IB Economics/Microeconomics/Elasticities

2.2 Elasticities

Price Elasticity of Demand (PED)

The responsiveness of the quantity demanded of a good to a change in its price

Elasticity measures the sensitivity of demand (quantity demanded) to changes in variables such as its own price
If the supply curve shifts because of government subsidies, it is useful to know the impact on the price and the quantity demanded

Formula

%Change in Quantity Demanded of Good A $/$ %Change in Price of Good A (where QD means ‘change in’)
Measures responsiveness by dividing the percentage change in quantity demanded by the percentage change in price
As price and quantity demanded are inversely related the equation is always negative, but we tend to ignore the negative sign and report a whole number
The term on the top is the slope of the demand curve, while the term on the bottom is the slope of the ray from the origin to the point on the curve where you are measuring elasticity

Possible range of values

PED > 1: Demand is elastic
PED < 1: Demand in inelastic
PED = 1: Demand is unit elastic
PED = 0: Demand is perfectly inelastic
PED = $\infty$ : Demand is perfectly elastic

Elastic demand (h > 1):

A subsidy leads to an outward shift in supply, prices fall leading to a large increase in quantity demanded (%Dq > %Dp)
If price fell by 10% and quantity demanded rose by 50%, the elasticity would be equal to 5, an unusually high number for elasticity

Inelastic demand: (h < 1):

A subsidy leads to an outward shift in supply, prices fall but there is only a small increase in quantity demanded (%Dq < %Dp)
If price fell by 10% and quantity demanded rose by only 5%, elasticity is equal to 0.5

Unit elastic demand (h = 1):

If the responsiveness is about the same as the change in price, then the measure will be equal to (minus) one (%Dq = %Dp)

Perfectly inelastic (h = 0):

No change in quantity demanded (%Dq = 0)

Perfectly elastic (h = $\infty$ ):

Infinite change in quantity demanded (%Dq = $\infty$ )

Diagrams illustrating the range of values of elasticity

Point Elasticity

Measures the responsiveness of quantity to price at a particular point on the demand curve
The slope is given by the tangent to that point, and is often measured as dq/dp, which is determined by calculus
The slope of the ray is given by: q/p, the p and q corresponding to that point are used (rather than average p and q over an arc of the curve)

Varying elasticity along a straight-line demand curve

Elasticity along a straight line demand curve varies from zero at the quantity axis to infinity at the price axis
In the diagram at right:

Below the midpoint of a straight line demand curve, elasticity is less than one and the firm wants to raise price to increase TR
Above the midpoint, elasticity is greater than one and the firm wants to lower price to increase TR
At the midpoint, E1, elasticity is equal to one

For the straight demand curve, the ranges of elasticity are given by the formula: η = EF / CE

For the curved demand curve, EF is the distance from the point where the tangent intersects the x axis to the tangency point divided by the distance from the tangency point to the intersection with the y axis

For a hyperbola, the point of tangency will always be the midpoint of a straight line and therefore, the elasticity is always equal to one along the curve

Where there are two straight line demand curves of the same slope, the one furthest from the origin is less elastic at each price than the closer one
Where two demand curves of different slopes intersect, the elasticities are different because the slopes are different at that point

Factors of PED

Closeness of substitutes

If there are many substitutes available, consumers can easily switch to other goods if prices rise
Demand within product groups tends to be fairly elastic:

The demand for gas versus electricity or gas versus diesel is fairly elastic
However, for energy as a whole, demand tends to be very inelastic because there are no close substitutes for hydrocarbons

Luxury or necessity

Addiction: some goods are habit forming and tend to be price inelastic: e.g., coffee
Need: medicine: e.g., insulin

Percentage of income spent on the good

Size of item in budget: if consumers spend only a small amount on the item (e.g., matches for lighting candles) relative to their budget, it is likely to be inelastic (not sensitive to price changes)

Time Period

It may be difficult to find substitutes in the short-run so demand is likely to be less elastic in the short run than in the long-run

Branding

Price Elasticity of Supply (PES)

The measure of the responsiveness of the quantity supplied of a particular good to a change in its price

%Change QS / %Change in Price

Possible range of values:

PES > 1: Supply is elastic
PES < 1: Supply is inelastic
PES = 0: if the supply curve is vertical, and there is no response to prices
PES = $\infty$ : if the supply curve is horizontal

Diagrams illustrating the range of values of elasticity:

