The Demand Side of the Market - Missouri S&T - Missouri...

The Demand Side of the The Demand Side of the MarketMarket

Econ Dept, UMR

Presents

u Utility Theory

u Consumer Surplus

u Elasticity

StarringStarring

FeaturingFeaturing

uuThe MU/P RuleThe MU/P RuleuuThe Meaning of ValueThe Meaning of ValueuuFour Elasticities:Four Elasticities:vvPrice Elasticity of DemandPrice Elasticity of DemandvvIncome ElasticityIncome ElasticityvvCross Price ElasticityCross Price ElasticityvvPrice Elasticity of SupplyPrice Elasticity of Supply

uuThe ElasticityThe Elasticity--TR RelationshipTR Relationship

In Three PartsIn Three Parts

Consumer Choice TheoryConsumer Choice Theory

Consumer SurplusConsumer Surplus

Elasticity Elasticity A. Price Elasticity of Demand A. Price Elasticity of Demand B. Other Important ElasticitiesB. Other Important Elasticities

ElasticityElasticity

Measures of ResponseMeasures of Response

Part 3

Consumers and producers move along their demand and supply curves when the price of the good changes

QUESTION: HOW CAN WE PREDICT THE MAGNITUDE OF THESE REACTIONS?

Demand and supply curves shift when factors other than price change in the marketplace

QUESTION: HOW CAN WE PREDICT THE MAGNITUDE OF THESE REACTIONS?

ANSWER: ELASTICITIES!!

A Generic Definition of A Generic Definition of ElasticityElasticityuu Y = f(x)Y = f(x)

uu Elasticity, Elasticity, ,,,, = %= %∆∆y/y/%%∆∆ x, where x, where ∆∆ is read is read ““change inchange in””

uu %%∆∆Y = (Y = (∆∆y/y)*100; y/y)*100; %%∆∆X = (X = (∆∆x/x)*100x/x)*100uu ((∆∆Y/y)/(Y/y)/(∆∆x/x), orx/x), oruu [([(∆∆Y/Y/∆∆x)/(x/y)]x)/(x/y)]uu In words, elasticity gives us the estimated In words, elasticity gives us the estimated

percentage change in one variable, y, in percentage change in one variable, y, in response to a percentage change in another response to a percentage change in another variable, x, variable, x, c.Pc.P

GGeneric Interpretation of Elasticityeneric Interpretation of Elasticity

uu,, = %= %∆∆Y/Y/%%∆∆x = 2x = 2vvThis means if x were to change by 1 percent This means if x were to change by 1 percent

we would expect y to change by 2 percent we would expect y to change by 2 percent in the in the samesame direction, direction, c.p.c.p.

uu,, = %= %∆∆Y/Y/%%∆∆x = x = -- 22vvThis means if x were to change by 1 percent This means if x were to change by 1 percent

we would expect y to change by 2 percent we would expect y to change by 2 percent in the in the oppositeopposite direction, direction, c.p.c.p.

Rewriting the Formula for ElasticityRewriting the Formula for Elasticityuu,, = %= %∆∆Y/Y/%%∆∆xx

uu Percentage change,Percentage change, %%∆∆y = (y = (∆∆ y/y)*100 y/y)*100 vv E.G., Percentage change from 50 to 100 is change E.G., Percentage change from 50 to 100 is change

(= +50), divided by the base (=100) times 100 = (= +50), divided by the base (=100) times 100 = (50/100)* 100 = 50%(50/100)* 100 = 50%

vv Since the numerator and denominator have 100, Since the numerator and denominator have 100, they cancel, andthey cancel, and

uu,, = %= %∆∆Y/Y/%%∆∆x = (x = (∆∆y/y)*(y/y)*(∆∆x/x) orx/x) or

uu,, = = ((∆∆Y/Y/∆∆x)*(x/y)x)*(x/y)uu ItIt’’s this last formula that is most convenient s this last formula that is most convenient

to use as we see laterto use as we see later

uu Price elasticity of demandPrice elasticity of demand

uu Cross price elasticity of demandCross price elasticity of demand

uu Income elasticityIncome elasticity

uu Price elasticity of supplyPrice elasticity of supply

D1

D

Some Important ElasticitiesSome Important Elasticities

%∆ in QS ∆QS

∆ P

P

Q,S = %∆ in P =

%∆ in D ∆D∆ I

I,I = %∆ in I=

%∆ in D1 ∆D1

∆ P2

P2,D1,P2 = %∆ in P2=

%∆ in QD ∆QD

∆ P

PQ

,D = - %∆ in P= -

This Slide Show DiscussesThis Slide Show DiscussesPrice Elasticity of DemandPrice Elasticity of Demand

uuOther Elasticities are discussed in slide Other Elasticities are discussed in slide show III.B.show III.B.

