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

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:
• Specific or unit taxes adds a fixed amount on to costs

• 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