Chapter 2 Elasticity P50-63 Chapter 2 Elasticity P50-63

ELASTICITY Defining elasticityDefining elasticity –the responsiveness of demand and supply –Firm might want a measure of how demand will respond to an increase in price –Government might want a measure of sensitivity of petrol demand to a tax increase –Sainsbury’s might want to know how supply of organic veg will respond to a price fall.

Market supply and demand Quantity Price O Q1Q1 P1P1 a S1S1 D

Quantity Price O Q2Q2 Q1Q1 P1P1 P2P2 b S2S2 S1S1 D a Market supply and demand

Quantity Price O Q2Q2 Q1Q1 P1P1 P2P2 S2S2 S1S1 D D'D' a b Market supply and demand

Quantity Price O Q3Q3 Q2Q2 Q1Q1 P1P1 P2P2 P3P3 c S2S2 S1S1 D D'D' a b Market supply and demand

ELASTICITY Elasticity Elasticity –use of proportionate or percentage changes E.g.Price elasticity of demand (P  d ):E.g.Price elasticity of demand (P  d ): Some books write  pSome books write  p

ELASTICITY Elasticity Elasticity –use of proportionate or percentage changes E.g.Price elasticity of demand (P  d ):E.g.Price elasticity of demand (P  d ): Some books write  pSome books write  p

ELASTICITY

Quantity (tonnes: 000s) Price (pence per kg) Demand Price (pence per kg) Market demand (tonnes 000s) ABCDEABCDE Point A B C D E Market demand for potatoes (monthly)

Elasticity Formula

A move from B to A…. Price (pence per kg) Market demand (tonnes 000s) ABCDEABCDE Point

Price (pence per kg) Market demand (tonnes 000s) ABCDEABCDE Point A move from B to A….

ELASTICITY Elasticity Elasticity –use of proportionate or percentage changes –the sign (positive or negative) –the value (greater or less than one) –Here –Sign is negative and less than 1 –We say that the demand curve is inelastic at this point

ELASTICITY If the elasticity of demand wasIf the elasticity of demand was Greater than 1 - we would say it was elastic.Greater than 1 - we would say it was elastic. Less than 1 – InelasticLess than 1 – Inelastic Note elasticity of demand is negative (usually) so when we say it is greater than one we mean the ABSOLUTE number is greater than oneNote elasticity of demand is negative (usually) so when we say it is greater than one we mean the ABSOLUTE number is greater than one E.g. 4 > 1 - so more elasticE.g. 4 > 1 - so more elastic What does inelastic demand mean?What does inelastic demand mean? Consider Total Expenditure on a goodConsider Total Expenditure on a good Total Expenditure = (P x Q)Total Expenditure = (P x Q)

Total expenditure or Total Revenue P(£) Q (millions of units per period of time) D

P(£) Q (millions of units per period of time) D Total expenditure or Total Revenue

Consumers’ total expenditure = firms’ total revenue = £2 x 3m = £6m P(£) Q (millions of units per period of time) D Total expenditure or Total Revenue P =£2 and Q = 3m

ELASTICITY Price elasticity of demand and consumer expenditure (P x Q)Price elasticity of demand and consumer expenditure (P x Q) –effects of a price change on expenditure: elastic demand

P(£) Q (millions of units per period of time) 0 a D 4 20 Elastic demand between two points TR= 4x20=80

P(£) Q (millions of units per period of time) 0 b a D Expenditure falls as price rises Elastic demand between two points 5x10=50 TR= 4x20=80

ELASTICITY Price elasticity of demand and consumer expenditure (P x Q)Price elasticity of demand and consumer expenditure (P x Q) –effects of a price change on expenditure: elastic demand –effects of a price change on expenditure: inelastic demand

Inelastic demand between two points P(£) Q (millions of units per period of time) 0 a D 4 20 TR= 4x20=80

P(£) Q (millions of units per period of time) 0 c a D Expenditure rises as price rises Inelastic demand between two points TR= 4x20=80 8x15=120

Elasticity Elastic demand:Elastic demand: Total Revenue falls when P risesTotal Revenue falls when P rises INelastic demand:INelastic demand: Total Revenue rises when P risesTotal Revenue rises when P rises