Price Elasticity of DemandPrice Elasticity of Demand

Measures How Responsive Measures How Responsive Consumers Are to Changes Consumers Are to Changes in the Price of a Productin the Price of a Product

DemandDemanduuWe know, from the law of demand, that We know, from the law of demand, that

price and quantity demanded are price and quantity demanded are inversely relatedinversely related

uuNow, we are going to get more specific Now, we are going to get more specific in defining that relationshipin defining that relationship

uuWe want to know just We want to know just how muchhow much will will quantity demanded change when price quantity demanded change when price changes? That is what changes? That is what elasticity of elasticity of demanddemand measuresmeasures

uuPrice elasticity of demandPrice elasticity of demand ((,,DD) ) measures the responsiveness of Qmeasures the responsiveness of QDD of a of a good to a changegood to a change in its Pin its Pvv %%∆∆ In QIn QDD

%%∆∆ in P in P vvNote thatNote that ∆∆ means “change”means “change”

uuAlso note that the law of demand Also note that the law of demand implies implies ∆∆QQDD ∆∆P is negative. Our P is negative. Our definition of definition of ,,DD includes a negative includes a negative sign, so sign, so ,,D D will always be a positive will always be a positive number (I know its confusing but …)number (I know its confusing but …)

Price Elasticity of DemandPrice Elasticity of Demand

,D = -

Ambiguity of the Sign of Ambiguity of the Sign of ,,DDuuSome economists define Some economists define ,,D D withwith a a

negative sign, thatnegative sign, that’’s what we dos what we douuSome economists leave the negative sign Some economists leave the negative sign

out of the formula and then talk about out of the formula and then talk about about the absolute value of about the absolute value of ,,DD

uuSome economists are just sloppy and talk Some economists are just sloppy and talk of negative of negative ,,D D sometimes and positive sometimes and positive sometimessometimes

uuRegardless the interpretation is the same:Regardless the interpretation is the same:vv IfIf = 2 or = 2 or --2 the meaning is clear, a 10% 2 the meaning is clear, a 10%

change in price is expected to change change in price is expected to change quantity demanded quantity demanded in the opposite directionin the opposite directionby 20%by 20%

,D

Calculating Elasticity of Calculating Elasticity of DemandDemand

P

Q/t0

56

2

6 16144

1 D

Consider the following Demand Curve:QD = 16 - 2P

12

Calculating ElasticityCalculating Elasticity

P

Q/t0

5

6

2

64

1 D

A …and let’s say we want to findthe Elasticity of Demand at point ANotice the slope of the demand curve, )P/)Q, = -1/2

uuWe know We know

uu %%∆ ∆ Can be calculated as the change divided Can be calculated as the change divided by starting pointby starting point

uu In this case, In this case, ∆∆QQDD//))P P is is --2 (the inverse of the 2 (the inverse of the slope of the demand curve)slope of the demand curve)

uu P/Q is 6/4 (we use the initial P and Q as our P/Q is 6/4 (we use the initial P and Q as our basebase

uu,,D D = = -- ((--22)()(6/46/4) ) = 3= 3


%∆ in QD ∆Q∆ P

PQ

,D = - %∆ in P= -


P

Q/t0

5

6

2

124

1 D

A Now, let’s find the Elasticity of Demand at point C

C

uuAgain, Again,

uu∆∆QQDD//∆∆P P is still is still --2 (the inverse of the slope of 2 (the inverse of the slope of the demand curve)the demand curve)

uu P/Q is 2/12 (again use the initial P and Q as P/Q is 2/12 (again use the initial P and Q as the basethe base

uu,,D D = = -- ((--2)(2/122)(2/12)) = 1/3= 1/3


%∆ in QD ∆Q∆ P

PQ

,D = - %∆ in P= -


uu Note that is different at different places Note that is different at different places along the curvealong the curvevv Specifically, it gets smaller as you move Specifically, it gets smaller as you move

down the curvedown the curveuu Note that elasticity and slope are NOT the Note that elasticity and slope are NOT the

same thingsame thing

,D

Calculating Elasticity Using Calculating Elasticity Using the Demand Equationthe Demand EquationuuQQDD = 16 = 16 -- 2p2puuThe parameter attached to price is The parameter attached to price is

