Ch03 - Demand and Supply -Part 2

8/3/2019 Ch03 - Demand and Supply -Part 2

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Chapter 3. DEMAND, SUPPLY, AND

MARKET EQUILIBRIUM (Part 2)

Economics 11- UPLBPrepared by T.B.Paris, Jr. 11/28/07


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Elasticity Concepts

Meaning of elasticity: If Y=f(X), elasticitymeasures the responsivenessof Y dueto changes in X.

A given change in X brings about achange in Y. The elasticity measureattempts to compare the relative change in

Y with to the relative change in X.

Mathematical formulation:

% /

% /

Y Y Y

X X X


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Elasticity Values

0 Perfectly inelastic

1 Inelastic

1 Unit elastic

1 Elastic

Perfectly elastic

The elasticity values (in absolute terms) can range from zero toinfinity; each with definite interpretations.


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3 Demand Elasticity Concepts

We shall study 3 demand elasticityconcepts:

Own price elasticity : responsiveness ofquantity demanded of a good to changes inown-price.

Cross price elasticity responsiveness of

quantity demanded of good A to changes inprice of good B (substitute or complement)

Income elasticity responsiveness of quantitydemanded of a good due to changes in

income.


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Own-Price Elasticity

Own price elasticity of demand()measure of responsiveness of quantitydemanded to changes in price

%

%

inQd

in P


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Two ways of measuring elasticity

Point elasticity elasticity is measuredfor a single point

More precise since elasticity changes at everypoint on demand curve

Can be obtained if demand function is known

Arc elasticity computed for two pointsalong a demand curve Done if we have limited number of

observations


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Point Elasticity

0 Q

P

Price

Quantity

Q1

D

AP1

% /

% /

slope P/Q

d d dQ Q Q Q P

P P P P Q


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Arc Elasticity

Q20 Q

P

Price

Quantity

Q1

D

AP1

P2B

2 1 2 1

2 1 2 1

Diff Q Diff P

Sum Q Sum P

Q Q P P

Q Q P P


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Arc Elasticity: Example

2000 Q

P

Price

Quantity

100

D

A30

20B

200-100 30-20

200+100 30+20

100 10 1 55 / 3 1.66

300 50 3 1


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Elasticity Along a Linear Demand Curve

Unit Elastic

Elastic

InelasticP

P1

Q10 QQ

P

Price

Quantity

D

D

Elasticity goes down asyou move down along alinear demand curve.

The upper half is elastic,

the lower half is inelastic.

At the mid-point of thedemand curve, elasticity isunitary.


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Geometric derivation of

B

O

Q

D

P

Price

Quantity

C

A

E

% /

% /

Q Q Q Q P

P P P P Q

DC BD DC

BD OD ODBC

AB


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Geometric derivation of

BC

AB

B

A

C

P

Q0

Elastic at B

B

A

C

P

Q0

Inelastic at B


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Demand function: Qd = 20 - 2P

Price Quantity Slope Elasticity10 0 -2

9 2 -2 -9.00

8 4 -2 -4.007 6 -2 -2.33

6 8 -2 -1.50

5 10 -2 -1.00

4 12 -2 -0.673 14 -2 -0.43

2 16 -2 -0.25

1 18 -2 -0.11

0 20 -2 0.00


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Special Case:

Perfectly Inelastic Demand Curve:

0Q

P

Price

Quantity

D A vertical demand curve

implies that any change in pricewill not lead to a change inquantity demanded.

% 00

%

dQ

P


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Special Case:

Perfectly Elastic Demand Curve:

0Q

P

Price

Quantity

D

A horizontal demand curveimplies that a very small changein price will lead to an infinitely

large change in quantitydemanded.

%

% 0

dQ

P


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Elasticity and Total Revenue

Total revenue (from the point of view of aseller) is equal to the quantity soldmultiplied by the price.

TR = P x Q

It is of interest to the seller what happensto his TR if he raises or lowers his price,knowing that if he does, consumers willadjust their purchases.


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What happens to TR when price increases?

