Topic 22.0 and 2.1 Price Theory and Applications 09-10

8/8/2019 Topic 22.0 and 2.1 Price Theory and Applications 09-10

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Price theory & applications

Demand , supply & market

equilibrium


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Tools of Analysis

Equilibrium Analysis

Optimization


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Analysis (pricedetermination)

In a free Market economy, price of aproduct/service is determined by demand &supplysituation in that market

Market for a product will be at equilibrium

when producers bring to the market exactlywhat consumers want to take out of themarket at that price.

Equilibrium is a market situation where

there is no inherent tendency for change

The market is at equilibrium when quantitydemanded is equal to quantity supplied


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Demand/Buying Side Demand for a good refers to the various

quantities of that good per unit of time thatpurchasers will take off the market at allpossible alternative prices, ceteris paribus

Willing to buy the product must satisfy aneed or want

Able to buy purchasers must have thepurchasing power to buy what they are willingto buy for there to be effective demand

Quantity thatpurchasers will take off the

market will be affected by a number of factors These factors are referred to asdeterminants of demand


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Determinants of Demand Price of the good (P)

Consumers tastes & Preferences (T)

No. of consumers under consideration (Pn)

Consumers income (I)

Prices of related goods (Pr)

Credit Availability (Ca) Consumers expectations regarding future

prices of the product (E)

Past levels of demand (Qt-1 )

Number of goods available to consumers (R) Q = f(P, T, Pn, I, Pr, R, Ca, E, Qt-1 )


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Curves Demand theory singles out the relationship between

possible alternative prices of the product & thequantities of it that purchasers will take off the

market per time period

Thus determinants 2 through 9 are held constant -ceteris paribus

Demand theory conjectures quantity to be inverselyrelated to price (law of demand)

Some exceptions may occur in which quantity takenvaries directly with price, but these must be few

A demand schedule lists different quantities ofcommodity that consumers will take opposite the

various prices of the good per period Demand curve is the demand schedule plotted on an

ordinary graph, Q = f(P) or P = f(Q)

By convention quantity demanded is measured on the

horizontal axis & price on the vertical axis


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Demand schedule and Curvecontd

Pd = a bQd or Qd = a/b (1/b) Pd

Qd = 50 1Pd

The downward slope reflects the law of demand people buy more of a product, service etc, as its

price falls. Why? Causality changes in price cause changes in

quantity demanded & not the other way round

A time-based relationship its quantity demandedper period of time, e.g., day, week, year etc

Derive a Demand schedule and plot the Demandcurve for an individual consumer

D d S h d l (i di id l)


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Demand Schedule (individual)

Price per KG Quantity per week

50 0

45 5

40 10

35 15

30 20

25 25

20 30

15 3510 40

5 45

0 50

0

10

20

30

40

50

60

0 10 20 30 40 50 60

PriceinPula

quantity per week

Demand Curve

Demand Curve

Demand Schedule (market)


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Demand Schedule (market)

Quantity per week Summary

price per k Thato Tebogo Tshepho Total qty d price per kg

50 0 0 0 0 50

45 5 2 1 8 45

40 10 5 3 18 40

35 15 8 5 28 35

30 20 11 7 38 30

25 25 14 9 48 25

20 30 17 11 58 2015 35 20 13 68 15

10 40 23 15 78 10

5 45 26 17 88 5

0 50 29 19 98 0

0

10

20

30

40

50

60

0 20 40 60 80 100 120

Priceinpula

quantity per week

Market denad curve


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Derivation of Marketdemand

Market demand is the sum of allindividual demand for a particulargood or service

20 10

pr

i

c

e

pr

i

c

e

pr

i

c

e

cake cake cake8 124 44


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Consumer surplus (CS) CS is a monetary measure of the extent to which

buyers benefit from a transaction it is a measure of

consumers well-being It is important for purposes of evaluating potential

government programmes

We use demand curves to measure consumer surplus

Recall that height of the demand curve at any givenquantity measures the most the consumer is willing topay for an extra unit of the good willingness to pay.