∆∆QQDD//∆∆P, here = P, here = --22uuThe negative sign in the price elasticity The negative sign in the price elasticity

formula makes formula makes -- 2 equal to 22 equal to 2uuSelect any price and find Select any price and find ,,DDvvFor example at P = 7, QFor example at P = 7, QDD = 2= 2vv,,DD = 2(7/2) = 7= 2(7/2) = 7

How Do We Interpret Price How Do We Interpret Price Elasticity of Demand?Elasticity of Demand?

uuThe number we get from computing the The number we get from computing the elasticity is a percentage elasticity is a percentage -- there are no there are no unitsunits

uuWe can read it as the percentage change We can read it as the percentage change in quantity for a 1% change in pricein quantity for a 1% change in price

How Do We Interpret Price How Do We Interpret Price Elasticity of Demand?Elasticity of Demand?uuThus, if = 2, that means that at that Thus, if = 2, that means that at that

point on the demand curve, a 1% point on the demand curve, a 1% change in price will cause a 2% change change in price will cause a 2% change in quantity demanded in the opposite in quantity demanded in the opposite direction. Or if we extrapolate, a 2% direction. Or if we extrapolate, a 2% increase in price will cause a 4% increase in price will cause a 4% decrease in quantity demanded, decrease in quantity demanded, c.p.c.p.

,D

Extreme Cases ofExtreme Cases ofuuPerfectly inelasticPerfectly inelasticvv = = --%%∆∆ In QIn QDD

%%∆∆ in Pin Pvv = = -- 0 0

%%∆∆ in Pin Pvv = 0= 0

uu No matter how much price changes, No matter how much price changes, consumers purchase the same amount of the consumers purchase the same amount of the goodgoodvvNo example exists according to the law of No example exists according to the law of

demand, but things like insulin have an demand, but things like insulin have an elasticity that is pretty largeelasticity that is pretty large

,D

,D

,D

,D

Perfectly Inelastic, Perfectly Inelastic, ,,DD = = 00

P

Q/t

PerfectlyInelastic

0

Extremes Cases ofExtremes Cases ofuuPerfectly elasticPerfectly elasticvv = = -- %%∆∆ In QIn QDD

%%∆∆ in Pin Pvv = = --%%∆∆ In QIn QDD ∞∞

%%∆∆ in P 0in P 0vv = = ∞∞

uu No matter how little the price changes, consumer No matter how little the price changes, consumer purchases drop to zero, or expand to infinitypurchases drop to zero, or expand to infinityvv As with perfectly inelastic demand no example As with perfectly inelastic demand no example

exists according to the law of demand, but we exists according to the law of demand, but we have use for the concept of perfectly elastic when have use for the concept of perfectly elastic when we look at the behavior of firmswe look at the behavior of firms

,D

,D

,D

,D

Perfectly Elastic, Perfectly Elastic, ,,DD = = ∞∞P

Q/t

PerfectlyElastic

0

Empirical Estimates of Empirical Estimates of ,,DD

uu0 < 0 < ,,dd < < ∞∞uu If 0 < If 0 < ,,DD < 1 we say demand is price inelastic< 1 we say demand is price inelasticvv Any % change in P leads to a smaller % change in Any % change in P leads to a smaller % change in

QQDD

uu If If ,,DD = 1 we say demand is unitary elastic= 1 we say demand is unitary elasticvv Any % change in P leads to the same % change in Any % change in P leads to the same % change in

QQDD

uu If 1< If 1< ,,DD < < ∞∞ we say demand is price elasticwe say demand is price elasticvv Any % change in P leads to a larger % change in Any % change in P leads to a larger % change in

QQDD

The Following Categories Help to The Following Categories Help to Describe Consumer Responsiveness:Describe Consumer Responsiveness:

uu If the elasticity coefficient is If the elasticity coefficient is less than 1 less than 1 demand is demand is inelasticinelastic. Consumers are . Consumers are relatively unresponsive to price changes.relatively unresponsive to price changes.

uu If the elasticity coefficient is If the elasticity coefficient is greater than greater than 1 1 demand is demand is elasticelastic. Consumers are . Consumers are relatively responsive to price changes.relatively responsive to price changes.

uu If the elasticity coefficient is If the elasticity coefficient is equal to 1equal to 1, , demand is demand is unitary elasticunitary elastic..

