economic analysis for business session v: elasticity and its application-1i

Economic Analysis Economic Analysis for Businessfor Business

Session V: Elasticity and its Session V: Elasticity and its Application-1IApplication-1I

InstructorInstructorSandeep BasnyatSandeep [email protected][email protected]

CHAPTER 5 ELASTICITY AND ITS APPLICATION

APPLICATION: APPLICATION: Does Drug Interdiction Does Drug Interdiction Increase or Decrease Drug-Related Crime?Increase or Decrease Drug-Related Crime?

One side effect of illegal drug use is crime: Users often turn to crime to finance their habit.

We examine two policies designed to reduce illegal drug use and see what effects they have on drug-related crime.

For simplicity, we assume the total dollar value of drug-related crime equals total expenditure on drugs.

Demand for illegal drugs is inelastic, due to addiction issues.


Policy 1: InterdictionPolicy 1: Interdiction

Price of Drugs

Quantity of Drugs

S1

S2D1

P1

Q1

P2

Q2

Interdiction reduces the supply of drugs.

Since demand for drugs is inelastic, P rises propor-tionally more than Q falls.

Result: an increase in total spending on drugs, and in drug-related crime

new value of drug-related crime

initial value of drug-related crime


Policy 2: EducationPolicy 2: Education

Price of Drugs

Quantity of Drugs

D1

S

P1

Q1

D2

P2

Q2

Education reduces the demand for drugs.

P and Q fall.

Result:A decrease in total spending on drugs, and in drug-related crime.

initial value of drug-related crime

new value of drug-related crime


Income Elasticity of Income Elasticity of DemandDemandThe income elasticity of demand measures the response of Qd to a change in consumer income.

Income elasticity of demand

=Percent change in Qd

Percent change in income

Calculating Income Elasticity of Calculating Income Elasticity of DemandDemandArc Elasticity:

◦ where Y stands for income.Example

◦ If a 1% increase in income results in a 3% decrease in quantity demanded, the income elasticity of demand is = -3%/1% = -3.

Q

Y

Y

Q

YY

QQ

Y

Q

%

%

Numerical ExampleNumerical Examplea) Suppose the demand for an automobile as a

function of income per capita is given by:Q = 50,000 + 5I

What is the income elasticity of demand when per capita income increases from $10,000 to $11,000?

Numerical ExampleNumerical Examplea) Suppose the demand for an automobile as a


What is the income elasticity of demand when per capita income increases from $10,000 to $11,000?

Solution:

When I1 = 10,000 Q1 = 100,000

When I2 = 11,000, Q2 = 105,000

Percentage Change in Q = 4.88

Percentage Change in I = 9.52

Income Elasticity of Demand = 4.88 / 9.52 = 0.512

Numerical Example-Point Income Numerical Example-Point Income ElasticityElasticityb) Suppose the demand for an automobile as a


What is the income elasticity of demand at the income level of $10,500?

Numerical ExampleNumerical Example

b) Suppose the demand for an automobile as a function of income per capita is given by:Q = 50,000 + 5I

What is the income elasticity of demand at the income level of $10,500?

Solution:

When I = 10,500; Q = 102,500

dQ / dI = b = 5

Income Elasticity of Demand = b x (P/Q)

= 5 x (10500 / 102500)

E = 0.512


Necessities, Inferior goods and Necessities, Inferior goods and luxuriesluxuries

Elasticity measurement as:

E < 0 : Inferior goods (negative)

0 < E ≤ 1 : Normal goods or necessities

E > 1 : Luxuries

An increase in income causes an increase in demand for a normal good and luxuries.

An increase in income causes a decrease in demand for inferior goods.


Cross Price Elasticity of Cross Price Elasticity of DemandDemandThe cross-price elasticity of demand

measures the response of demand for one good to changes in the price of another good.

Cross-price elast. of demand

=% change in Qd for good 1

% change in price of good 2

For substitutes, cross-price elasticity > 0 (positive)E.g., an increase in price of goat meat causes an increase in demand for chicken.

