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Managerial Economics ©Oxford
University Press, 2006
All rights reserved
Chapter 3
Comparative Statics and Demand
Managerial Economics ©Oxford
University Press, 2006
All rights reserved
Meaning of “comparative statics”
• The analysis which enables us to arrive at new
optimal decisions when underlying assumptions
change
Managerial Economics ©Oxford
University Press, 2006
All rights reserved
Changes in equilibrium when prices
change
• Relative price changes get reflected in changes in
slope of the budget line.
• New point of tangency between the indifference
curve and the new budget line
Managerial Economics ©Oxford
University Press, 2006
All rights reserved
Changes in equilibrium
• Joining all these points of tangency gives the
Price Consumption Curve. (PCC)
X
Y
PCC
Price of X is falling.
Managerial Economics ©Oxford
University Press, 2006
All rights reserved
Derivation of the demand curve
• Data contained in the PCC:
- Optimal level of consumption of X
- Optimal level of consumption of Y
- Prices of X and Y
• Demand curve for X requires –
- Price of X.
- Quantity consumed of X.
Managerial Economics ©Oxford
University Press, 2006
All rights reserved
Demand Curve
• Every point on the PCC gives the price of X and
quantity demanded/consumed of X
Thus,
Qx
Px
Managerial Economics ©Oxford
University Press, 2006
All rights reserved
Shifts in and movements along a
Demand Curve
• Effect on demand of changes in its own price
results in movement along the demand curve.
• Effect on demand of changes in other factors
results in shifts in demand curve
Managerial Economics ©Oxford
University Press, 2006
All rights reserved
Changes in equilibrium when
income changes
• Income changes show up as parallel shifts of the
budget line
• New points of tangency between indifference
curves and the new budget lines
Managerial Economics ©Oxford
University Press, 2006
All rights reserved
Changes in equilibrium
• Joining all these points of tangency gives
the Income Consumption Curve (ICC)
X
Y
ICC
Managerial Economics ©Oxford
University Press, 2006
All rights reserved
Slope of the ICC
• If the goods are ‘Superior’, the ICC is
upward sloping
• If one of the goods is ‘Inferior’, the ICC
is downward sloping
Managerial Economics ©Oxford
University Press, 2006
All rights reserved
Slope of the PCC
• If the goods are normal, PCC is upward
sloping
• If PCC is downward sloping, then one of them
is a Giffen Good
Managerial Economics ©Oxford
University Press, 2006
All rights reserved
Giffen good
Income effect
• Price effect +
Substitution effect
• Substitution effect is inversely related to price.
• Income effect can be inversely related to
changes in income – Inferior Good
• Income effect can be positively related to
income-Superior good
Managerial Economics ©Oxford
University Press, 2006
All rights reserved
Giffen Good
• If income effect is inverse and large enough to
offset the substitution effect, then it is a Giffen
Good
• The Demand curve for Giffen Good will have a
positive slope
Managerial Economics ©Oxford
University Press, 2006
All rights reserved
Elasticity
• Price Elasticity: Proportionate change in
quantity demanded due to a
proportionate change in price
- ∆Qx/ ∆Px * Px/Qx
- negative for normal goods
- negative sign is ignored while making
comparisons among normal goods
Managerial Economics ©Oxford
University Press, 2006
All rights reserved
Elasticity