Generalizing About ElasticityGeneralizing About ElasticityuuNotice that the vertical D curve has an Notice that the vertical D curve has an

elasticity of zero and the flat D curve has elasticity of zero and the flat D curve has an elasticity of infinityan elasticity of infinity

uuAs the demand curve goes from vertical As the demand curve goes from vertical to horizontal the elasticity goes from 0 to to horizontal the elasticity goes from 0 to infinityinfinity

uuUnfortunately, we can’t say the flatter Unfortunately, we can’t say the flatter the demand curve, the greater the the demand curve, the greater the elasticityelasticity

Linear Demand Curves Have Linear Demand Curves Have Elastic, Unitary, and Inelastic Elastic, Unitary, and Inelastic Regions Regions

P

DQ/t

ELASTIC

UNITARY ELASTIC

INELASTIC

Midpoint

10

5

7 14

,D = ∞

,D > 1

,D = 1

,D < 1

,D = 0

Why Would a Business Firm Why Would a Business Firm Need to Calculate Them, Need to Calculate Them, and How Would the Firm and How Would the Firm Use the Information?Use the Information?

Now that you can calculate the price elasticity of demand, what would you use it for?

There Is an Important Relationship There Is an Important Relationship Between Between Price Elasticity of Demand Price Elasticity of Demand and and Total RevenuesTotal Revenues::

uuWhen demand is When demand is inelasticinelastic, price and , price and total revenues are total revenues are directlydirectly related. related. Price increases generate higher Price increases generate higher revenues.revenues.

uuWhen demand is When demand is elasticelastic, price and total , price and total revenues are revenues are indirectlyindirectly related. Price related. Price increases generate lower revenues.increases generate lower revenues.

Total RevenueTotal Revenue

uuTotal revenue = P*QTotal revenue = P*QuuThe firm is interested in how TR (total The firm is interested in how TR (total

revenue) changes as p and q changerevenue) changes as p and q change

Total Revenue Calculation Total Revenue Calculation --ExampleExample

uuPrice $1 QPrice $1 QDD = 100= 100vvTR = $100TR = $100


uuPrice $5 QPrice $5 QDD = 10= 10vvTR = $ 50TR = $ 50


Total Revenue and ElasticityTotal Revenue and Elasticity

uuLet’s say demand is inelastic. Then if Let’s say demand is inelastic. Then if the firm raises prices 10%, the sales will the firm raises prices 10%, the sales will drop by less than 10%: drop by less than 10%: (%(%∆∆QQDD < < %%∆∆P)P)

uu In other words, the gain in revenue In other words, the gain in revenue from higher prices is greater than the from higher prices is greater than the loss in revenue from lost loss in revenue from lost sales.Therefore, total revenue will risesales.Therefore, total revenue will rise


uu If they lowered prices, though, the loss If they lowered prices, though, the loss of revenue from higher prices would be of revenue from higher prices would be greater than the gain from increased greater than the gain from increased sales, so total revenue will fallsales, so total revenue will fall


uuLet’s say demand is elastic. Then if the Let’s say demand is elastic. Then if the firm raises prices 10%, the sales will firm raises prices 10%, the sales will drop by more than 10% drop by more than 10% (%(%∆∆QQDD > > %%∆∆P)P)in other words, the gain in revenue in other words, the gain in revenue from higher prices is less than the loss from higher prices is less than the loss in revenue from lost sales.Therefore, in revenue from lost sales.Therefore, total revenue will falltotal revenue will fall


uu If they lowered prices, though, the loss If they lowered prices, though, the loss of revenue from higher prices would be of revenue from higher prices would be less than the gain in revenue from less than the gain in revenue from increased sales, so total revenue will increased sales, so total revenue will riserise

Total Revenue and DemandTotal Revenue and Demand

uuSo we can look at what happens to total So we can look at what happens to total revenue as we move down a demand revenue as we move down a demand curvecurve

uuAs we move down a demand curve we As we move down a demand curve we know that we start off elastic and as we know that we start off elastic and as we lower price we get less and less elastic lower price we get less and less elastic (but total revenue rises, since it is (but total revenue rises, since it is elastic) until we hit the point that we elastic) until we hit the point that we are inelastic and then as we continue to are inelastic and then as we continue to lower price, total revenue fallslower price, total revenue falls

