Economic Analysis for Business Session V: Elasticity and its Application-1I

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Economic Analysis for BusinessSession V
Elasticity and its Application-1I
InstructorSandeep Basnyat 9841892281 Sandeep_basn
yat_at_yahoo.com
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APPLICATION Does Drug Interdiction Increase or
Decrease Drug-Related Crime?
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• 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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Policy 1 Interdiction
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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
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Policy 2 Education
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Education reduces the demand for drugs.
P and Q fall.
ResultA decrease in total spending on drugs,
and in drug-related crime.
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Income Elasticity of Demand

• The income elasticity of demand measures the
  response of Qd to a change in consumer income.

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Calculating Income Elasticity of Demand

• Arc 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 x -3/1 -3.

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Numerical Example

• a) 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 Example

• a) 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 Elasticity

• 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?

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Numerical 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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Necessities, Inferior goods and luxuries

• Elasticity measurement as
• E lt 0 Inferior goods (negative)
• 0 lt E 1 Normal goods or necessities
• E gt 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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Cross Price Elasticity of Demand

• The cross-price elasticity of demand measures the
  response of demand for one good to changes in the
  price of another good.

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

• 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.

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Numerical Example

• Demand for a publishers book is given as
• Qx 12,000 5,000Px 5I 500Pc
• Px Price of the book 5
• I Income per capita 10,000
• Pc Price of the books from competing publishers
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• Find Price elasticity of demand for the book.
  What effect a price increase would have on total
  revenues?
• Find income elasticity of demand for the book.
  Find if the book is inferior good, normal good or
  luxury.
• 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 Example

• 1) 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 Example

• Demand for a publishers book is given as
• Qx 12,000 5,000Px 5I 500Pc
• Px Price of the book 5
• I Income per capita 10,000
• Pc Price of the books from competing publishers
  6
• Find Price elasticity of demand for the book.
  What effect a price increase would have on total
  revenues?
• Find income elasticity of demand for the book.
  Find if the book is inferior good, normal good or
  luxury.
• 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 Example

• 2) 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 gt 1 for the book, the book is
  luxury.

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Numerical Example

• Demand for a publishers book is given as
• Qx 12,000 5,000Px 5I 500Pc
• Px Price of the book 5
• I Income per capita 10,000
• Pc Price of the books from competing publishers
  6
• Find Price elasticity of demand for the book.
  What effect a price increase would have on total
  revenues?
• Find income elasticity of demand for the book.
  Find if the book is inferior good, normal good or
  luxury.
• 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 Example

• 3) 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 competitors book price will
  increase the demand for the book by 0.075
• b) Since, the E C gt 0 for the book, the book is
  substitute to competing producers book.

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Basic Concept on Marginal Effects
Consider a simple linear equation for a demand
curve Q 180 -2p .(i) When p 5
Q 180 - 2 x 5 170 P 6 Q 168 P 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 -
0.5Q Q is the marginal effect of quantity on
price.
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Numerical Applications of Marginal Effects
PK Corp estimates that its demand function is as
follows Q 150 - 5.4P 0.8A 2.8Y-
1.2P Where Q quantity demanded per
month Pprice of the product Afirms advertising
expenditure per month Yper capita disposable
income P 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 firms sales?
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Numerical Applications of Marginal Effects

• PK Corp estimates that its demand function is as
  follows
• Q 150 - 5.4P 0.8A 2.8Y- 1.2P
• During the next five years, per capita disposable
  income is expected to increase by 2,500. What
  effect will this have on the firms sales?
• Solution
• For 1 unit increase I Y Q increases by 2.8 unit
• For 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 Effects
PK 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 Effects
PK 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
units Therefore Cross price elasticity of Demand
is negative (lt0) Hence, both companies are
producing complementary products.
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Numerical Applications of Marginal Effects
PK 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 BJs price will be 3,
calculate the income elasticity of demand.
What does this tell you about the nature of PKs
product?
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Numerical Applications of Marginal Effects
PK 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 BJs price will be 3,
calculate the income elasticity of demand.
What does this tell you about the nature of PKs
product? Solution YED 2.8 x (12000 / 41665.4)
0.806 PK is selling normal goods.
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Numerical Applications of Marginal Effects
PK 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 Effects
PK 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 12,000 Increase in
Costs 800 x 10 advertisement (A)1000
9,000 Thus every additional 1,000 spent on
advertising increases profit by 3,000.
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Basic Concepts on Power form Elasticity
Recall the basic non-linear (power form)
function Q Pa Here, Price Elasticity of Demand
a Eg. If, Q P2 PED 2 Meaning 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 good A
Advertisement expenditure Y Income level of
the people PO Price of other goods.
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Basic Concepts on Power form Elasticity
Consider a non-linear demand function Q
9.83P-1.2A2.5Y1.6P01.4 Here, P price of the
good 60 A Advertisement expenditure
120,000 Y Income level of the people
28,000 P0 Price of other goods 45 Find
the equation for the demand curve.
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Basic Concepts on Power form Elasticity
Consider a non-linear demand function Q
9.83P-1.2A2.5Y1.6P0-1.4 Here, P price of the
good 60 A Advertisement expenditure
120,000 Y Income level of the people
28,000 P0 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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Price Elasticity of Supply
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• Price elasticity of supply measures how much Qs
  responds to a 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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Price Elasticity of Supply
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Example
P rises by 8

• Price elasticity of supply equals

Q rises by 16
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The Variety of Supply Curves
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• 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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Perfectly inelastic (one extreme)
0
0
0
10
S curve
vertical
Sellers price sensitivity
P1
0
P rises by 10
Elasticity
Q1
0
Q changes by 0
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Inelastic
0
lt 10
lt 1
10
S curve
relatively steep
Sellers price sensitivity
P1
relatively low
P rises by 10
Elasticity
Q1
lt 1
Q rises less than 10
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Unit elastic
0
10
1
10
S curve
intermediate slope
Sellers price sensitivity
P1
intermediate
P rises by 10
Elasticity
Q1
1
Q rises by 10
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Elastic
0
gt 10
gt 1
10
S curve
relatively flat
Sellers price sensitivity
P1
relatively high
P rises by 10
Elasticity
Q1
gt 1
Q rises more than 10
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Perfectly elastic (the other extreme)
0
any
infinity
0
S curve
horizontal
P1
P2
Sellers price sensitivity
extreme
P changes by 0
Elasticity
infinity
Q changes by any
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The Determinants of Supply Elasticity

• The more easily sellers can change the quantity
  they produce, the greater the price elasticity of
  supply.
• Example Supply of Kings 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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A C T I V E L E A R N I N G 3 Elasticity
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?

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A C T I V E L E A R N I N G 3 Answers

• Beachfront property (inelastic supply)

When supply is inelastic, an increase in demand
has a bigger impact on price than on quantity.
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A C T I V E L E A R N I N G 3 Answers

• New cars(elastic supply)

When supply is elastic, an increase in demand
has a bigger impact on quantity than on price.
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How the Price Elasticity of Supply Can Vary
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• Supply often becomes less elastic as Q rises,
  due to capacity limits.

elasticity lt 1
elasticity gt 1
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Thank you