• Pe Greater than1 (ignoring – sign): Elastic
• Pe Equal to 1 (ignoring – sign) : Unit Elastic
• Pe Less than 1 ( ignoring – sign): Inelastic
• Price Elasticity and Expenditure:
- Pe less than 1 a fall in price lower exp
- Pe equal to 1 a fall in price exp constant
- Pe greater than 1 a fall in price higher exp
Managerial Economics ©Oxford
University Press, 2006
All rights reserved
Elasticity
• Income Elasticity
∆Qx/∆I * I/Qx
• Could be negative or positive:
Negative for Inferior goods
Positive for Superior goods
Managerial Economics ©Oxford
University Press, 2006
All rights reserved
Elasticity
• Cross Price Elasticity:
∆Qx/∆Py * Py/Qx
• Could be negative or positive
- Negative for complements
- Positive for substitutes
Managerial Economics ©Oxford
University Press, 2006
All rights reserved
Point and arc elasticity
• Point Elasticity: when price is very small
• Arc Elasticity: when price change is large
• Price Elasticity measurements:
• i) Proportionate method: ∆Q/ ∆P x P/Q
Examples: if demand function is Q =30 -5P + P2or
Therefore ∆Q/ ∆P = 5+ 2P and average function, or
Q/P = (30 -5P + P2)
/ P
Managerial Economics ©Oxford
University Press, 2006
All rights reserved
• Now ed = ∆Q/ ∆P x P/Q, so it equals
• Marginal function/average function, or
• Ed= (-5 +2P) x P/( 30 -5P + P2)
• If P = Rs. 5, ed = (-5 + 10) x 5/( 30 – 10 +
25) = 50/45 = 1.1,
• Find ed when P = Rs.3/2, Rs 10…
Managerial Economics ©Oxford
University Press, 2006
All rights reserved
Hyperbolic demand functions
• Q = ap-n
or Q = a/Pn
where a and n are
constants,
• Suppose a = 1800 and n = 2, demand funct
• Q = 1800/P2
= 1800x p-2,theresultingdemandscheduleatdifferentpricescanbeas
follows:
Managerial Economics ©Oxford
University Press, 2006
All rights reserved
Demand schedule
Price Rs. Quantity demanded
6 50
5 72
4 112.5
3 200
2 450
Managerial Economics ©Oxford
University Press, 2006
All rights reserved
Elasticity ….
• The interesting feature of this type of
demand function is that price elasticity of
demand is constant and is equal to to the
exponent of P.
• Let P = 3, ed = P/Q> dQ/dP = 3/200X –
3600/27 = -2,
• Let P = 2, ed = 2/450X -3600/8 = -2
Managerial Economics ©Oxford
University Press, 2006
All rights reserved
Elasticity…
• If Q = 20/(P + 1), find elasticity with
respect to price.
• Now dQ/dP = -20( P +1)-2,
• Ed
= P/Q. dQ/dP = P/Q X -20P/ Q( P + 1)2
• = -20P/20/(P + 1)( P + 1)2
= -P/( P + 1)
• If, P = 5, ed = -5/6 = .833
Managerial Economics ©Oxford
University Press, 2006
All rights reserved
Income elasticity…
• Q. If income increases from Rs. 80,000 to
Rs. 81000, the quantity demanded of good
Q1 increases from 3000 to 3050, find
income elasticity of demand.
• Given a small change in income, we use
point elasticity method, therefore
• Ed (income) = I/Q1XdQ1/dI=
(80000/3000) X 50/1000 = 1.33
Managerial Economics ©Oxford
University Press, 2006
All rights reserved
Cross price elasticity of demand
• The price of desktop computers declines from
Rs.50,000 to rs.25,000, sale of printers goes up
from 50 to 150 per month:
• Ed (cross price) = dQx/dPy x Py/Qx, Sincethe the change is
large, we use arc elasticity measure, so Qx= (50 +
150)/2 = 100,
• Py = (50000 + 25000)/2 = 37500, dQx= 100, and
dPy = 25000, Ed = 100/25000(37500/100) = - 1.5
Managerial Economics ©Oxford
University Press, 2006
All rights reserved
Elasticity…
• If price elasticity of petrol is 0.5, how much
of price increase would be required to
reduce consumption by 10%?
