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Topic 3 - Elasticities.docx

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Economics 1021A/B
Arvin Dar

Topic 3: Elasticities 1. Introduction 2. Price elasticity of demandD(E ) 2.1 Formula 2.2 Elasticity for an entire D curve 2.3 Elasticity for points along a straight line D curve 2.4 Relationship between ΔP and Δ in revenue under different elasticity values 2.5 Determinants of D 3. Price of elasticity of suppSy (E ) 4. Income elasticity of demand (Y ) 5. Cross (cross) elasticity of demanX (E ) 1. Introduction  Elasticity shows the responsiveness/sensitivity of one variable to a change in another variable o Q to a change in P o Acceleration to a change in mass, etc. o The responsiveness of quantity demanded when we change price  The changes are necessary to see responsiveness, but on their own are not enough to see the change without knowing the numbers o Change price by $-1 and ten more products are ordered o Change may not be significant:  Annual number of orders: if you produce a million bags of coffee a year, then no. But if you produce 10, then yes)  Original cost: if the product costs a million dollars or ten dollars, the $1 change will vary in significance  Responsiveness of y to a change in x o % Δ in Y = Δ Y x 100 Y = ΔY/ΔX o % Δ in X = Δ X x 100 X 2. Price elasticity of demand (E ) D  Point elasticity measure ED  Arc elasticity measure 2.1 Formula  The point you use to put things in perspective are the original cost and the original quantity you started with  We use the average of the old and new values to… something. o P = $5 Q = 100 d o P = $4 Q = 120 o ΔP = $1 ΔQ = +20 d d o Point elasticity measure: E D ΔQ /ΔP ∙ P/Q  Original price & quantity demanded  ED= +20/-1 ∙ $5/100 = 100/-100 = -1  This value will always be negative o Arc elasticity measure: E D ΔQ /ΔP ∙ P/Q d  ED= +20/-1 ∙ 4.5/110 = - 90/110  Use the average values of price and quantity demanded  Absolute value = ignore the negative sign – some text books do this 2.2 Elasticity for an entire D curve Jargon Description Graph Perfectly elastic E = - ∞ Demand is horizontal (ΔQ not P) D d Q is infinitely responsive Slope: fairly flat Elastic -∞ < E D-1 d Between -1 and –infinity +P by 1 – Q falds by 10 (cross multiply – 10/1 = %delta Qd/%delataP) Q is very responsive Slope: negative curve (not pie) Unit elastic E D -1 P=dC/Qd (P x corresponding Qd = C) Q is equally responsive to a change in price Inelastic -1 < ED< 0 (between -1 & 0) Slope: fairly steep d Q is not very responsive – things like gas & necessities Perfectly inelastic E D 0 Demand is perfectly vertical (ΔP not Q ) Quantity demanded does not change. It’s stuck at one point  A typical demand curve slopes downward (like unit or in/elastic)– perfectly in/elastic are strange examples 2.3 Elasticity for points along a straight line D curve  Picking a point on a curve and seeing if the point is elastic or inelastic  Use the point measure  Slope = Δy/Δx = -2  Flip the axis = -.5 o Y = 5 – 2x 2x = 5 – y x = 5/2 – 1/2y x = 2.5 – ½ y d  While sitting on the Y axis (P), the coordinate for Q is 0 ( ½ times #/0) o Anything divided by zero gives you (-)infinity  While sitting on the X axis (Qd) the coordinate for P is 0 ( ½ times 0/#)
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