Motivation for Elasticity

Motivation for Elasticity

• Elasticity measures sensitivity to price changes.
• Sensitivity helps understand how consumers/firms respond to price changes
• Sensitivity can show how quantity demanded (Qd) or quantity supplied (Qs) change when price (P) varies.
• It addresses concerns such as: If the price of a product increases, how much less will be sold?
• It addresses concerns such as: Will revenue increase if the price of a product increases?
• It addresses Sensitivity can apply when the price of a good increases due to a tax which can show how much less suppliers will be willing to sell?
• Elasticity is important for policymakers and business owners.

Slope as a Measure of Sensitivity

• The slope of the demand curve is a measure to consider sensitivity.
• Slope is calculated as ΔQd/ΔP or (Qdnew-Qdold) / (Pnew-Pold).
• A $1 increase in price results in buyers consuming 0.43 less of the good.
• Identical demand curve exists but use of hundreds of dollars instead.

Price Elasticity of Demand

• Price elasticity of demand measures how sensitive consumers are to changes in a product's price.
• It can be made robust by including percent change instead of absolute change.
• ED = (% ΔQd) / (%ΔP).
• ED is known as the elasticity coefficient.
• ED is always negative.
• The value of ED represents %change in quantity demanded (% ΔQd) from a 1% change in price (P).

Midpoint Method

• To calculate ED, use midpoint method.
• %change in quantity demanded (% ΔQd) = [(Qnew - Qold) / ((Qnew + Qold)/2)] * 100.
• %change in price (% ΔP) = [(Pnew - Pold) / ((Pnew + Pold)/2)] * 100.
• The midpoint method calculates percent change and is invariant to direction compared to how percent change is normally calculated.
• Interpretation: |ED| > 1 is elastic, |ED| = 1 is unit elastic, |ED| < 1 is inelastic.
• Example: If price increases from 10 to 20 the elasticity (Ep) will be -1.5 is elastic. So, |Ed| = 1.5 means it is elastic demand.

Elasticity Along a Demand Curve

• Flatter demand curves are relatively more elastic.
• For some demand curves, the value of Ep changes along the demand curve.
• If price increases from 4.50 to 4.75, the % ΔP = 5.41%
• Quantity demanded then decreases from 0.25 to 0.125 with %change in quantity (% AQd)= -66.67%.
• |ED| = 12.32.
• If price increases from 0.25 to 0.5, the % ΔP = 66.67% in price
• Quantity demanded then decreases from 2.38 to 2.25 and the % change in quantity (% AQd)= -5.62%
• |ED| = 0.084.
• Along a linear demand curve, the upper region is elastic, the midpoint is unit elastic, and the lower region is inelastic while the slope is constant.

Price Elasticity of Demand and Revenue

• Total revenue (TR) is the money earned from selling goods.
• Total revenue (TR) = Price (P) x Quantity (Q).
• If demand is elastic and prices increase, TR decreases.
• For a linear demand curve, if demand is inelastic and prices increase, TR increases.
• For a linear demand curve, TR is maximized at the unit elastic price.
• Firms/industries can increase prices and expect an increase in revenue.
• If a firm increases prices, it may earn more revenue and this depends on the elasticity of demand. For unit elastic demand, ↑PxQ ⇒ TR

Elastic Demand

• For elastic demand, ↑PxQ ⇒ TR

Inelastic Demand

• For inelastic demand, ↑PxQ ⇒ TR

Determinants of Price Elasticity of Demand

Availability of Close Substitutes

• More substitutes results in a more elastic demand
• When there are few subsitutes is results in a less elastic demand

Passage of Time

• In the Short-run ⇒ less elastic demand
• In the Long-run ⇒ more elastic demand
• More time allows people to adjust to price change

Definition of Market

• Broad categories of products ⇒ less elastic demand
• specific products ⇒ more elastic demand

Necessity of Product

• Necessity is less elastic demand
• Luxury is more elastic demand

Share of Budget

• A smaller share of the budget means less elastic demand.
• A larger share of the budget means more elastic demand.

Cross-Price Elasticity

• Cross price elasticity measures how a change in the price of one good relates to the consumption of another good.
• Ex/y = (% ΔQDx) / (% ΔΡΥ)
• The value of Ex/y is the % ΔQDx from a 1% change in Py.
• If Ex/y > 0, the goods are substitutes.
  • iPhones and Samsungs are an example.
• If Ex/y < 0, the goods are complements.
  • iPhones and apps in Apple Store are an example.
• If Ex/y = 0, the goods are unrelated.
  • iPhones and peanut butter are an example.

Income Elasticity

• Income elasticity measures how a change in income relates to changes in consumption.
• ε1 = (% ΔQd) / (% ΔI).
• The value of ε1 is the % ΔQd from a 1 % change in I.
• If ε₁ > 0, the good is normal such as a steak, cars, and iPads.
• Greater ε₁, the more luxurious the good is.
• If ε₁ < 0, the good is inferior such as ramen noodles, generic brand products and public transportation.
• If ε₁ = 0, income change has no effect some medications are example of this.

Price Elasticity of Supply

• Price elasticity of supply measures how a change in the price relates to changes in quantity supplied.
• ες = (% ΔQs) / (% ΔP).
• The value of εs is the % ΔQs from a 1% change in P.
• εs is non-negative.
• If es > 1, supply is elastic.
• If es < 1, supply is inelastic.
• If es = 1, supply is unit elastic.

Determinants of Elasticity of Supply

Cost to Scale Up Production

• To increase the supply of gold, it need to dramatically increase costs.
• To increase the supply of paper clips, it does not need to increase much cost.
• Difficult to increase production at constant cost ⇒ Less elastic.
• Easy to increase production at constant cost ⇒ More elastic.

Market for Inputs

• To increase in the supply of toothpicks, it requires more trees (input).
• Scaling up housing would require substantially more trees, which takes time to plant and harvest.
• Big disturbance in input market to expand ⇒ Less elastic.
• Small disturbance in input market to expand ⇒ More elastic.

Scope of Supply

• Global supply for oil is costly to expand, so a global supply ⇒ less elastic.
• Supply for oil in San Antonio, TX would is easier to expand, so a local supply ⇒ more elastic.

Passage of time

• Short-run ⇒ less elastic because there is less time to adjust.
• Long-run ⇒ more elastic because there is more time to adjust.