That amount less the market price is the surplus hegets from consuming the last unit or

The area below the demand curve & above the pricemeasures consumer surplus in a market


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Consumer Surplus

cakecake

p

r

ic

e

p

r

i

c

e

1

1

4

3 12

3

1

3

1

5

CB

A

CB

A

Consumer

surplus

Market demand

(a) (b)

2 12


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Consumer surplus Panel (a): the most the consumer is willing to pay

for:

1st unit of cake is P14. Since cake costs only P3/unit,he obtains a surplus of P11 (P14-P3) from thepurchase of the 1st unit of cake per week

2nd unit of cake is P13. His surplus from thepurchase of that unit will be smaller (P13-P3) only

P10 Continuing as above & the adding the surpluses we

get total CS of the consumer

For any other perfectly divisible good we can usepanel (b) to derive the CS, which is given by the

area ABC CS from consuming 12 units/wk.


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Loss/gain in consumersurplus

If price of cake is increased fromP3/unit to p4/unit resulting in 11units/wk of cake consumed, how will

that affect well being of consumers? Itwill fall by the area BCED

If government reduces the price of

cake from P4/unit to P3/unit, what willbe the new CS? ADE


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cake cake

p

r

i

ce

p

r

ic

e

1211 1211

4

343

D E

A

D

B C

A

B C E

Initial CS

additional CSInitial consumers

CS to new consumerLoss in CS


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Change in Demand Vs Changein quantity demanded

P

rice

perkg

Quantity per week

Movement along demand curve

Shift in demand curve

Initial demand curve

New demand curve

1020

25

20

0

ange n eman vs ange


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ange n eman vs angein qty demanded

A movement alonga given demand curverepresents a change in quantity

demanded from a change in price of thegood itself, ceteris paribus

When any of the circumstances heldconstant in the definition of demand curveare changed, the demand curve itself willshift (change in demand)Take for example an increase in wages &

salaries (Income), consumers will be willing topurchase more at any given price

The same reasoning applies in the case of No. ofconsumers and other determinants


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Determinants of demand Consumers tastes (preferences) a change

in consumer tastes that makes the productmore desirable means more of it will be boughtat each price

No. of buyers an increase in the number ofbuyers in the market increases product demand

Income for most products (normal/superiorgoods) , a rise in income causes an increase indemand. For inferior goods, an increase inincome reduces their demand


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contd

Prices of related goods a change in the

price of a related good may increase ordecrease the demand for a product,depending on whether it is a substitute orcompliment

Substitute good is a good that can beused in the place of another good. Anincrease in the price of a substituteincreases the demand for the other good.

Complimentary good is a good that isused together with another good. Anincrease in the price of a complimentarygood reduces demand for the other.

upp y s e


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upp y s e Supply of a good is defined as the various quantities of

that good that sellers will place on the market at allpossible prices, ceteris paribus

Quantities of a good that suppliers will put in the marketwill depend on a No. of factors

Such factors include, Price of the good (P)

Set of prices of resources used in producing the good (Pf)

Range of production techniques available (K)

Size, structure & nature of industry (Ms)

Government policy (Taxes and subsidies (Ts))

Therefore Qs = f(P, Pf, K, Ms, Ts)


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Supply schedule & Curve Supply schedule lists different quantities per unit of

time of the good that suppliers are willing to put in

the market, ceteris paribus Supply curve is supply schedule plotted on a graph &

is usually upward sloping to the right

For the supply curve, Pf, Ts andK are held constant,I.e. Qs = f(P) or Ps = f(Qs)

Example: Qs = Ps 10 or Ps = Qs + 10

From the equation above, derive the supply scheduleand plot the supply curve (Do it on the board)

The law of supply states that as price rises the

quantity supplied rises; as price falls quantitysupplied falls. Why?

S l h d l &


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Supply schedule & curve

Supply schedule

Price/trip trips perweek

A 10 0

B 15 5

C 20 10

D 25 15E 30 20

F 35 25

G 40 30

H 45 35

I 50 40

Supply curve

trips/wk

price/trip

0

40

20

10

30

10 20 30 40

Supply

curve


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Producer surplus (PS) PS is a monetary measure of the extent to which

sellers benefit from a transaction it is a measure of

producers well-being It is important for purposes of evaluating potential

government programmes

We use supply curves to measure producer surplus

Recall that height of the supply curve at any givenquantity measures the least the producer is willingto accept for an extra unit willingness to accept.

