Income consumption curve,price consumption curve, engles law

Managerial Economics ©Oxford
University Press, 2006
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Chapter 3
Comparative Statics and Demand

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Meaning of “comparative statics”
• The analysis which enables us to arrive at new
optimal decisions when underlying assumptions
change

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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

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Changes in equilibrium
• Joining all these points of tangency gives the
Price Consumption Curve. (PCC)
X
Y
PCC
Price of X is falling.

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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.

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Demand Curve
• Every point on the PCC gives the price of X and
quantity demanded/consumed of X
Thus,
Qx
Px

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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

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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

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Changes in equilibrium
• Joining all these points of tangency gives
the Income Consumption Curve (ICC)
X
Y
ICC

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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

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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

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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

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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

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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

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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

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Elasticity
• Income Elasticity
∆Qx/∆I * I/Qx
• Could be negative or positive:
Negative for Inferior goods
Positive for Superior goods

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Elasticity
• Cross Price Elasticity:
∆Qx/∆Py * Py/Qx
• Could be negative or positive
- Negative for complements
- Positive for substitutes

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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

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• 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…

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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:

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Demand schedule
Price Rs. Quantity demanded
6 50
5 72
4 112.5
3 200
2 450

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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

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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

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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

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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

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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%

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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

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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

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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.

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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

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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.

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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

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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.

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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

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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

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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

Income consumption curve,price consumption curve, engles law

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