ELASTICITY Elasticity Elasticity –use of proportionate or percentage changes –the sign (positive or negative) –the value (greater or less than one) Price elasticity of demand (P  d):Price elasticity of demand (P  d): Determinants of Elasticity: –number and closeness of substitute goods –the proportion of income spent on the good –time

ELASTICITY Price elasticity of demand and consumer expenditure (P x Q)Price elasticity of demand and consumer expenditure (P x Q) –effects of a price change on expenditure: elastic demand –effects of a price change on expenditure: inelastic demand –extreme cases

Totally inelastic demand (P  D = 0) P Q O Q1Q1 P1P1 D a

P Q O Q1Q1 P1P1 P2P2 D b a

Elasticity Formula

P Q O Q1Q1 P1P1 P2P2 D b a Totally inelastic demand (P  D = 0) P  D = 0 Note TR has still risen, but P  D = 0

Infinitely elastic demand (P  D =  ) P Q O Q1Q1 P1P1 D a

P Q O Q1Q1 P1P1 Q2Q2 D b a

Why Infinitely Elastic?

P Q O Q1Q1 P1P1 Q2Q2 D b a Note strictly speaking this should be a negative number, i.e., Infinitely elastic demand (P  D = -  )..and total revenue rises when p falls!

P Q O Q1Q1 P1P1 Q2Q2 D b a Note strictly speaking this should be a negative number, i.e., Infinitely elastic demand (P  D = -  )..really saying p falls by teeny weeny tiny amount!

P Q O Q1Q1 P1P1 Q2Q2 D b a Note strictly speaking this should be a negative number, i.e., Infinitely elastic demand (P  D = -  )..OR total revenue falls when p rises!

Unit elastic demand (P  D = -1) P Q O D a This is a very special case We will see this in more detail later

P Q O D 8 a b Unit elastic demand (P  D = -1) TR= 20 x 40 =800 8 x 100=800

P Q O D 8 a b Unit elastic demand (P  D = -1) TR= 20 x 40 =800 8 x 100=800 P  D = -1, Total Revenue stays the same when P rises When P  D = -1, Total Revenue stays the same when P rises

ELASTICITY In Economics instead of writing Q 1 - Q 0, we use the notation Q 1 - Q 0 =  Q,In Economics instead of writing Q 1 - Q 0, we use the notation Q 1 - Q 0 =  Q, where  means ‘change in’where  means ‘change in’ So:So:

Arc v Point Elasticity Earlier we calculated the elasticity when moving between B and A. The answer wasEarlier we calculated the elasticity when moving between B and A. The answer was -4/5-4/5 You might expect that moving from A to B would produce the same result. Let’s check.You might expect that moving from A to B would produce the same result. Let’s check.

A move from A to B…. Price (pence per kg) Market demand (tonnes 000s) ABCDEABCDE Point

Price (pence per kg) Market demand (tonnes 000s) ABCDEABCDE Point A move from B to A….

Whoops, before we found that elasticity of demand was –4/5 now What is going on here.

ELASTICITY The answer is to measure elasticity by the arc method:The answer is to measure elasticity by the arc method: arc elasticityarc elasticity –using the average or 'mid-point' Eg. In the term (Q 1 - Q 0 ) / Q * Instead of using Q 0 or Q 1 under the line, we use the mid-point between the two.Instead of using Q 0 or Q 1 under the line, we use the mid-point between the two.

Quantity (tonnes: 000s) Price (pence per kg) Demand A B C D E Arc Method

Quantity (tonnes: 000s) Price (pence per kg) Demand A B C D E Market demand for potatoes (monthly)

Now since using mid-point elasticity is the same whether we are moving from point A to B or point B to A.Now since using mid-point elasticity is the same whether we are moving from point A to B or point B to A. From now on when we write P or Q we will mean the mid-point.From now on when we write P or Q we will mean the mid-point.