• Ed = (dQ/Q)/ dP/P= 0.5
Now dQ/Q = 10% = 0.1, so dP/P = .1/.5= .2
or 20%
Managerial Economics ©Oxford
University Press, 2006
All rights reserved
Elasticity of demand…
• Elasticity of demand can also be expressed
as: ed = Marginal quantity demanded
divided by Average quantity demanded=
∆Q/ ∆P divided by Q/P,
Managerial Economics ©Oxford
University Press, 2006
All rights reserved
Determinants of price elasticity
• Availability of substitutes: Cases of close
substitutes like cold drinks and no substitutes like
salt
• Number of uses for a commodity: greater uses
leads to greater elasticity like for electricity, when
restricted uses like for wheat demand is relatively
inelastic
• Relative importance of a commodity in total
expenditure of a consumer: Salt/ match box cases
vs cloth/ readymade garments. Consider the
impact of doubling of their prices on total demand
of consumer
Managerial Economics ©Oxford
University Press, 2006
All rights reserved
Determinants of elasticity continued
• Nature of the need being satisfied by a
commodity, like necessities, comforts, luxuries
• Time allowed for adjustment to price change, the
longer the time period
greater the elasticity and vice versa
* Habits tend to make demand inelastic
* Joint demand like for machine oil and machines
makes demand relatively inelastic
Managerial Economics ©Oxford
University Press, 2006
All rights reserved
Determinants of elasticity continued
• Nature of the need being satisfied by a
commodity, like necessities, comforts, luxuries
• Time allowed for adjustment to price change, the
longer the time period
greater the elasticity and vice versa
* Habits tend to make demand inelastic
* Joint demand like for machine oil and machines
makes demand relatively inelastic
Managerial Economics ©Oxford
University Press, 2006
All rights reserved
Distinctive types of elasticity
• Industry elasticity:
Refers to the change in total industry sales
with a change in the general level of prices
for the industry as a whole. The industry
demand has elasticity with respect to
competition from other industries.
Managerial Economics ©Oxford
University Press, 2006
All rights reserved
Distinctive types of ela
• Market share elasticity:
Relates the change in company’s share of
industry-wide sales to the price differential
between the company’s price and industry-
wise price level.
Expectations elasticity:
Refers to responsiveness of sales to buyer’s
Managerial Economics ©Oxford
University Press, 2006
All rights reserved
Distinctive types….
guesses about the values of demand determinants, such as
the future price of a commodity or of its substitutes, future
incomes of buyers, prospects of easy availability or
otherwise in the future, or future promotional outlays.
• Interest rate elasticity and demand for consumers
durables:
In USA elasticity of interest rates to housing demand is
estimates at .15 which means a ten per cent increase in
interest rates would result in 1.5% change in housing
demand.
Managerial Economics ©Oxford
University Press, 2006
All rights reserved
Engle’s Law of Consumption
• Dr. Engle was a German statistician.
• He made a study of family budgets around the
middle of the nineteenth century
• He arrived at the following major conclusions:
• i) As income increases the percentage expenditure
on food decreases and vice versa
• ii) The percentage expenditure on clothing, etc.
remains more or less constant at all levels of
income
Managerial Economics ©Oxford
University Press, 2006
All rights reserved
Engle’s …
iii) The percentage expenditure on fuel, light,
rent, etc. also remains practically the same
at all levels of income.
iv) However, the percentage expenditure on
what may be called comforts and luxuries
of life increases with increase in income
and vice versa.
Managerial Economics ©Oxford
University Press, 2006
All rights reserved
Propensity to consume and save
concepts
• These are macro-economic concepts.
• The propensity to consume refers to the
proportion of income consumed
• Average propensity to consume refers to economy
as a whole, say like C/I
• Marginal propensity to consume refers to the
proportion of change in consumption to
proportion of change in income, say, ∆C/ ∆I
income to
Managerial Economics ©Oxford
University Press, 2006
All rights reserved
Propensity to save and consume..
• The propensity to save is reverse of
propensity to consume.