The market price less that amount is the surplus hegets from supplying the last unit or

The area above the supply curve & below the pricemeasures producer surplus in a market


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Consumer Surplus

cakecake

p

r

ic

e

p

r

i

c

e

1 3 12

3

1

3

1

5

CB

A

CB

A

producer surplus

Market supply

(a) (b)

2 12


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Loss/gain in producersurplus

If price of cake is increased fromP3/unit to p4/unit resulting in 13units/wk of cake supplied, how will that

affect well being of producers? It willincrease by the area BCED

If government reduces the price of

cake from P3/unit to P2/unit, what willbe the new PS?


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Consumer Surplus

cakecake

p

r

ic

e

p

r

ic

e

1 3 12

3

1

3

1

5

CB

A

CB

A

producer surplus

Market supply

(a) (b)

2 12

ED


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Change in Supply vs Changein qty supplied

A change in the price of the goodwill occasion a movement along thesupply curve, this is change in

quantity suppliedS0 S1

a

b

15

20

5 10 trips per day

Price

per

t rip

0

A change in any of the factors

held constant will result in a shift

in the entire supply curve from S0to S1 change in supply

10

Ch i l


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Change in supply If costs of factor input increase,

Quantity supplied at any given pricewill fall. For instance we may haveQs=Ps-15 as the new supply function(Use board)

Price pertrip

Trips per week

B1 15 0 (5)

C2 20 5 (10)

D3 25 10 (15)

E4 30 15 (20)

F5 35 20 (25)

G6 40 25 (30)

H7 45 30 (35)

I8 50 35 (40)


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Market price Determination If the demand & supply curves of any given good

are placed on a single diagram, then forces that

determine its market price will be highlighted Demand curve highlights what consumers are

willing to do

Supply curve shows what sellers are willing to do

Consumers demand is assumed to be independentof the activities of suppliers

Sellers supply is assumed to be independent ofconsumers activities

Equilibrium a situation of balance where there

is no inherent tendency to change. It occurs whenthe plans of consumers match those of producers.


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Market Price Determination

Supply curve

Dem

an

dcurve

Excess supply

Excess demand

e

a b

c d

35

30

15 20 25

25

Quantity per week

P

rice

perkg

10

50


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Some explanations

At a price of P10 (intercept) or lower, the

price is so low that none of the good willbe supplied.

On the demand, at a price of P50(intercept) or higher, the price is so high

that none of the good will be consumed. For every P1 increase in price, qty

consumed fall by 1 kg per week (slopeof demand curve)

Similarly, for every P1 increase in theprice, qty supplied increases by 1 kg perweek (slope of supply curve)


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determination At price of P35, producers will bring 25 kg of

beef/wk to the market Consumers will buy only 15 kg of beef/wk Suppliers bring to mkt more than consumers can

take off the mkt, there will be disequilibrium withexcess supply (a surplus (25-15)) of 10

Suppliers will cut prices to dispose off theirsurpluses

As price goes down so will be the goods brought tothe market

On the other hand, as price falls qty taken off themkt by consumers will increase

Eventually price will drop to P30/kg & consumerswill be willing to take exactly the amount thatsellers want to place on the market at that price This is equilibrium price

Assume the starting point was a price of P25 and dothe equilibrium analysis.

Ch i d d


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Changes in demand What happens to the equilibrium

price & qty exchanged of a goodwhen its demand changes, saycoz of changes in income?

30

20 3025

35e1

e2

b

Excess

demand

supply

D2D1

kg per wk

Pric

e

perkg

0

Changes in Demand contd


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Changes in Demand contd.. Demand curve shifts from D1 to D2

At the initial price of P30, suppliers supply

20kg/wk, but consumers are willing & ableto buy 30kg/wk

Consumers will bid against each other,

thus pushing up the price But as price increases, consumers will

demand less & less of the beef.

On the other side producers will producemore beef as its price rises

The bidding & increase in qty supplied willcontinue until a new equilibrium is reached

at e2

Changes in Supply


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Changes in Supply What happens to the equilibrium

price & qty exchanged of a goodwhen its supply changes, say cozof increases in wage level?

