ELASTICITY

LEARNING OBJECTIVE
The purpose of studying elasticity is to determine how a small
change in price may result in either a large or small change in
quantity. The concept is first defined and explained. Its
measurement is discussed. The relationship between total revenue
and elasticity is outlined. Supply elasticity and its
determinants are analyzed. The concepts are applied to analyze
price ceilings, price supports and tax incidence.

ELASTICITY
The concept of elasticity is intended to measure the degree of
responsiveness of a buyer or seller to a change in a key
determinant, in particular price. The degree of responsiveness
of the quantity demanded to a price change is called the price
elasticity of demand. If the price change is that of another
good then the study deals with cross elasticities of demand.

 Suppose a store manager wants to run a sale. Should he lower
the price of a given item? and, if yes, by how much?
The answer will depend on whether the increase in purchases by
customers will be larger than the price decrease, (both
calculated on a relative basis). This change in purchases by
customers is what elasticity is intended to measure.

ELASTICITY MEASUREMENT
If elasticity were measured by absolute quantities, then it
would be affected by the units of measure used for both price and
quantity. To avoid this difficulty, elasticity is a ratio of
relative changes in quantity and price:

Ed = (dQ/Q) / (dP/P)

or


Ed = % change in quantity / % change in price .

 If a grocery store can increase its sale of milk by 12 quarts
(from 24 to 36) when the price is dropped by 10 cents (from $1.00
to $.90), the elasticity measured in absolute terms is 1.2 (that
is 12/10). But, when the quantity of milk is expressed in
gallons, the elasticity in absolute terms is now 0.4 (4/10). If
dollars instead of cents are used, it becomes 40 (4/0.1). This
difficulty disappears when the elasticity is a relative measure.

MIDPOINT ELASTICITY
The calculation of elasticity using the formula of change in
relative quantity over change in relative price results in
different values depending on whether the starting point of the
calculation is the highest or lowest price. To avoid this
difficulty, both price and quantity are averaged: this is the
equivalent of taking the elasticity at the midpoint of the
price-quantity range.

Ed = ((Q2-Q1)/((Q1+Q2)/2)) / ((P2-P1)/((P1+P2)/2))

It should be noted that price elasticity of demand is always negative
and absolute values are often quoted without indicating the negative sign.

 If price is decreased by -10 percent (from $1.00 to $.90) to
increase sales of milk by 50% (from 24 to 36), the elasticity is
-5 (that is 50% divided by -10%). Looking at the same number the
other way: there is a decrease in quantity of -33.3% (from 36 to
24) when the price is increased 11.1% (from $.90 to $1.00): an
elasticity of -3. The presence of 2 values does not make sense.
The midpoint (and correct) elasticity is -3.8 (that is (12/30)/(-0.10/0.95)).

ELASTIC DEMAND
If the demand is elastic, it means that a small price change
results in a large quantity change. This would generally take
place on the upper portion of the demand curve. If the demand is
perfectly elastic (which means that the smallest possible price
change results in a virtually infinite quantity change), the
demand curve is then horizontal.

 A mother wants to surprise her children by bringing home
some fancy pastry for desert. But, after discovering that the
pastry shop has raised its prices to unreasonable levels, she
decides to skip the pastry. Her reaction shows very high,
virtually infinite, elasticity.

INELASTIC DEMAND
If the demand is inelastic, it means that even a substantial
change in price leads to hardly any change at all in quantity
demanded. This generally occurs in the lower portion of the
demand curve. If the demand is perfectly inelastic, quantity
does not change at all. A perfectly inelastic demand is vertical.

 For most people, items that are considered as necessities are
items for which the demand is inelastic. No matter how much the
price may change, if we think we really need an item, we will
buy it. Medicine or basic food items are probably in this
category. Milk for a family with children is such a basic food:
you will always find it somewhere in the refrigerator, no matter its price.

TOTAL REVENUE AND ELASTICITY
If demand is elastic, then price and total revenue are inversely
related; that is, if price is increased, total revenue decreases.
If demand is inelastic, price and total revenue are directly
related; that is, if price is increased, then total revenue
increases as well.

 In the previous milk example, the demand was elastic: 3.8. The
revenues increase from $24 (when the price is $1.00 for 24
gallons) to $32.40 (when the price is lowered to $.90 for 36
gallons). Thus, total revenue is indeed inversely related to
price change when demand is elastic.

DEMAND ELASTICITY DETERMINANTS
The determinants of demand elasticity are
- the time framework (market period, short run or long run),
- the availability of substitutes,
- the proportion the item represents in total income,
- the perception of the item as necessity or luxury.

 The ability to switch to another brand, another product or
another form of consumption, is the overall criterion of all
the determinants of demand elasticity. It is clearly a very
subjective factor, quite different from person to person.

SUPPLY ELASTICITY
Supply elasticity is the degree of responsiveness of the quantity
supplied to a change in price. It is calculated as


Es = % change in quantity / % change in price .