For complements, cross-price elasticity < 0 (Negative)E.g., an increase in price of computers causes decrease in demand for software.

Calculating Cross Price Elasticity of Calculating Cross Price Elasticity of DemandDemand

Arc Elasticity,

◦ where Po stands for price of another good.

Example◦ If a 1% increase in the price of a related good

results in a 3% decrease in quantity demanded, the cross-price elasticity of demand is = -3%/1% = -3.

Q

p

p

Q

p

pQQ

p

Q o

o

o

oo

%

%

Numerical ExampleNumerical ExampleDemand for a publisher’s book is given as:Qx = 12,000 – 5,000Px + 5I + 500Pc

Px = Price of the book = $5 I = Income per capita = $10,000Pc = Price of the books from competing publishers =

$6

1. Find Price elasticity of demand for the book. What effect a price increase would have on total revenues?

2. Find income elasticity of demand for the book. Find if the book is inferior good, normal good or luxury.

3. Assess the probable impact on demand for the book if competing publishers raise their prices. Are the books substitute for each other or complements?

Numerical ExampleNumerical Example1) a) Find Price elasticity of demand for the book. b) What effect a price increase would have on total revenues?Solution:a) Substituting the values of I and Pc

Qx = 12,000 – 5,000Px + 5(10000) + 500(6)

Or, Qx = 65,000 – 5,000Px

When Px = $5 (given), Qx = 40,000

Now, dQx/dPx = b = - 5000

Therefore, E p = -5000 x (5 / 40000) = - 0.625

b) Since, the demand for the book is inelastic, an increase in the price of the book would increase total revenue.



$6




DONE

Numerical ExampleNumerical Example2) a) Find income elasticity of demand for the book. b) Find if the book is inferior good, normal good or

luxury.Solution:a) Substituting the values of Px and Pc

Qx = 12,000 – 5,000(5) + 5I + 500(6)

Or, Qx = - 10,000 + 5I

When I = $10000 (given), Qx = 40,000

Now, dQx/dI = b = 5

Therefore, E I = 5 x (10000 / 40000) = 1.25

b) Since, the E I > 1 for the book, the book is luxury.



$6




DONE

DONE

Numerical ExampleNumerical Example3) a) Assess the probable impact on demand for the book if

competing publishers raise their prices. b) Are the books substitute for each other or complements?Solution:a) Substituting the values of Px and I

Qx = 12,000 – 5,000(5) + 5(10000) + 500Pc

Or, Qx = 37,000 + 500Pc

When Pc = $6 (given), Qx = 40,000

Now, dQx/dPc = b = 500

Therefore, Cross price elasticity of demand for the book E c = 500 x (6 / 40000) = 0.075

1% increase in competitor’s book price will increase the demand for the book by 0.075%

b) Since, the E C > 0 for the book, the book is substitute to competing producer’s book.

Basic Concept on Marginal EffectsBasic Concept on Marginal EffectsConsider a simple linear equation for a demand curve:Q =180 -2p ………………………….……(i)When p = 5; Q = 180 - 2 x 5 = 170

P = 6; Q = 168P = 7; Q = 166

For every 1 unit increase in the p, Q decreases by 2 units.So, -2 = Marginal effect of Price on Quantity

Similarly for multivariate equation:Q = a + bP + cI‘c’ is the Marginal Effect of Income on quantity.

For the inverse demand function of equation (i) above,P = 90 - 0.5QQ is the marginal effect of quantity on price.

Numerical Applications of Marginal Numerical Applications of Marginal EffectsEffectsPK Corp estimates that its demand function is as follows:

Q = 150 - 5.4P + 0.8A + 2.8Y- 1.2P*

Where;

Q = quantity demanded per monthP=price of the productA=firm’s advertising expenditure per monthY=per capita disposable incomeP *=price of BJ Corp

a) During the next five years, per capita disposable income is expected to increase by $2,500. What effect will this have on the firm’s sales?