Demand curve

S1S2

30

2010 15

35e1

e2

Excess

demand0 kg per week

Pricep

erkg


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Changes in Demand &supply

An increase in demand alone leads to an increase inboth equil price & qty (D : P , Q )

A decrease in demand alone leads to a decrease inboth equil price & qty (D : P , Q )

An increase in supply alone leads to an increase inequil qty & fall in equil price (S : P , Q )

A decrease in supply alone leads to an increase inequil price & fall in equil qty (S : P , Q )

What happens if both supply & demandincrease/decrease together?

Surplus & shortage


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Surplus & shortage A surplus is an excess of quantity supplied

over quantity demanded. When there is

surplus, sellers cannot sell the quantities theydesire to supply.

A shortage is an excess of quantitydemanded over quantity supplied. When there

is a shortage buyers cannot purchase thequantities they desire

An equilibrium is a situation in which thereare no inherent forces that produce change


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mechanism

Price variations act as a signal in

response to changes in demand orsupply or both

It directs resources to where they are

needed the most

Algebra of Demand-Supply


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Algebra of Demand-SupplyAnalysis

Qd = 50 P: demand

Qs = P 10: supply To find Equilibrium we

equate Demand toSupply, I.e Qd = Qs

50 P = P 10 & solve

for P 2P = 60

P* = 30

Insert P* = 30 into eitherQs or Qd to get Q*

Q

d

=50-30 = 20 = Qs

= Q*

Or Pd = Ps 50 Qd = 10 + Qs

40 = Qd + Qs, but Qs =

Qd = Q*, so 40 = 2Q*

Q* = 20

Insert Q* into either Psor P

dto get P*

P* = Pd =50-20=Ps=30


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Generalization

Demand: Pd = a bQd, a,b>0

Supply: Ps = c + dQs, c,d>0

Equil: Qs = Qd or Ps = Pd

a - bQd = c + dQs

Qd = Qs = Q

a c = bQ + dQ

a c = (a + d)Q*

db

caQ

+

=*


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Generalization contd

( ) ( )

db

bcdaP

db

bcabdaabP

dbcabdbaP

db

cabaP

bQdaP

++

=

+

++

=

++=

+

=

=

*

*

*

Public Policy Issues


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Public Policy Issues Microeconomic models above can help

illuminate public policy issues

Price floors governments intervene in mktsto raise prices of particular goods or resources,minimum wage (to protect unskilled labourfrom exploitation), sorghum price (to protect

incomes of farmers) Price ceilings to keep prices of certain

goods at less than certain prices, ex. Rentcontrols, interest rates, petrol prices,food prices in Zim!

Do these policies always help their intendedbeneficiaries?


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Price ceiling (max. fare)

Supply curve

Dem

an

dcurve

shortage

e

c d

20

15

15 20 25

12

trips per day

P

rice

pertrip

10

50


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Price floor (min. wage)

Supply curve

Dem

an

dcurve

surplus

e

a b20

15

15 20 25

12

Labor hours per day

P

rice

perhour

10

50

The elasticity of demand


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The elasticity of demand Have so far dealt with the direction of change in

demand, and the direction of its impact on pricesand quantity demanded.

Now we look at the magnitude of its impact

Elasticity is a numerical measure of theresponsiveness of quantity demanded or quantitysupplied to one of its determinants

Price elasticity of demand measures how much thequantity demanded responds to a change in price.

Demand for a good is said to be elastic if thequantity demanded responds more thanproportionately to changes in the price

demand is said to be inelastic if the quantitydemanded responds only slightlyto changes in theprice

Price elasticity of demand


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Price elasticity of demand Measures the sensitivity of quantity demanded to changes in own

price.

Defined as %change in qty demanded resulting from 1% change in

price Varies from one point to another along a single demand curve,

i.e., from one price range to another, why?

Price elasticity for same good may vary from market to market,why?

Why should we care about elasticity of demand? Later! Why use percentages: absolute changes may bias our perception

of the responsiveness depending on the units used. Example: P1change & changes in grams

Percentages also permit comparison of sensitivities to changes inprices of different products. Example: response to P1 change ofhouses & matches

Computing price elasticity of


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Computing price elasticity ofdemand

Problem!A price decrease and increase between two pointsalong a given demand curve gives different percentagechanges (draw demand curve & elasticity coefficients whenmoving from A to B & from B to A)

Example: a price change from P1 to P2 is 100%, but a change from P2

to P1 is 50%. Similarly, a qty change from 10 to 20 is 100%, but from20 to 10 is 50%

Which of these changes should we use in the calculation of elasticity?