Any straight line supply curve intersecting:

The origin has an elasticity of one: at every point along the curve, the slope of the ray (q/p) equals the slope of the line (Dq/Dp)
The price axis is elastic
The quantity axis is inelastic

Determinants of PES:

Number of producers (ease of entry): the fewer the barriers to entry, the easier for firms to enter the industry to increase supply in response to an increase in price and supply is elastic
Spare capacity: if there is unused capacity, it is easy to increase production if demand should start to shift out
Ease of switching: if land and labour can be shifted easily from growing one crop to another, the supply will be more elastic:

Even if it is possible to shift inputs, if the cost of inputs rises production costs will rise rapidly as output rises and supply will be inelastic
Over the longer term as cheaper inputs are substituted and new production methods incorporated into the firm, outputs will tend to increase and prices will tend to moderate

Ease of storage: if it is easy to store production, the more elastic supply response to increases in demand
Length of production period: the more quickly the good can be made, the easier to respond to an increase in price
Time period of training: over time the firm can train labour and invest in more capital equipment and supply is more elastic in its response to price increases
Factor mobility: the easier it is to move resources into the industry, the more elastic the supply curve
How costs react:

If costs rise only slowly as production increases, a rise in price will stimulate a large increase in quantity supplied
If costs of production rise rapidly as output rises, then the stimulus to production which comes from rising prices will quickly be choked off

Income Elasticity of Demand (YED)

The responsiveness of the quantity demanded of a good to a change in income

Income elasticity measures the percentage change in quantity demanded as income changes

Formula

%Change in QD / %Change Y

Normal goods: when income increases, demand for normal goods increases as well

Positive YED
An increase in income leads to an increase in consumption, demand shifts to the right

Inferior goods: when income increases, demand for this good falls
Negative YED
The demand curve shifts left as income rises. As income rises, the proportion spent on food tends to fall while the proportion spent on services tends to rise

For basic or necessity goods, where 0 < h < 1:

Quantity demanded will not increase much as income increases (income elasticity for food = 0.2)

For luxury goods, h > 1:

Quantity demanded rises faster than income, e.g., for restaurant meals income elasticity is higher than for food, because of the additional restaurant service

Income and Substitution Effects

When the price of a good falls there are two effects:

Substitution effect: people buy more because it is relatively cheaper.
Income effect: real income rises because of the lower price of the good:

Normal goods: the consumer buys more of all normal goods, the income effect reinforces the substitution effect
Inferior goods: the consumer buys less of all inferior goods, the income effect works against the substitution effect

Application of income elasticity to economic growth:

As economies grow, income elasticity helps determine what should be produced:

Firms will want to avoid producing inferior goods
Countries are at various stages of economic development and so have widely different income elasticities for the same products
As overseas incomes grow it may create new markets as demand shifts from inferior to normal goods

Cross Elasticity of Demand

The responsiveness of the quantity demanded of one good to a change in price of another good

Price cross elasticity tells us the relationship amongst goods:

Bottle makers find they are in competition with producers of cans

Formula

%Change in QD of Good A / %Change in the Price of Good B

Significance of signs with respect to complements and substitutes

If the goods are complements, the value will be negative

Complementary goods:

Quantity demanded increases when the price of the complement falls
If the price of gas fell to 10 cents a litre, sales of cars would increase

A positive value signifies that the two goods are substitutes

Substitute goods:

Quantity demanded of one good falls when the price of the substitute falls
If the price of coffee rises, people tend to consume less coffee and more tea

Taxes (HL)

Flat rate and ad valorem taxes

A flat rate tax is a tax which is the same rate regardless of price or income

Greater burden on those with lower income

An ad valorem tax is a tax which is a percentage of the price of a good

The United States has an ad valorem tax of ten percent

Incidence (burden) of indirect taxes and subsidies on the producer and consumer

Firms try to pass these increased costs on to consumers

An indirect tax raises the price of a good: its elasticity determines if the burden of the tax is on the producer or on the consumer

In the case of a good with inelastic demand the tax burden can be easily passed on to the consumer (PED is less than PES)

Who actually pays the tax very much depends on the elasticities of the two curves

Implication of elasticity of supply and demand for the incidence (burden) of taxation

If the product is demand inelastic or supply elastic, the consumer would need to bear the majority of the burden of tax

If demand is more inelastic than supply the consumer will pay a greater proportion or incidence of tax
It is easier for consumers to shift the tax back to the producer if there are easily available substitutes