We can simplify the formula for elasticity to :

Elasticity along a straight line demand curve. P (£) Q (000s) Demand

Elasticity along a straight line demand curve. P (£) Q (000s) Demand

Elasticity along a straight line demand curve. P (£) Q (000s) Demand

Elasticity along a straight line demand curve. P (£) Q (000s) Demand

Now look lower down the line P (£) Q (000s) Demand

Now look lower down the line P (£) Q (000s) Demand

Now look lower down the line P (£) Q (000s) Demand

So along the line the elasticity varies P (£) Q (000s) Demand   Elastic INElastic

So along the line the elasticity varies P (£) Q (000s) Demand Highly Elastic Inelastic Portion

Which demand curve is the more elastic? P (£) Q Q Can’t really say – elasticity varies along the length. So it depends P (£)

Which demand curve is the more elastic? P (£) QQ Suppose instead both demand curves were on the same graph P (£)

Which demand curve is the more elastic? P (£) QQ Suppose instead both demand curves were on the same graph

Which demand curve is the more elastic? P (£) Q Suppose instead both demand curves were on the same graph Now we have a common point, so we can say flatter line is more elastic.. It has the smaller slope

ELASTICITY Measurement of elasticity: We also use a concept called point elasticityMeasurement of elasticity: We also use a concept called point elasticity If you haven’t A-level maths you can come back to this is a few weeks. Ignore for now.If you haven’t A-level maths you can come back to this is a few weeks. Ignore for now. –the formula for price elasticity of demand: dQ/dP x P/Q –the elasticity of a straight-line demand ‘curve’ (constant dQ/dP) –the elasticity of a curved demand curve: dQ/dP is the tangent to the curve

Measuring elasticity at a point P Q 0 D r P  d = (1 / slope) x P/Q

P Q D r P  d = (1 / slope) x P/Q Measuring elasticity at a point

P Q D r P  d = (1 / slope) x P/Q =  100/50 x 30/40 Measuring elasticity at a point

P Q D r P  d = (1 / slope) x P/Q =  100/50 x 30/40 =  60/40 Measuring elasticity at a point

P Q D r P  d = (1 / slope) x P/Q =  100/50 x 30/40 =  60/40 =  1.5 Measuring elasticity at a point

ELASTICITY Price elasticity of supplyPrice elasticity of supply –measurement

Price (pence per kg) Quantity (tonnes: 000s) Supply a b c d e P Q abcdeabcde Market supply of potatoes (monthly)

ELASTICITY P Q abcdeabcde

ELASTICITY P Q abcdeabcde

ELASTICITY P Q abcdeabcde

ELASTICITY So the Elasticity of Supply in this example =1 and it is positive However, once again, it is possible to have elastic and inelastic demand curves.

Supply in different time periods reflects different Elasticities D1D1 P1P1 Q1Q1 P Q O a

D1D1 D2D2 P1P1 Q1Q1 P Q O a Supply in different time periods Suppose Demand rises, How will supply react?

D1D1 D2D2 SiSi P1P1 P2P2 Q1Q1 P Q O a b Supply in different time periods Very Short Run Supply is Inelastic

D1D1 D2D2 SiSi S P1P1 P3P3 P2P2 Q1Q1 Q3Q3 P Q O a b c Supply in different time periods Medium Run Supply is More Elastic

D1D1 D2D2 SiSi S SLSL P1P1 P4P4 P3P3 P2P2 Q1Q1 Q3Q3 Q4Q4 P Q O a b c d Supply in different time periods Long Run

ELASTICITY Income elasticity of demand (  eta)Income elasticity of demand (  eta) Measures the responsiveness of demand to changes in incomeMeasures the responsiveness of demand to changes in income

ELASTICITY  D p   D p  > 0 Normal Good 0-1 Normal Necessity >1 Luxury or superior good spending proportionally more as Income rises  D p  D p < 0 Inferior Good

ELASTICITY Cross-price elasticity of demandCross-price elasticity of demand –Measures the responsiveness of a good to changes in the price of other goods

ELASTICITY Cross-price elasticity of demandCross-price elasticity of demand –Measures the responsiveness of a good to changes in the price of other goods If the elasticity is a positive numberIf the elasticity is a positive number A & B are substitutesA & B are substitutes If the elasticity is a negative numberIf the elasticity is a negative number A & B are complementsA & B are complements

SUMMARY In this series of lectures based on Ch.2 of Sloman we have learnt aboutIn this series of lectures based on Ch.2 of Sloman we have learnt about –The demand curve  And Movements along versus Shifts in –The supply curve  And Movements along versus Shifts in –Determination of Equilibrium :- D=S  The Effects of a variety of shifts –Elasticity  Of Demand, Supply, Income and Cross Price