EC611--Managerial Economics

Demand Elasticity

Dr. Savvas C Savvides, European University Cyprus

1

Determinants of Demand for a Product

QX = f (PX, AX ,OX , FX … Yc , Tc , Ec ….

… PY, AY ,OY , FY … G, N, FX, W…)

Strategic vbls.

Competitor vbls.

Consumer vbls.

Environmental vbls.

Uncontrolled Variables

Controlled vbls. Uncontrolled vbls.

2

Linear Demand Function

QX = a0 + a1PX + a2N + a3I + a4PY + a5T

PX

QX

Intercept:a0 + a2N + a3I + a4PY + a5T

Slope:∆QX/∆PX = a1

QX = f(PX, N, I, PY, T)

3

The price elasticity of demand

…measures the sensitivity of the quantitydemanded of a good to a change in its price

It is defined as:

% change in quantity demanded% change in price

4

Price Elasticity of Demand

//P

Q Q Q PEP P P Q

∆ ∆= = ⋅∆ ∆

Linear Function

Point Definition

1PPE aQ

= ⋅

5

Price Elasticity –Example 1

Assume that the demand function for a commodity is:

Q = 245 – 3.5P What is Ep if P = 10?

Recall that

To find Ep we need to find values for P, Q and α1 (or dQ/dP)

1PPE aQ

= ⋅

At P=10, Q = 245 –3.5 (10) = 210

dQ/dP is found by the first derivative of the demand eq.

dQ/dP = -3.5 Substituting in the elasticity eq. we get:

Ep = (dQ/dP) (P/Q) = -3.5 (10/210) = -1/6 = - 0.167

Therefore, if P changes by 10%, Q will fall by 1.67%.

The demand for this product is inelastic

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Price Elasticity–Example 2

Assume the following demand equation:

P = 125 –5Q What is Ep if Q = 10 units?

To find Ep we must first invert the eq. in terms of P:

-5Q = P – 125 5Q =125 –P Q = 25 –0.2P

At Q= 10 10 = 25 –0.2 P 0.2P = 15 P =75P =75

Substituting in the Ep expression we get:

Ep = (dQ/dP) (P/Q) = -0.2 (75/10) = --1.51.5

Therefore, if P changes by 10%, Q will fall by 15%.

The demand for this product is elastic

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Relationship between Demand Curve and Marginal Revenue Curve

AR = P = a – bQ

TR = P * Q = Q (a – bQ ) = aQ – bQ2

MR = dTR / dQ = a –2bQ

slope of demand curve (or AR) = - b

Slope of Marginal Revenue = -2b

The slope of MR is twice the slope of Demand curve

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Marginal Revenue, Total Revenue, and Price Elasticity

TR

QX

1PE <MR<0MR>0

1PE >

1PE = MR=0

TR

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Elasticity and Total RevenueAssume a price reduction

(1) Elastic demand:Increase in revenue (due to more sales, Q) will exceedthe fall in revenue (due to fall in P)

MR is positiveTotal Revenue will rise.

(2) Inelastic demand: Increase in revenue (due to more sales, Q) will be lessthan the fall in revenue (due to fall in P)

MR is negativeTotal Revenue will fall.

(+)TR > (-)TR (+)TR < (-)TR

TR

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Relationship Between Price Elasticity & Revenue

P X Q = TRP X Q = TRP X Q = TRPrice Decrease

P X Q = TRP X Q = TRP X Q = TRPrice Increase

Price Inelastic Demand

Unitary Elastic Demand

Price Elastic Demand

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Marginal Revenue and Price Elasticity of Demand

PX

QX

MRX

1PE >

1PE <

1PE =11P

MR PE

⎛ ⎞= +⎜ ⎟

⎝ ⎠

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Application of Elasticity —Relationship between MR, P and Elasticity

We know that TR =P*Q

MR = dTR/dQ = d(P*Q)/dQ

Using the Product Rule: P (dQ/dQ) + Q (dP/dQ)

Multiplying and dividing through by P, we get:

MR = P [ 1 + Q/P(dP/dQ)]

Recall that Ep = (dQ/dP) (P/Q)

Therefore, the second term in the MR expression above is the inverse of Ep 11

P

M R PE

⎛ ⎞= +⎜ ⎟

⎝ ⎠

If, for example, P=24 and Ep = -2 MR = 4 (1 + 1/-2) = 2

In perfect comp., we know that Ep = ∞ and MR = P

MR = P ( 1 + 1/ ∞ ) = P

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Application of Elasticity — Elasticity and Pricing Policy for Profit Maximization