Elasticity should be the same whether price falls or rises

Xproductofpriceinchange

XproductofdemandedquantityinchangePED d

%

%)( =

Xofpriceoriginal

Xofpriceinchange

Xofdemandedquantityoriginal

Xofdemandedquantityinchanged =

Point elasticity measured at a single point on the curve

Arc elasticity measured between two points on the curve

price elasticity of demand


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price elasticity of demand(midpoint formula)

This problem is solved by using the

midpoint formula, where

Examples: when P1 =2, Q1=10; whenP2=1, Q2=40; calculate price elasticity

of demand using midpoint formula.

]2/)/[()(

]2/)/[()(

1212

1212

PPPP

QQQQd +

+

=


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curves

Demand is elastic when the elasticity is greater than 1, sothat quantity moves proportionately more than price.Example: a 3% decline in price of lunch results in a 5%

increase in the quantity demanded Demand is inelastic when the elasticity is less than 1, so

that quantity moves proportionately less than price:Example: a 3% decline in price of lunch results in a 1%increase in quantity demanded

Demand is unit elasticwhen elasticity equals to 1, so

that quantity moves the same amount proportionately toprice: E.g., a 3% fall in price results in a 3% increase inquantity demanded

The flatterthe demand curve through a point, thegreaterthe price elasticity of demand

The steeperthe demand curve through a point, the

smallerthe price elasticity of demand


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curves

For a verticaldemand curve,

demand is said to beperfectlyinelastic. Quantity demanded staysthe same irrespective of the price

Demand isperfectly elasticfor ahorizontaldemand curve. Thisimplies that very small changes inthe price lead to huge changes in

quantity demanded.

Determinants of PED


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Determinants of PED Range & attractiveness of substitutes the

greater the number & closer the substitutes,

the higher the PED Quality & accessibility of info on substitutes

Degree to which product is a necessity

Addictive properties of product; brand image

Relative expense of the product the largerthe proportion of income that the pricerepresents, the larger the PED, why?

Time In the short run PED is less sensitive(coz of habits, patterns, etc)

Price elasticity & total revenue


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Price elasticity & total revenuetest

Price per

can (P)

Cans of

coke (Q)

Elasticity

coefficient

TR(PxQ) TR test

8 1

5

2.601.57

1.00

0.64

0.38

0.20

8

7 2 14 elastic

6 3 18 elastic

5 4 20 elastic

4 5 20 Unit elastic

3 6 18 inelastic

2 7 14 inelastic

1 8 8 inelastic

Price elasticity along linear


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Price elasticity along lineardd curve

For linear demand curve,

Elasticity of demand is Greater than 1 above the midpoint of curve

Less than 1 below the midpoint of the curve

Equals to 1 at the midpoint of the curve

Elasticity & Total revenue


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Elasticity & Total revenueP

Q

Q

4

4

4

6

6

8

82

20

0

16

Elasticity=1; total revenue is at maximum

Elasticity1; A price reduction increases total

revenue; a price increase reduces it8


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Elasticity & Total revenue

If total revenue changes in theopposite direction from price,demand is elastic

If total revenue changes in the samedirection as price, demand is inelastic

If total revenue does not change

when price changes, demand is unitelastic

Price elasticity & total


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Price elasticity & totalRevenue

elasticity Priceincrease Price fall

Elastic(>1)

Totalrevenue falls

(why?)

Total revenueincreases

Unitary(=1)

Totalrevenue

stays thesame (why?)

Total revenuestays the same

Inelastic

(


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p ydemand

Substitutability the larger the number of substitutegoods that are available, the greater the price elasticityof demand. The more narrowly defined the product, thelarger the number of substitutes & thus more elastic

Proportion of income the higher the price of a goodrelative to consumers incomes, the greater the priceelasticity of demand. Examples:

Luxuries vs necessities the more that a good isconsidered to be a luxury the greater the priceelasticity of demand.

