Elasticity, The Basics

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Elasticity, The Basics

• Elasticity Responsiveness
• Elasticity - percentage change in Y / percentage
  change in X
• Elasticity is a Ratio!!!
• Price elasticity of demand - a measure of
  responsiveness of quantity demanded to changes in
  price.
• Elasticity Percentage Change in Quantity
  (Sales)/ Percentage Change in (X)
• Percentage change (X2-X1)/X1

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The Point Formula

• ((Q2-Q1)/Q1) / ((P2-P1)/P1)
• Problems
• Order of events dictate outcomes
• Does not impose ceteris paribus.

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The Arc Formula

• ((Q2-Q1)/(Avg.Q) / ((P2-P1)/(Avg.P)
• Problem
• 1. Does not impose ceteris paribus

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The Slope Formula

• Elasticity
• ?Q / ?P ((Q2-Q1)/Q1) / ((P2-P1)/P1)
• Note Q2-Q1 ?Q and P2-P1 ?P
• Therefore Elasticity ?Q /Q / ?P/P
• Note If you divide by a fraction you multiply
  by the reciprocal.
• Therefore Elasticity ?Q /Q P/?P
• or Elasticity ?Q / ?P P/Q
• Where do we get ?Q / ?P?
• This is the inverse slope of the demand curve,
  which we can estimate empirically (via basic
  econometrics), and therefore we can impose
  ceteris paribus.

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Interpretation of Price Elasticity

• change in Q gt change in P
• (elastic or responsive) Ep gt 1
• change in Q lt change in P
• (inelastic or unresponsive) Ep lt 1
• change in Q change in P
• (unitary elastic) Ep 1

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Next 10 slides are from Colander (2003)
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Elasticity Is Not the Same as Slope

• The steeper the curve at a given point, the less
  elastic is supply or demand.
• There are two limiting examples of this.

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Elasticity Is Not the Same as Slope

• When the curves are flat, we call the curves
  perfectly elastic.

• The quantity changes enormously in response to a
  proportional change in price (E ).

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Elasticity Is Not the Same as Slope

• When the curves are vertical, we call the curves
  perfectly inelastic.

• The quantity does not change at all in response
  to an enormous proportional change in price (E
  0).

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Perfectly Inelastic Demand Curve
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Perfectly Elastic Demand Curve
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Elasticity Changes Along Straight-Line Curves

• Elasticity is not the same as slope.
• Elasticity changes along straight line supply and
  demand curvesslope does not.

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Elasticity Changes Along Straight-Line Curves

• On a demand curve, elasticity is perfectly
  elastic (E ) at the price intercept.

• It becomes smaller as you move down the demand
  curve until it becomes zero at the quantity
  intercept.

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Elasticity Changes Along Straight-Line Curves

• Elasticity is perfectly elastic (ES ) where a
  straight line supply curve intercepts the price
  axis.

• Points become less elastic as you move out along
  the supply curve.

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Elasticity Changes Along Straight-Line Curves

• Elasticity is perfectly inelastic (ES 0) where
  a straight line supply curve intercepts the
  quantity axis.

• Points become more elastic as you move out along
  the supply curve.

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Elasticity Along a Demand Curve
Elasticity declines along demand curve as we move
toward the quantity axis
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Total Revenue and Elasticity

• Total Revenue Price Quantity Total dollar
  value of units sold
• If change in Q gt change in P decreasing the
  price will increase TR
• If change in Q lt change in P increasing the
  price will increase TR

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Profit and Elasticity

• Profit Total Revenue - Total Cost
• If demand is inelastic (i.e. change in Q lt
  change in P) an increase in price will increase
  TR.
• Because Q falls (law of demand), so too will
  Total Cost
• Why? Total Cost (which we will discuss later) is
  an increasing function of output. The more you
  produce, the higher your total cost.
• Consequently, if demand is inelastic, a firm can
  raise its price and increase its profits.

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Summarizing Demand

• The Law of Demand - Quantity demanded rises as
  price falls, ceteris paribus. Quantity demanded
  falls as price rises, ceteris paribus
• The Law of Demand is based upon Gossens First
  and Second Laws.
• The Law of Demand gives us the Demand Curve
• Via own-price elasticity, we move from the demand
  curve to total revenue.
• Total Revenue Price Quantity
• Without own-price elasticity we do not know how
  changes in price and quantity will impact total
  revenue.
• The variation in total revenue gives us the
  concept of marginal revenue.

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Marginal Revenue

• Marginal Revenue - amount of revenue from the
  last unit sold.
• the rate of change in total revenue
• the slope of the total revenue curve.
• If demand is downward sloping, then price will
  exceed marginal revenue. In other words, the
  amount of revenue generated by an additional sale
  will be less than the price the firm charges.
• Why? To increase quantity the firm will need to
  lower the price, not just for the last unit sold,
  but also for every unit the firm wishes to sell.

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Determinants of the price elasticity of demand

• Determinants of price elasticity of
  demand Substitutes and Elasticity
• Time
• Necessity vs. Luxury
• More specific the good the more elastic demand
• Price of the good relative to income

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Short-Run and Long-Run Elasticities of Demand
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Other Elasticity Concepts

• Cross price elasticity of demand
• change in quantity / change in the
• price of another good
• Income elasticity
• change in quantity / change in income

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Income Elasticities of Selected Goods
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Cross-Price Elasticities