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Quantitative Demand Analysis

The Elasticity Concept

Elasticity:

a measure of the responsiveness of one variable to changes in another variable; the percentage change in one variable that arises due to a given percentage change in another variable.

Own Price Elasticity Of Demand Own price elasticity:

a measure of the responsiveness of the quantity demanded of a good to a change in the price of that good; the percentage change in quantity demanded divided by the percentage change in the price of the good

EQx, Px = (% Qx) / (% Px)

Own Price Elasticity Of Demand (continued)Qx = f (Px, Py, M, H).EQx, Px = (dQx / dPx) (Px / Qx)

Elastic demand:Absolute (EQx,Px) > 1

Inelastic demand:Absolute (EQx,Px) < 1

Unitary elastic demand:Absolute (EQx,Px) = 1

Elasticity And Total Revenue

Figure 3-1 Page 77.

Factors Affecting The Own Price Elasticity:- Available substitutes,

--the more substitutes available for the good,

the more elastic the demand for it.

--when there few close substitutes for a good,

demand tends to be relatively inelastic.

Example:

Market Own price elasticity

Transportation -0.6

Motor vehicles -1.4

Motorcycles and bicycles -2.3

Food -0.7

Cereal -1.5

Clothing -0.9

Women’s clothing -1.2

Factors Affecting The Own Price Elasticity (continued):- Time,

-- demand trends to be more inelastic in the

short term than in in the long term.

-- the more time consumers have to react to a

price change, the more elastic the demand

for the good.

Example:

Market Short term own price elasticity

Long term own price elasticity

Transportation -0.6 -1.9

Food -0.7 -2.3

Alcohol and tobacco

-0.3 -0.9

Recreation -1.1 -3.5

Clothing -0.9 -2.9

Factors Affecting The Own Price Elasticity (continued):- Expenditure share,

-- goods that comprise a relatively small share

consumer’s budgets tend to be more

inelastic, than goods for which consumers

spend a sizeable portion of their incomes.

Marginal Revenue And The Own Price Elasticity Of Demand Figure 3-3 Page 83.

MR = P {(1 + E)/E}

MR: marginal revenue

P: price

E: demand elasticity

Cross Price Elasticity:

A measure of the responsiveness of the

demand for a good to changes in the price of

related good;

The percentage change in the quantity

demanded of one good divided by the

percentage change in the price of a related

good.

Cross Price Elasticity (continued):EQx, Py = (% Qx) / (% Py)

Qx = f (Px, Py, M, H).

EQx, Py = (dQx / dPy) (Py / Qx)

Example:

Cross price elasticity

Transportation and recreation

-0.05

Food and recreation 0.15

Clothing and food -0.18

Income Elasticity:

A measure of the responsiveness of the

demand for a good to changes in consumer

income;

The percentage change in quantity demanded

divided by the percentage change in income.

Income Elasticity (continued):EQx, M = (% Qx) / (% M)

Qx = f (Px, Py, M, H).

EQx, Py = (dQx / dM) (M / Qx)

Example:

Income elasticity

Transportation 1.80

Food 0.80

Ground beef, nonfed -1.94

Obtaining Elasticities From Demand Functions

Qx = a0 + a1 Px + a2 Py + a3 M + a4 H

Own price elasticity:EQx, Px = a1 (Px / Qx)

Cross price elasticity:EQx, Py = a2 (Py / Qx)

Income elasticity:EQx, M = a3 (M / Qx)

Case:

Qdx = 100 – 3 Px + 4 Py – 0.1 M + 2Ax

the own price elasticity?

the cross price elasticity?

the income elasticity?