economic analysis for business session v: elasticity and its application-1i
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Economic Analysis for Business Session V: Elasticity and its Application-1I. Instructor Sandeep Basnyat 9841892281 [email protected]. 0. APPLICATION: Does Drug Interdiction Increase or Decrease Drug-Related Crime?. - PowerPoint PPT PresentationTRANSCRIPT
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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]
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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.
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CHAPTER 5 ELASTICITY AND ITS APPLICATION
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
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CHAPTER 5 ELASTICITY AND ITS APPLICATION
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
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CHAPTER 5 ELASTICITY AND ITS APPLICATION
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
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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
Y
Q
%
%
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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?
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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?
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
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Numerical Example-Point Income Numerical Example-Point Income ElasticityElasticityb) 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?
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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
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CHAPTER 5 ELASTICITY AND ITS APPLICATION
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.
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CHAPTER 5 ELASTICITY AND ITS APPLICATION
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.
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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
%
%
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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?
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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.
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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?
DONE
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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.
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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?
DONE
DONE
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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.
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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.
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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?
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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*
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.
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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*
b) What is the relationship between the products of PK and BJ??
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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*
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.
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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*
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?
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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*
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.
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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*
d) What effect would an increase in advertising of $1000 have on profitability, if each additional unit costs $10 to produce?
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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*
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.
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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.
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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.
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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
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CHAPTER 5 ELASTICITY AND ITS APPLICATION
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.
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CHAPTER 5 ELASTICITY AND ITS APPLICATION
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:
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CHAPTER 5 ELASTICITY AND ITS APPLICATION
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.
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CHAPTER 5 ELASTICITY AND ITS APPLICATION
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
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CHAPTER 5 ELASTICITY AND ITS APPLICATION
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%
Sellers’ price sensitivity:
S curve:
Elasticity:
relatively steep
relatively low
< 1
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CHAPTER 5 ELASTICITY AND ITS APPLICATION
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%
Sellers’ price sensitivity:
S curve:
Elasticity:
intermediate slope
intermediate
= 1
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CHAPTER 5 ELASTICITY AND ITS APPLICATION
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%
Sellers’ price sensitivity:
S curve:
Elasticity:
relatively flat
relatively high
> 1
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CHAPTER 5 ELASTICITY AND ITS APPLICATION
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
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CHAPTER 5 ELASTICITY AND ITS APPLICATION
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.
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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
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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.
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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.
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CHAPTER 5 ELASTICITY AND ITS APPLICATION
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
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