We know that for profit max. MR must be equal to MC

MC =

Solving for P, we get

P = MC = [1 /(1+1/Ep)]

11P

M R PE

⎛ ⎞= +⎜ ⎟

⎝ ⎠

If, for example, MC = £10 and Ep = -2

Solving for P we get:

P = 10 (1 /(1+1/-2)] = £20

If, on the other hand, Ep = -5,

Then, P = 10 (1 /(1+1/-5)] = £12.5

Therefore, we see that for profit maximization, given MC,

price is inversely related to its price elasticity

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Real World Price & Income Elasticities

2.00.5Housing*

0.60.5Beer*

0.750.25Gasoline*

0.10.2Residential Electricity*

0.10.6Fresh vegetables

0.40.5Tobacco*

1.71.3Alcoholic beverages

0.01.4Fresh meat

* Estimates for Cyprus

1.50.9Durable goods

1.81.0Services

Income ElasticityPrice ElasticityGood

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Elasticity and Air Fares

Holiday travellers can use boats, and cars or trains (for domestic travel). They can also plan their vacation and shop around for discounts and special prices.

so demand may be elastic (greater than one, e.g. - 1.3)and an increase in fares will reduce the number of journeys demanded and total spending

Business travellers do not have good travel optionsdemand may be inelastic (less than one, e.g. - 0.5)so raising fares will have less effect on journeys demandedand revenue will improve

How should air fares be changed to increase revenues?

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Price & Income Elasticities for Airline Travel

2.371.83Excursion fare

1.381.30Regular Economy

1.500.45First Class

Income ElasticityPrice ElasticityType of Ticket

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Determinants of Price Elasticity of Demand

The number of close substitutesthe more the substitutes, the higher EP

How narrowly the product is definedEP (car industry) > EP (small car) > EP (1200 cc)

The time available for adjustments in prices to take place; the more time available to adjust to price changes the more elastic the demand

E long term > E short term

Price elasticity is affected by:

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SR & LR Price Elasticities in US

0.660.30Gasoline

0.560.47Stationery

0.920.31Medical Insurance

1.200.20Bus Transport (local)

1.890.13Electricity (Household)

1.890.46Tobacco Products

3.670.87Motion Picture

3.840.47Radio & TV Repair

LR ElasticitySR ElasticityCommodity

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Income Elasticity of Demand

Linear Function

Point Definition//I

Q Q Q IEI I I Q

∆ ∆= = ⋅

∆ ∆

3IIE aQ

= ⋅

Normal Good Inferior Good0IE > 0IE <

20

Demand Response to 1% Rise in Income

BreadFallsFallsNegativeInferior

FoodFallsRises less than 1%

0< Ep <1-Necessity

BMWRisesRises more than 1%

Above 1-Luxury

RisesPositiveNormal

ExampleBudget Share

Quantity Demanded

Income Elasticity

Good

Income Elasticity of Demand

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Application of Income Elasticity1. Long-range planning of firm’s growth

Over LR, we expect people’s incomes to rise. High income elasticities are good news for luxury good producers in the LR. Over the SR, however, there will more volatility.

Income elasticity for cars was estimated to be 2.5 –3.9. This may explain why car sales fall dramatically during recessions and rebound strongly during recoveries

2. Developing Marketing Strategies

Income elasticity of market segments influences

•the location and nature of distribution outlets

•The extent and focus of advertising

•The choice of promotional activities

Sellers of luxury items direct advertising and promotions to YUBBIE groups whose incomes are expected to rise

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Cross-Price Elasticity of Demand

Linear Function

Point Definition //

X X X YXY

Y Y Y X

Q Q Q PEP P P Q

∆ ∆= = ⋅

∆ ∆

4Y

X YX

PE aQ

= ⋅

Substitutes Complements

0XYE > 0XYE <

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Using Elasticity in Managerial Decision Making

If the demand for the product is inelastic (Ep < 1),the firm would be hesitant to lower prices, since this will lead to lower TRIf the firm has estimated that the cross-price elasticity of its product w.r.t. a competitors product’s price is very high, it will be quick to respond to a competitor’s price reduction so that it does not lose sales and market share.Therefore, the first should first identify the important variables and then try to obtain estimates of the marginal effects of a change in each vbl. on demand.This will be accomplished using regression analysis.

Knowing the elasticity of demand with respect to themajor controlled and uncontrolled variables and forces, thefirm can determine the optimal policies to maximize itsobjective function(s)

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Other Factors Related to Demand Theory

International Convergence of TastesGlobalization of MarketsInfluence of International Preferences on Market Demand

Growth of Electronic CommerceCost of SalesSupply Chains and LogisticsCustomer Relationship Management