Income consumption curve,price consumption curve, engles law

Managerial Economics ©Oxford University Press, 2006

Chapter 3

Comparative Statics and Demand

Meaning of “comparative statics”

• The analysis which enables us to arrive at new

optimal decisions when underlying assumptions

change

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

Changes in equilibrium

• Joining all these points of tangency gives the Price Consumption Curve. (PCC)

Price of X is falling.

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.

Demand Curve

• Every point on the PCC gives the price of X and quantity demanded/consumed of X

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

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

Changes in equilibrium

• Joining all these points of tangency gives the Income Consumption Curve (ICC)

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

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

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

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

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

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

Elasticity

• Income Elasticity

∆Qx/∆I * I/Qx

• Could be negative or positive:

Negative for Inferior goods

Positive for Superior goods

Elasticity

• Cross Price Elasticity:

∆Qx/∆Py * Py/Qx

• Could be negative or positive

- Negative for complements

- Positive for substitutes

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 + P2

Therefore ∆Q/ ∆P = 5+ 2P and average function, or Q/P = (30 -5P + P2)/ P

• 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…

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 , the resulting demand schedule at

different prices can be as follows:

Demand schedule

Price Rs. Quantity demanded

4 112.5

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

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

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

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, Since the 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

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%

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,

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

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

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

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.

Distinctive types of elasticity….

• 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

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.

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

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.

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

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

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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