• The concepts, especially marginal
propensity to consume and save, exercise
considerable influence on the growth
performance of an economy
Managerial Economics ©Oxford
University Press, 2006
All rights reserved
Propensity continued
• A higher marginal propensity to consume
leads to faster economic growth through its
multiplier effects, unless there exist
bottlenecks on the supply side like in the
developing world
• The propensity to consume declines as
incomes keep on increasing

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Income consumption curve,price consumption curve, engles law

  • 1. Managerial Economics ©Oxford University Press, 2006 All rights reserved Chapter 3 Comparative Statics and Demand
  • 2. Managerial Economics ©Oxford University Press, 2006 All rights reserved Meaning of “comparative statics” • The analysis which enables us to arrive at new optimal decisions when underlying assumptions change
  • 3. Managerial Economics ©Oxford University Press, 2006 All rights reserved Changes in equilibrium when prices change • Relative price changes get reflected in changes in slope of the budget line. • New point of tangency between the indifference curve and the new budget line
  • 4. Managerial Economics ©Oxford University Press, 2006 All rights reserved Changes in equilibrium • Joining all these points of tangency gives the Price Consumption Curve. (PCC) X Y PCC Price of X is falling.
  • 5. Managerial Economics ©Oxford University Press, 2006 All rights reserved Derivation of the demand curve • Data contained in the PCC: - Optimal level of consumption of X - Optimal level of consumption of Y - Prices of X and Y • Demand curve for X requires – - Price of X. - Quantity consumed of X.
  • 6. Managerial Economics ©Oxford University Press, 2006 All rights reserved Demand Curve • Every point on the PCC gives the price of X and quantity demanded/consumed of X Thus, Qx Px
  • 7. Managerial Economics ©Oxford University Press, 2006 All rights reserved Shifts in and movements along a Demand Curve • Effect on demand of changes in its own price results in movement along the demand curve. • Effect on demand of changes in other factors results in shifts in demand curve
  • 8. Managerial Economics ©Oxford University Press, 2006 All rights reserved Changes in equilibrium when income changes • Income changes show up as parallel shifts of the budget line • New points of tangency between indifference curves and the new budget lines
  • 9. Managerial Economics ©Oxford University Press, 2006 All rights reserved Changes in equilibrium • Joining all these points of tangency gives the Income Consumption Curve (ICC) X Y ICC
  • 10. Managerial Economics ©Oxford University Press, 2006 All rights reserved Slope of the ICC • If the goods are ‘Superior’, the ICC is upward sloping • If one of the goods is ‘Inferior’, the ICC is downward sloping
  • 11. Managerial Economics ©Oxford University Press, 2006 All rights reserved Slope of the PCC • If the goods are normal, PCC is upward sloping • If PCC is downward sloping, then one of them is a Giffen Good
  • 12. Managerial Economics ©Oxford University Press, 2006 All rights reserved Giffen good Income effect • Price effect + Substitution effect • Substitution effect is inversely related to price. • Income effect can be inversely related to changes in income – Inferior Good • Income effect can be positively related to income-Superior good
  • 13. Managerial Economics ©Oxford University Press, 2006 All rights reserved Giffen Good • If income effect is inverse and large enough to offset the substitution effect, then it is a Giffen Good • The Demand curve for Giffen Good will have a positive slope
  • 14. Managerial Economics ©Oxford University Press, 2006 All rights reserved Elasticity • Price Elasticity: Proportionate change in quantity demanded due to a proportionate change in price - ∆Qx/ ∆Px * Px/Qx - negative for normal goods - negative sign is ignored while making comparisons among normal goods
  • 15. Managerial Economics ©Oxford University Press, 2006 All rights reserved Elasticity • Pe Greater than1 (ignoring – sign): Elastic • Pe Equal to 1 (ignoring – sign) : Unit Elastic • Pe Less than 1 ( ignoring – sign): Inelastic • Price Elasticity and Expenditure: - Pe less than 1 a fall in price lower exp - Pe equal to 1 a fall in price exp constant - Pe greater than 1 a fall in price higher exp