If the product is demand elastic or supply inelastic, the producer would need to bear the majority of the burden of tax

If supply is more inelastic than demand, the supplier will pay a greater proportion or incidence of tax

A tax on pure profits should not have any influence on price or output, thus the producer bears the full burden

If the govt imposed a 15% tax, then profits would fall, but this would be true no matter what level of output would be produced
If the definition of profits includes payments to factors such as shareholders, the incidence of a profits tax could be shared by shareholders (lower profits on capital), wage earners (lower wages) or by consumers (higher prices)

PED and government

Used by government:

Will help determine the impact of an indirect (sales) tax on quantity demanded and the resulting tax revenue
Will help determine the impact of any shift in supply due to subsidies in terms of consumer spending and producer revenues

Indirect taxes are placed on suppliers and have the effect of raising costs shifting the supply curve in:

Ad valorem taxes add a percentage on to prices
Specific or unit taxes adds a fixed amount on to costs

Deadweight Loss

If landlords try to raise rents by the amount of the tax, from A to B, there will be excess supply, rents fall and a new equilibrium at C
The landlord receives the rental price of R1, but pays the tax equal to the difference between R1 and R1-t
The landlord’s share of the burden is the difference between Ro and R1-t
The tenant’s share of the burden is the difference between R1 and Ro
The deadweight loss represents the loss in social net benefits that no-one receives: it occurs because less is supplied than is socially optimal

If demand were perfectly inelastic, the tenant would bear the whole burden
If demand were perfectly elastic, the landlord would bear the whole burden
The deadweight loss is less the more inelastic the demand and supply

Often referred to as a distortion: the more quantity responds because the curves are elastic, the more quantity will fall as taxes are imposed

This is referred to as a tax distortion because it distorts the way demand and supply would normally respond in a tax-free market

Applications of concepts of elasticity

PED and business decisions (the firm): the effect of price changes on total revenue

PED may be important for businesses attempting to distinguish how to maximize revenue

For example, if a business finds out its PED is very inelastic, it may want to raise its prices
If a business finds that its PED is very elastic, it may wish to lower its prices

PED may be important for a government to find the impact of a tax or subsidy

Total Revenue: is equal to P*Q

By estimating the effect of a price change, firms can plan the number of goods to produce and estimate their potential revenue

Inelastic demand: price and total revenue are positively related

If firms cut prices by 10% but sales only increase by 5%, revenues fall
A rise in price will not only increase revenue but will also increase profit as costs will fall because less is produced
The increase in the number demanded is too small to offset the drop in the price of each good sold

Example: the oil industry where demand is inelastic, as prices rise, quantity demanded does not fall very much

Elastic demand: price and total revenue are negatively related

If demand is elastic, a fall in price will increase revenue but not necessarily increase profit as production must increase quantity demanded increases
If quantity demanded increased 50% when price fell by 10%, revenues increase
The increase in the number demanded is more than enough to offset the fall in the price of each good sold

Unit elastic demand:

Total revenue is constant regardless of changes in prices
The cut in prices is exactly offset by the increase in the quantity demanded, and total revenue to producers will stay the same

PED and taxation

Governments may wish to know how a tax or subsidy will affect a good

Cross-elasticity of demand:

Competitors may wish to know what will happen if there is a change in complements, or substitutes
Firms can determine the impact on sales and revenues of price changes by rivals, or when they or another industry changes the price of complements
During the oil crisis in the 1970s prices rose 400% in the space of three months but quantity demanded fell by less than 5% the first year

More energy efficient cars were bought by consumers
Companies switched to using coal instead of oil in their furnaces

In the longer term, new supplies of oil were found, and the real price of oil declined as consumers switched to substitutes
For goods like energy it takes time to use up the stock of appliances and machinery and switch to those using energy in a more efficient manner

Significance of income elasticity for sectoral change (primary> secondary > tertiary) as economic growth occurs

As economies grow (and move from primary to secondary to tertiary production)

Firms will plan on producing fewer inferior goods
Production and purchasing of capital goods and other factors can be planned
Production for exports can be planned as new markets open and close

Primary sector is generally income inelastic
Just because a person's income changes does not mean he will buy more tomatoes
However, secondary and tertiary sectors tend to be income elastic; a change in income will have a big impact on quantity demanded of cars, or the demand for personal massages