Answer: it depends on the elasticity of demand

ElasticP Q

TR decreases

UnitaryP Q

TR unchanged

Inelastic

P Q

TR increases

%

%

Q

P


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What happens to TR when price decreases?

Answer: it depends on the elasticity of demand

ElasticP Q

TR increases

UnitaryP Q

TR unchanged

Inelastic

P Q

TR decreases

%

%

Q

P


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Determinants of price elasticity ofdemand

(1) the availability of good substitutes for thecommodity more substitutes, more elastic

(2) the number of uses the good can be put into more uses, more elastic

(3) the price of the good relative to the consumer'spurchasing power if good takes a larger share of budget, likely to be more

elastic

(4) the time frame under consideration longer period of time, more elastic

(5) location along the demand curve. recall ideas on elasticity and the linear demand curve


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Cross Price Elasticity ofDemand

Definition: responsiveness of quantitydemand of a good to changes in price ofother goods.

Formula:

Sign: + for substitutes,- for complements

%%

dxxy

y

QeP


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Income Elasticity of Demand

Definition: responsiveness of quantitydemanded of a good to changes in income

Formula:

Sign: + for normal goods- for inferior goods

%

%

dxxI

Q

I


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Some Applications

Minimum Price Policy floor prices toprotect producers (price support) orworkers (minimum wage)

Maximum Price Policy price ceilings toprotect consumers (fares, rice price, LPGprice, etc.

Tax Incidence who bears the burdenwhen tax is imposed on the producer?


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Minimum price policies

prices cannot go below a specifiedprice

E.g. price support for agriculturalcommodities, minimum wages

floor price is usually set above theequilibrium price and it causes asurplus


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Floor Price(minimum price policy)

Pf

Q10 QQ*

P

Price

Quantity

S

D

P*

surplus

To be effective, a floor price(Pf) must be set above theequilibrium price(P*)

Examples:

Minimum wages,price support forrice farmers


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Maximum price policy(price ceiling)

price cannot be set above a specifiedprice

Example: maximum fares allowedpublic transport operators

Usually set below the equilibrium priceand causes a shortage


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Price Ceiling(maximum price policy)

Pf

Q10 QQ*

P

Price

Quantity

S

D

P*

shortage

To be effective, a priceceiling (Pf) must be setbelow the equilibriumprice(P*)

Pc

Examples:

Price control ofrice, rents, LPG


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Tax incidence

Concerned with effects of governmenttax policies on consumption andproduction.

The tax could either be a specific orexcise taxor an ad valorem tax. specific tax or excise tax tax per unit of

the product

ad valorem tax

tax as percentage of theselling price.


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Tax incidence

Question: Who bears the greaterportion of tax? Is it the consumer or theproducer?

Supply and demand analysis of aspecific tax: the tax is likely to be paid for by producers

and consumers

the tax is likely to raise the equilibriumprice, but by an amount less than the tax.


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Tax Incidence

Q00 Q

P

Price

Quantity

S0

D

P0

S1

tax

P1

P1+ t

P0+ t

Q2Q1


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Tax Incidence

Q00 Q

P

Price

Quantity

S0

D

P0

S1

tax

P0+ t

If demand is PerfectlyInelastic : all of thetax is passed on toconsumers.


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Tax Incidence: Perfectly Elastic Demand

Q00 Q

P

Price

Quantity

S0

DP0

S1

tax

If demand is PerfectlyElastic : all of the taxburden is borne by the

producer.

Q1


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Consumer Surplus

0 Q

P

Price

Quantity

Q1

D

P1

S1Consumer surplus:

difference betweenwhat a consumer iswilling to pay andwhat he actually paysfor the good.


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Consumer Surplus

0 Q

P

Price

Quantity

Q1

D

P1

S1S2

When market pricedecreases, consumersurplus becomesbigger

P2

Q2

S2S2

P2

S2

P2

S2

P2

S2

Q2

P2

S2


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Producer Surplus

0 Q

P

Price

Quantity

Q1

D

P1

S1Producer surplus:

difference between what aproducer receives (marketprice) and the amount that willmotivate him to supply theproduct (marginal costs mustbe recovered).


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EndChapter 3

Documents

Ch03 - Demand and Supply -Part 2