Q = 150 - 5.4P + 0.8A + 2.8Y- 1.2P*

a)During the next five years, per capita disposable income is expected to increase by £2,500. What effect will this have on the firm’s sales?

Solution:For 1 unit increase I Y; Q increases by 2.8 unitFor 2500 units increase in Y; Q increases by 2500 x 2.8 units.Therefore, Increase in sales = 7000 units.


Q = 150 - 5.4P + 0.8A + 2.8Y- 1.2P*

b) What is the relationship between the products of PK and BJ??


Q = 150 - 5.4P + 0.8A + 2.8Y- 1.2P*

b) What is the relationship between the products of PK and BJ??

Solution:For 1 unit increase Price of BJ (P*); Quantity of PK (Q) decreases by 1.2 unitsTherefore Cross price elasticity of Demand is negative (<0)Hence, both companies are producing complementary products.


Q = 150 - 5.4P + 0.8A + 2.8Y- 1.2P*

c) PK intends to charge $15 and spend $10,000 per month on promotion, while it believes per capita income will be $12,000 and BJ’s price will be $3, calculate the income elasticity of demand. Whatdoes this tell you about the nature of PK’s product?


Q = 150 - 5.4P + 0.8A + 2.8Y- 1.2P*

c) PK intends to charge $15 and spend $10,000 per month on promotion, while it believes per capita income will be $12,000 and BJ’s price will be $3, calculate the income elasticity of demand. Whatdoes this tell you about the nature of PK’s product?

Solution:YED = 2.8 x (12000 / 41665.4) = 0.806PK is selling normal goods.


Q = 150 - 5.4P + 0.8A + 2.8Y- 1.2P*

d) What effect would an increase in advertising of $1000 have on profitability, if each additional unit costs $10 to produce?


Q = 150 - 5.4P + 0.8A + 2.8Y- 1.2P*

d) What effect would an increase in advertising of $1000 have on profitability, if each additional unit costs $10 to produce?

Solution:If Increase in A = 1; Increase in Q = 0.8 = 800 units; Increase in R = 800 x 15 = $12,000Increase in Costs = 800 x 10 + advertisement (A)$1000= $9,000Thus every additional $1,000 spent on advertising increases profit by $3,000.

Basic Concepts on Power form Basic Concepts on Power form ElasticityElasticityRecall the basic non-linear (power form) function:Q = Pα

Here, Price Elasticity of Demand = αEg. If, Q = P2

PED = 2Meaning: for 1 % increase in the P, Q decreases by 2%.

Analysis can be extended to a multivariate functions:Q= aPb Ac Yd P0e

Here, P = price of the goodA = Advertisement expenditureY = Income level of the peoplePO = Price of other goods.

Basic Concepts on Power form Basic Concepts on Power form ElasticityElasticityConsider a non-linear demand function:

Q = 9.83P-1.2A2.5Y1.6P01.4

Here, P = price of the good =$60A = Advertisement expenditure = $120,000Y = Income level of the people = $28,000P0 = Price of other goods = $45

Find the equation for the demand curve.

Basic Concepts on Power form Basic Concepts on Power form ElasticityElasticityConsider a non-linear demand function:

Q = 9.83P-1.2A2.5Y1.6P0-1.4

Here, P = price of the good =$60A = Advertisement expenditure = $120,000Y = Income level of the people = $28,000P0 = Price of other goods = $45

Find the equation for the demand curve.Solution:Q = 9.83P-1.2(120000)2.5(28000)1.6(45)-1.4

Q = 3100718641762767839.13P-1.2


Price Elasticity of SupplyPrice Elasticity of Supply

Price elasticity of supply measures how much Qs responds to a change in P.

Price elasticity of supply

=Percentage change in Qs

Percentage change in P

Loosely speaking, it measures the price-sensitivity of sellers’ supply.

Again, use the midpoint method to compute the percentage changes.