Time product demand is more elastic the longer thetime period under consideration. Consumers need time to

adjust to price changes.

Price elasticity of supply


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Measures sensitivity of quantity

supplied to changes in price Defined as % change in qty supplied

resulting from a 1% change in price

= % change in quantity supplied/% change in price

)//()/(sssss

PPQQ =

)]2/)/((/[)]2/)/(([ 2121 sssssss PPPQQQ ++=

s



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Price elasticity of supply Suppose a 2% increase in price of

beef results in a 6% increase in thesupply of beef. Calculate thecoefficient of elasticity

=6%/2%=3; supply is elastic

Go back to the original supply curve &compute supply elasticity betweenpoints C & E. Using

)//()/( sssss PPQQ =

10;101020)( 112====

ssss QQQQ 20;102030)( 112 ==== ssss PPPP

220

1010

10)//()/( 11 === sssss PPQQ

s



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Price elasticity of supply If we compute the elasticity by moving from point E

to C we get:

But the two should be the same as theymeasure elasticity between the same points!!!!

)//()/( sssss PPQQ =

20;102010)( 221 ==== ssss QQQQ

30;103020)( 221 ==== ssss PPPP

5.130

1020

10)//()/( 22 === sssss PPQQ

r ce e as c y o supp y( id i ) f l


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y pp y(midpoint) formula

From C to E

From E to C

)]2/)/((/[)]2/)/(([ 2121 sssssss PPPQQQ ++=

152/)(;101020)(2112

=+===sssss

QQQQQ

252/)(;102030)( 2112 =+=== sssss PPPPP

66.1)]25/(10/[)]15/10[==

s

152/)(;102010)( 1221 =+=== sssss QQQQQ

252/)(;103020)( 1221 =+=== sssss PPPPP)]2/)/((/[)]2/)/(([ 1212 sssssss PPPQQQ ++=

66.1)]25/(10/[)]15/10[ ==s

supply


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supply The degree of price elasticity of supply

depends on how easily & quickly producers

can shift resources between alternative uses. The easier & more quickly producers can

shift resources between alternative uses, thegreater the price elasticity of supply.

In the immediate market period supply isperfectly inelastic because supplier doesthave time to respond

The market period is the period that occurswhen the time immediately after a change inmarket price is too short for producers torespond with change in quantity demanded.

long run


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long run The ease with which firms can accumulate or

reduce stocks of goods the more easily firmscan do this, the higher the PES

The short run is a period of time too short tochange plant capacity but long enough to usefixed plant more or less intensively.

The price elasticity of supply is greater than inthe case of immediate market period. i.e., anincrease in demand and hence price results inan increase in supply.

The long run is a time period long enough forfirms to adjust their plant sizes & for new firmsto enter the industry. So there is a greatersupply response to change in price.

Income elasticity of dd


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Income elasticity of dd Measures the sensitivity of the amount consumed

to changes in consumers money income at anypoint on an Engel curve.

Defined as % change in qty consumed resultingfrom a 1% change in consumers money income.

superior

inferior a luxury

a necessity

)//()/( IIQQI =

Incomemoneyinchange

XproductofdemandedquantityinchangexI

%

%) =

0, = orbecanxIornormalisgoodtheIf

xI

,0>

isgoodtheIf xI ,0isgoodtheIf xI ,10


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Cross price elasticity of dd Measures responsiveness of qty

demanded of good to changes in priceof another good

Defined as % change in qty demandedof good x to 1% change in price of goody

)//()/( yyxxxy PPQQ =ssubstitutearegoodstheIf xy 0>

entscomparegoodstheIf xy lim0


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ydemand & supply

Helps understand: price variations in

a market, the impact of changingprices on consumer spending,corporate revenues and government

indirect tax receipts Helps determine tax incidence

Relevance of Price elasticity of


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ydemand & supply

The extent to which a change in supply

will affect the equilibrium price andquantity traded depends on PED

The higher the PED, smaller the changeequilibrium price & the larger the change inequilibrium quantity

The lower the PED, the larger the change inequilibrium price and the smaller thechange in equilibrium quantity.

Do examples on the board

Topic 22.0 and 2.1 Price Theory and Applications 09-10

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Transcript of Topic 22.0 and 2.1 Price Theory and Applications 09-10