Total Revenue and DemandTotal Revenue and Demand

Total Revenue

Demand

$

$Q/t

Q/t

Elasticity = 1Elastic

Inelastic

Total Revenue TestTotal Revenue Test

uu If P and total revenue move togetherIf P and total revenue move togethervvDemand is inelasticDemand is inelastic

uu If P and TR move in opposite directionsIf P and TR move in opposite directionsvvDemand is elasticDemand is elastic

uu If changes in P doesn’t change TRIf changes in P doesn’t change TRvvDemand is unitary elasticDemand is unitary elastic

TR and Farm RevenueTR and Farm Revenueuu In 1988, wheat farmers experienced the worst In 1988, wheat farmers experienced the worst

drought since the 1930sdrought since the 1930suu Estimates of the price elasticity of demand for Estimates of the price elasticity of demand for

wheat range from 0.3 to 0.7wheat range from 0.3 to 0.7uu Due to the poor harvest, supply decreased by Due to the poor harvest, supply decreased by

14%14%uu What happened to wheat price?What happened to wheat price?vv $2.57 in 1987 and $3.72 in 1988, a 45% increase$2.57 in 1987 and $3.72 in 1988, a 45% increasevv The implied The implied ,,D D = 14/45 = 0.31= 14/45 = 0.31

uu What happened to total revenue?What happened to total revenue?vv It increased (of course for farmers whose crops were It increased (of course for farmers whose crops were

wiped out, their TR fell)wiped out, their TR fell)

Now...Now...What Factors Help What Factors Help to Determine Price to Determine Price Elasticity of DemandElasticity of Demand??

Notice that this gives the firm information that it can use to establish pricing policy.

Determinants Of Price Determinants Of Price Elasticity Of DemandElasticity Of Demand

uu Availability of substitutes Availability of substitutes ---- demand demand is more elastic when there are more is more elastic when there are more substitutes for the product.substitutes for the product.

uu Importance of the item in the budget Importance of the item in the budget ----demand is more elastic when the item demand is more elastic when the item is a more significant portion of the is a more significant portion of the consumer’s budget.consumer’s budget.

uuTime frame Time frame ---- demand becomes more demand becomes more elastic over time.elastic over time.

Determinants of Determinants of ,,DD

uuAvailability of substitutesAvailability of substitutesvvAs there are more substitutes, demand is As there are more substitutes, demand is

more elastic (and vice versa)more elastic (and vice versa)

uuExample:Example:vv Insulin has no substitutes if diabetic and Insulin has no substitutes if diabetic and

demand is very inelasticdemand is very inelasticvvKroger brand cola has many substitutes Kroger brand cola has many substitutes

and hence, demand is very elasticand hence, demand is very elastic

Determinants of Determinants of ,,DDuuAmount of consumers budgetAmount of consumers budgetvvThe less expensive a good is as a fraction of The less expensive a good is as a fraction of

our total budget, the more inelastic the our total budget, the more inelastic the demand for the good is (and vice versa)demand for the good is (and vice versa)

uuExample:Example:vvPrice of cars go up 10% (from $20,000 to Price of cars go up 10% (from $20,000 to

$22,000)$22,000)vvPrice of soda goes up 10% (from $0.50 to Price of soda goes up 10% (from $0.50 to

$0.55)$0.55)vvDemand is more effected by the price of Demand is more effected by the price of

cars increasingcars increasing

Determinants of Determinants of ,,DD

uuTimeTimevvThe longer the time frame is, the more The longer the time frame is, the more

elastic the demand for a good (and vice elastic the demand for a good (and vice versa)versa)

uuExample Example -- price of gasoline increasesprice of gasoline increasesvv Immediately: can’t do much, still need to Immediately: can’t do much, still need to

get to work, school, etcget to work, school, etcvv ShortShort--run: find a car pool, ride bike, etcrun: find a car pool, ride bike, etcvvLongLong--run: next car you buy uses less gasrun: next car you buy uses less gas

Some Estimates of Some Estimates of ,,D D : : Short Short and Long Runand Long Run**

Short Run Long RunCigarettesWaterPhysicians’ servicesGasolineAutomobilesChevroletsElectricity, h’holdAir Travel

------

------

0.60.2

0.10.1

0.350.4

0.5 to 1.51.54.01.92.4

---

* The long run is a period so full adjustment occurs. Elasticity estimates are reported by Browning, et.al., Microeconomic Theory,5th ed., 1996

The End

Check out other elasticities in III.b.

The Demand Side of the Market - Missouri S&T - Missouri...

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