 The government is interested to know how much more electricity
electric companies would be willing to supply if they were
allowed an increase in the rates they charge. What
measures this responsiveness of the electric companies is the
supply elasticity. Naturally, building a power plant takes a long
time. Thus, the supply price elasticity of electricity can be expected
to be higher in the long run than in the short run.

SUPPLY ELASTICITY DETERMINANTS
The major determinants of supply elasticity are
- the time framework (market period, short run or long run),
- the ability to shift resources.

INCREASING COST INDUSTRY
When a resource is scarce and the cost of that resource
increases over time, the long run equilibrium price of products made from it
increases and the industry is referred to as an increasing cost
industry. Most industries have increasing costs over time. Some
industries do not have scarce resources; they are constant cost
industries. New emerging industries may experience decreasing
costs for a while.

 Production of electricity is very likely to be of increasing
cost industry type. The various energy sources (gas, coal, fuel,
hydropower) are all extensively used. Alternative sources
(nuclear, sun, wind) have their own additional danger or costs.
That is why our electric bill usually goes up, and is likely to
do the same in the future.

PRICE CEILING
A price ceiling creates a shortage in the short run. Since both
demand and supply curves are more elastic as the time framework
lengthens, this causes the shortage to increase over time. This
can be verified by observing that a price below equilibrium is
an incentive for buyers to buy more and a disincentive for suppliers to supply
more.

 In most major cities, rent control laws have been enacted to
provide affordable housing to low and middle income families.
But, landlords have been discouraged to keep increasing the
number of apartments available at those moderate rents, and have
often preferred to convert ownership to cooperative or
condominium form. This has taken apartments off the rental market
and increased shortages of affordable housing in many cities.

PRICE SUPPORT
In the short run a price support creates a surplus. In the long
run, both demand and supply become more elastic. This
causes the surplus to increase over time. The price support,
being higher than equilibrium, acts as an incentive for
producers to produce more and as a disincentive for buyer
to buy.

 Milk production has been subject to price support for many years in many countries.
Consequently, governments have been forced to buy up
excess milk produced by farmers. These government stock piles are
regularly converted into cheese distributed free to poor people.
The surplus of milk continues because farmers have a price
incentive to produce more. Now, the government is trying to cut
the number of cows farmers are allowed to have.

TAX INCIDENCE AND ELASTICITY
Technically a sales tax is paid by the consumer; the seller only
collects the tax on behalf of the taxing authority. A further
analysis of the incidence of a sales tax (i.e. the analysis of
who really bears the burden of the tax) reveals that the burden
of the tax is shared. The price increase resulting from
the sales tax reduces the quantity traded and forces the seller
to lower the selling price.

TAX INCIDENCE AND ELASTIC DEMAND
If the demand is highly elastic (that is, customers are able to
switch), the supplier will be forced to lower selling prices
considerably to continue on selling some of his/her products.
Thus, if demand is elastic while supply is inelastic the
burden of the tax is shifted almost in its entirety to the
supplier.

 Suppose a county increases its sales tax while its adjoining
county does not. The residents will prefer to buy their products
in the county which does not have a sales tax. To retain their
customers, merchants of the county which has enacted the
sales tax will have to lower their prices. Thus the
incidence of the tax has been shifted onto sellers.

TAX INCIDENCE AND INELASTIC DEMAND
If the demand is inelastic, the quantity demanded will not
change much after the sales tax is imposed, the supplier will
not have to lower the price and the burden of the tax is borne
almost in its entirety by the buyer.

 In the example of the adjoining counties, the shift in the
incidence takes place because the residents are assumed to be
able to shop equally in one or the other county. (That is, they
have a highly elastic demand). But, if some barrier existed, such
as a toll bridge between the two counties or customs duties, the incidence of the tax
would then remain entirely on the consumers.

TAX REVENUE AND ELASTICITY
If the purpose of a sales tax is to raise revenue for the
government, such tax will be effective only if demand and supply
are inelastic. Indeed, if both or either are elastic - which they
usually are in the long run - the decrease in quantity purchased
will cause the additional revenue from the tax to be minimal or even negative.

 Many countries have import duties on luxury items. When those
import duties are very high (30% or more), smugglers are willing
to take the chance on breaking the law. Then, revenues from those
duties decline.

SUMPTUARY TAX AND ELASTICITY
The purpose of a sumptuary tax is to change the pattern of
consumption in a society. Such a sales tax will be effective only
if the demand and supply are elastic. Indeed, if both or either
are highly inelastic, no matter how large the tax is, the
quantity will not change.

 Sumptuary taxes exist in virtually every country, including the
United States. They are most often assessed on items such as
cigarettes, wines and liquor.

TAX INCIDENCE AND SUPPLY ELASTICITY
When supply is elastic, an increase in sales taxes will result in
a large increment in the price paid by consumers and the tax
burden being largely paid by consumers. When supply is
inelastic, an increase in sales taxes will result in a price
reduction by sellers, and the tax burden is largely paid by
sellers.

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