  • 16. Managerial Economics ©Oxford University Press, 2006 All rights reserved Elasticity • Income Elasticity ∆Qx/∆I * I/Qx • Could be negative or positive: Negative for Inferior goods Positive for Superior goods
  • 17. Managerial Economics ©Oxford University Press, 2006 All rights reserved Elasticity • Cross Price Elasticity: ∆Qx/∆Py * Py/Qx • Could be negative or positive - Negative for complements - Positive for substitutes
  • 18. Managerial Economics ©Oxford University Press, 2006 All rights reserved Point and arc elasticity • Point Elasticity: when price is very small • Arc Elasticity: when price change is large • Price Elasticity measurements: • i) Proportionate method: ∆Q/ ∆P x P/Q Examples: if demand function is Q =30 -5P + P2or Therefore ∆Q/ ∆P = 5+ 2P and average function, or Q/P = (30 -5P + P2) / P
  • 19. Managerial Economics ©Oxford University Press, 2006 All rights reserved • Now ed = ∆Q/ ∆P x P/Q, so it equals • Marginal function/average function, or • Ed= (-5 +2P) x P/( 30 -5P + P2) • If P = Rs. 5, ed = (-5 + 10) x 5/( 30 – 10 + 25) = 50/45 = 1.1, • Find ed when P = Rs.3/2, Rs 10…
  • 20. Managerial Economics ©Oxford University Press, 2006 All rights reserved Hyperbolic demand functions • Q = ap-n or Q = a/Pn where a and n are constants, • Suppose a = 1800 and n = 2, demand funct • Q = 1800/P2 = 1800x p-2,theresultingdemandscheduleatdifferentpricescanbeas follows:
  • 21. Managerial Economics ©Oxford University Press, 2006 All rights reserved Demand schedule Price Rs. Quantity demanded 6 50 5 72 4 112.5 3 200 2 450
  • 22. Managerial Economics ©Oxford University Press, 2006 All rights reserved Elasticity …. • The interesting feature of this type of demand function is that price elasticity of demand is constant and is equal to to the exponent of P. • Let P = 3, ed = P/Q> dQ/dP = 3/200X – 3600/27 = -2, • Let P = 2, ed = 2/450X -3600/8 = -2
  • 23. Managerial Economics ©Oxford University Press, 2006 All rights reserved Elasticity… • If Q = 20/(P + 1), find elasticity with respect to price. • Now dQ/dP = -20( P +1)-2, • Ed = P/Q. dQ/dP = P/Q X -20P/ Q( P + 1)2 • = -20P/20/(P + 1)( P + 1)2 = -P/( P + 1) • If, P = 5, ed = -5/6 = .833
  • 24. Managerial Economics ©Oxford University Press, 2006 All rights reserved Income elasticity… • Q. If income increases from Rs. 80,000 to Rs. 81000, the quantity demanded of good Q1 increases from 3000 to 3050, find income elasticity of demand. • Given a small change in income, we use point elasticity method, therefore • Ed (income) = I/Q1XdQ1/dI= (80000/3000) X 50/1000 = 1.33
  • 25. Managerial Economics ©Oxford University Press, 2006 All rights reserved Cross price elasticity of demand • The price of desktop computers declines from Rs.50,000 to rs.25,000, sale of printers goes up from 50 to 150 per month: • Ed (cross price) = dQx/dPy x Py/Qx, Sincethe the change is large, we use arc elasticity measure, so Qx= (50 + 150)/2 = 100, • Py = (50000 + 25000)/2 = 37500, dQx= 100, and dPy = 25000, Ed = 100/25000(37500/100) = - 1.5
  • 26. Managerial Economics ©Oxford University Press, 2006 All rights reserved Elasticity… • If price elasticity of petrol is 0.5, how much of price increase would be required to reduce consumption by 10%? • Ed = (dQ/Q)/ dP/P= 0.5 Now dQ/Q = 10% = 0.1, so dP/P = .1/.5= .2 or 20%
  • 27. Managerial Economics ©Oxford University Press, 2006 All rights reserved Elasticity of demand… • Elasticity of demand can also be expressed as: ed = Marginal quantity demanded divided by Average quantity demanded= ∆Q/ ∆P divided by Q/P,
  • 28. Managerial Economics ©Oxford University Press, 2006 All rights reserved Determinants of price elasticity • Availability of substitutes: Cases of close substitutes like cold drinks and no substitutes like salt • Number of uses for a commodity: greater uses leads to greater elasticity like for electricity, when restricted uses like for wheat demand is relatively inelastic • Relative importance of a commodity in total expenditure of a consumer: Salt/ match box cases vs cloth/ readymade garments. Consider the impact of doubling of their prices on total demand of consumer