Q2

Price Elasticity of SupplyPrice Elasticity of Supply

Price elasticity of supply equals

P

Q

S

P2

Q1

P1

P rises by 8%

Q rises by 16%

16%

8%= 2.0

Price elasticity of supply

=Percentage change in Qs

Percentage change in P

Example:


The Variety of Supply CurvesThe Variety of Supply Curves

Economists classify supply curves according to their elasticity.

The slope of the supply curve is closely related to price elasticity of supply.

Rule of thumb: The flatter the curve, the bigger the elasticity. The steeper the curve, the smaller the elasticity.

The next 5 slides present the different classifications, from least to most elastic.


S

““Perfectly inelastic” Perfectly inelastic” (one extreme)(one extreme)

P

QQ1

P1

P2

Q changes by 0%

0%

10%= 0

Price elasticity

of supply

=% change in Q

% change in P=

P rises by 10%

Sellers’ price sensitivity:

S curve:

Elasticity:

vertical

0

0


S

““Inelastic”Inelastic”

P

QQ1

P1

Q2

P2

Q rises less than 10%

< 10%

10%< 1

Price elasticity

of supply

=% change in Q

% change in P=

P rises by 10%


S curve:

Elasticity:

relatively steep

relatively low

< 1


S

““Unit elastic”Unit elastic”

P

QQ1

P1

Q2

P2

Q rises by 10%

10%

10%= 1

Price elasticity

of supply

=% change in Q

% change in P=

P rises by 10%


S curve:

Elasticity:

intermediate slope

intermediate

= 1


S

““Elastic”Elastic”

P

QQ1

P1

Q2

P2

Q rises more than 10%

> 10%

10%> 1

Price elasticity

of supply

=% change in Q

% change in P=

P rises by 10%


S curve:

Elasticity:

relatively flat

relatively high

> 1


S

““Perfectly elastic”Perfectly elastic” (the other (the other extreme)extreme)

P

Q

P1

Q1

P changes by 0%

Q changes by any %

any %

0%= infinity

Price elasticity

of supply

=% change in Q

% change in P=

Q2

P2 =Sellers’ price sensitivity:

S curve:

Elasticity:

horizontal

extreme

infinity


The Determinants of Supply ElasticityThe Determinants of Supply Elasticity

The more easily sellers can change the quantity they produce, the greater the price elasticity of supply.

Example: Supply of King’s Way property is harder to vary and thus less elastic than supply of new cars.

For many goods, price elasticity of supply is greater in the long run than in the short run, because firms can build new factories, or new firms may be able to enter the market.

AA CC TT II VV E LE L EE AA RR NN II NN G G 33: : Elasticity and changes in equilibriumElasticity and changes in equilibrium

The supply of beachfront property is inelastic. The supply of new cars is elastic.

Suppose population growth causes demand for both goods to double (at each price, Qd doubles).

For which product will P change the most?

For which product will Q change the most?

41

AA CC TT II VV E LE L EE AA RR NN II NN G G 33: : AnswersAnswers

42

Beachfront property (inelastic supply):

P

Q

D1 D2S

Q1

P1 A

B

Q2

P2

When supply is inelastic, an increase in demand has a bigger impact on price than on quantity.

AA CC TT II VV E LE L EE AA RR NN II NN G G 33: : AnswersAnswers

43

New cars(elastic supply):

P

Q

D1 D2

S

Q1

P1

A

Q2

P2

B

When supply is elastic, an increase in demand has a bigger impact on quantity than on price.


S

How the Price Elasticity of Supply Can How the Price Elasticity of Supply Can VaryVary

P

Q

Supply often becomes less elastic as Q rises, due to capacity limits.

Supply often becomes less elastic as Q rises, due to capacity limits.

$15

525

12

500

$3

100

4

200

elasticity > 1

elasticity < 1

Thank youThank you

economic analysis for business session v: elasticity and its application-1i

Documents

function of income

income increases

income level

consumer income

income results

illegal drugs

drug interdiction increase

drugrelated crimechapter