4: Elasticity
Propensity: tendency; slope represents the magnitude of change between the exogenous and endogenous variable. Referred to as tendency as it’s a linear line drawn through a scatter plot.
Elasticity: the responsiveness of quantity demanded to changes in price. Sensitivity to a change.
Elastic: when quantity demanded is responsive to changes in price.
Inelastic: when quantity demanded is relatively unresponsive to changes in price.
The more responsive quantity demanded is to changes in price, the less the change in equilibrium price and the greater the change in equilibrium quantity resulting from any given shift in the supply curve.
The slope of a demand curve tells us the amount by which price must change to cause a unit change in quantity demanded.
Computing elasticity of demand:
\left|\eta=\frac{\Delta\%quantity}{\Delta\%price}=\frac{\frac{\left(Qd1-Qd0\right)}{Q0}}{\frac{\left(P1-P0\right)}{P0}}\right|
Q_ = Qd1 - Qd0 / 2
P_ = P1 - P0 / 2 → the midpoint between those two.
How sensitive the consumer is to a change in price.
nd = 1 where numerator is equal to denominator → unit elastic.
nd > 1 where numerator is greater than denominator → elastic.
0 < nd < 1 where numerator is less than denominator. → inelastic.
e.g. addiction.
Middle of the curve: unit elastic.
e.g. (1/50.5) / (-1/50.5) = 1, unit elasticity.
Further down: more elastic
e.g. (1/99.5) / (1/1.5) =
Higher up: more inelastic.
e.g. (1/1.5) / (1/99.5)
Elasticity changes as you calculate it
We like to calculate and represent this as an absolute value. Elasticity is unit-free, but demand elasticity is represented as a negative number. The more responsive to price, the bigger the number.
Elasticity is zero when a change in price results in no change to demand.
Elasticity approaches infinity when a change in price results in astronomical change in demand; based on the slope.
Moving down a demand curve, price elasticity falls continuously. Elasticity approaches zero when y approaches zero. Elasticity approaches infinity as x approaches zero.
When the percentage change in quantity demanded is less than the percentage change in price, where n < 1, the demand is inelastic.
If the percentage change in quantity demanded is greater than the percentage change in price, where n > 1, the demand is elastic.
Unit elasticity occurs where price and demand changes are equal.
Determining Elasticity
Availability of substitutes: Some products have quite close substitutes. A change in the price of these products, with the prices of substitutes remaining constant, will cause much substitution.
Products with close substitutes tend to have elastic demands. Products with no close substitutes tend to have inelastic demands.
Narrowly-defined products have more elastic demands than broadly defined products.
Importance of Product in Consumer Budgets: products that represent a small fraction of consumer’s budgets tend to have inelastic demands. Products that represent a large fraction do have elastic demands.
Short & Long Run: elasticity depends on the time period considered.
A demand that is inelastic in the short run may prove to be elastic when enough time has passed and enough substitutes have been produced.
The longer the timespan, the more elastic is the price elasticity of demand.
Short run demand curve: shows the immediate response of quantity demanded to a change in price.
Long-run demand curve: shows the response of quantity demanded to a change in price after enough time has passed to develop or switch to substitute products.
Elasticity and Total Expenditure
The response of a consumer’s total expenditure on a product depends on the price elasticity of demand.
price * quantity = total expenditure
If demand for a product is inelastic, a reduction in price leads to a decline in total expenditure.
If demand for a product is elastic, a reduction in price leads to an increase in total expenditure.
The flatter the demand curve, the more elastic it is.
Elasticity of Supply
\eta=\frac{\Delta\%quantity}{\Delta\%price} = ((Qs1 - Qs0) / Q_) / )(P1 - P0) / P_)
Q_ = Qs1 + Qs0 / 2
P_ = P1 + P0 / 2
When n > 1, supply is elastic. → approaches a vertical slope and perfect elasticity.
When n < 1, supply is inelastic. → approaches a slope of 0 and perfect inelasticity.
When n = 1, supply is unit elastic.
The flatter the line, the more elastic the supply is.
The stepper the line, the more inelastic the supply is.
Perfect elasticity: a flat line.
Perfect inelasticity: a vertical line.
Determinants of Supply Elasticity
Ease of substitution: If the price of a product rises, how much more can firms produce profitably? Depends on how easy it is for firms to shift from the production of other products. If factors can be shifted easily, the supply will be more elastic.
Short run and long run: The long-term supply for a product is more elastic than the short term supply.
Elasticity and taxation
Excise taxes: special sales taxes on products such as cigarettes, alcohol and gasoline.
Tax incidence: who bears the burden of taxation?
The burden of an excise tax is distributed between consumers and producers in a manner that depends on the relative elasticities of supply and demand.
The burden of the excise tax is shared between consumers and producers in proportion to the rise in price to consumers relative to the fall in price received by producers.
After the imposition of an excise tax, the difference between the consumer and seller prices is equal to the tax. In the new equilibrium, the quantity exchanged is less than what occurred without the tax.
When demand is inelastic, the fall in quantity is small, while the price rises. Sellers bare little burden of the tax.
When supply is inelastic, consumers can more easily substitute away from gasoline. Little change in the consumer’s price, hence they bear little of the burden.
When demand is inelastic relative to supply, consumers bear most of the burden of excise taxes. When supply is inelastic relative to demand, producers bear most of the burden.
Other elasticity applications
Elasticity of demand based on income:
\eta=\frac{\Delta\%quantity}{\Delta\%income}
Normal goods: income elasticity of normal goods can be elastic or inelastic depending on whether the percentage change in quantity demanded is greater or less than the percentage change in income that brought it about.
Income inelastic: n < 1
Income elastic: n > 1
The more necessary an item is in the consumption pattern of consumers, the lower is its income elasticity.
With inferior goods, a negative income elasticity is exhibited because an increase in income leads to a reduction in quantity demanded. n < 0, e.g. spam.
With normal goods, a positive income elasticity is exhibited. n > 0
0 < n < 1: a necessity
n > 1: a luxury.
Cross elasticity of demand:
\eta=\frac{\Delta\%quantityX}{\Delta\%priceY} = ((d1 - d0) / Q_) / ((y1-y0) / y_),
Q_ = q1 - q0 / 2
y_ = y1 - y0 / 2
The responsiveness of quantity demanded to changes in the price of another product. → subjective.
The positive or negative signs of cross elasticities tell us whether products are substitutes or compliments.
Compliments: negative
Substitutes: positive
Corrections:
Further down the demand curve, the more inelastic you become.
The higher up the demand curve, the more elastic you become.