  • 29. Managerial Economics ©Oxford University Press, 2006 All rights reserved Determinants of elasticity continued • Nature of the need being satisfied by a commodity, like necessities, comforts, luxuries • Time allowed for adjustment to price change, the longer the time period greater the elasticity and vice versa * Habits tend to make demand inelastic * Joint demand like for machine oil and machines makes demand relatively inelastic
  • 30. Managerial Economics ©Oxford University Press, 2006 All rights reserved Determinants of elasticity continued • Nature of the need being satisfied by a commodity, like necessities, comforts, luxuries • Time allowed for adjustment to price change, the longer the time period greater the elasticity and vice versa * Habits tend to make demand inelastic * Joint demand like for machine oil and machines makes demand relatively inelastic
  • 31. Managerial Economics ©Oxford University Press, 2006 All rights reserved Distinctive types of elasticity • Industry elasticity: Refers to the change in total industry sales with a change in the general level of prices for the industry as a whole. The industry demand has elasticity with respect to competition from other industries.
  • 32. Managerial Economics ©Oxford University Press, 2006 All rights reserved Distinctive types of ela • Market share elasticity: Relates the change in company’s share of industry-wide sales to the price differential between the company’s price and industry- wise price level. Expectations elasticity: Refers to responsiveness of sales to buyer’s
  • 33. Managerial Economics ©Oxford University Press, 2006 All rights reserved Distinctive types…. guesses about the values of demand determinants, such as the future price of a commodity or of its substitutes, future incomes of buyers, prospects of easy availability or otherwise in the future, or future promotional outlays. • Interest rate elasticity and demand for consumers durables: In USA elasticity of interest rates to housing demand is estimates at .15 which means a ten per cent increase in interest rates would result in 1.5% change in housing demand.
  • 34. Managerial Economics ©Oxford University Press, 2006 All rights reserved Engle’s Law of Consumption • Dr. Engle was a German statistician. • He made a study of family budgets around the middle of the nineteenth century • He arrived at the following major conclusions: • i) As income increases the percentage expenditure on food decreases and vice versa • ii) The percentage expenditure on clothing, etc. remains more or less constant at all levels of income
  • 35. Managerial Economics ©Oxford University Press, 2006 All rights reserved Engle’s … iii) The percentage expenditure on fuel, light, rent, etc. also remains practically the same at all levels of income. iv) However, the percentage expenditure on what may be called comforts and luxuries of life increases with increase in income and vice versa.
  • 36. Managerial Economics ©Oxford University Press, 2006 All rights reserved Propensity to consume and save concepts • These are macro-economic concepts. • The propensity to consume refers to the proportion of income consumed • Average propensity to consume refers to economy as a whole, say like C/I • Marginal propensity to consume refers to the proportion of change in consumption to proportion of change in income, say, ∆C/ ∆I income to
  • 37. Managerial Economics ©Oxford University Press, 2006 All rights reserved Propensity to save and consume.. • The propensity to save is reverse of propensity to consume. • The concepts, especially marginal propensity to consume and save, exercise considerable influence on the growth performance of an economy
  • 38. Managerial Economics ©Oxford University Press, 2006 All rights reserved Propensity continued • A higher marginal propensity to consume leads to faster economic growth through its multiplier effects, unless there exist bottlenecks on the supply side like in the developing world • The propensity to consume declines as incomes keep on increasing

Editor's Notes

  1. ICC