# econ 503 chp3

Pages: 22 (2261 words) Published: September 27, 2014
ECON 503: Chapter 3
Quantitative Demand Analysis
Dr. Fida Karam
Gulf University for Science and Technology
Department of Economics and Finance
Oﬃce N1-115
email: karam.f@gust.edu.kw

Dr. Fida Karam

(GUST)

Quantitative Demand Analysis

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Introduction
The shapes of demand and supply curves inﬂuence how much shifts in demand or supply aﬀect market equilibrium.
• Shape is best summarized by elasticity.
• Elasticity indicates how responsive one variable is to a change in another variable:
Elasticity of A with respect to B = % A/% B

Common Elasticities
Price elasticity of demand.
Income elasticity of demand.
Cross-price elasticity of demand.
Price elasticity of supply.

Dr. Fida Karam

(GUST)

Quantitative Demand Analysis

2 / 19

Price Elasticity of Demand
Deﬁnition
The price elasticity of demand measures the sensitivity of the quantity demanded to price. The price elasticity of demand (denoted by D ) is the percentage change in quantity demanded (Q) brought about by a 1 percent change in price (P ), holding the other determinants of demand constant. D

=

percentage change in quantity
percentage change in price

If Q is the change in quantity and P is the change in price, then Q
percentage change in quantity = Q × 100%
and
percentage change in price = PP × 100%. Hence,
D

Dr. Fida Karam

(GUST)

=

Q P
×
P
Q

Quantitative Demand Analysis

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Price Elasticity of Demand
Interpretation
if

D

= 0, we say that the we have a perfectly inelastic demand

if −1 <
if
if

D
D

D

< 0;, we say that we have an inelastic demand

= −1, we say that the we have a unitary elastic demand
= −∞, we say that the we have a perfectly elastic demand

if −∞ <

D

< −1 we say that the we have an elastic demand

Example
Suppose the price is initially \$5.00, and the corresponding quantity demanded is 1,000 units. Also suppose, that when the price rises to \$5.75, the quantity demanded falls to 800 units. What the is the price elasticity of demand over this region of the demand curve? Is demand elastic or inelastic? Solution

D = −1.33. Thus, over the range of price between \$5.00 and \$5.75, the quantity demanded falls at a rate of 1.33 percent for every 1 percent increase in price. Demand is elastic over this price range.

Dr. Fida Karam

(GUST)

Quantitative Demand Analysis

4 / 19

Price Elasticity of Demand
In the previous example, calculate the price elasticity of demand for a price decrease from \$5.75 to \$5. D = −1.92!
• Our calculation of the percentage change is sensitive to the choice of the base year.
• A more precise way of calculating percentages is to use the average price and the average quantity for the base year (midpoint formula).
Arc Price Elasticity of Demand (Midpoint Formula)
Q2 −Q1
percentage change in quantity = (Q2 +Q1 )/2 × 100%
and
2 −P1
percentage change in price = (PP+P1 )/2 × 100%. Hence,
2

D

=

Q2 − Q1
(P2 + P1 )/2
×
P2 − P1
(Q2 + Q1 )/2

The preceding formula calculates elasticity over a discrete range of the demand curve. Because elasticity is diﬀerent at each price point, arc elasticity is a measure of the average elasticity over that range.

Dr. Fida Karam

(GUST)

Quantitative Demand Analysis

5 / 19

Price Elasticity of Demand

Example
Suppose price is initially \$18, and the corresponding quantity demanded is 18,000 units. Also suppose, that when the price rises to \$19, the quantity demanded falls to 14,000 units. What is the arc price elasticity of demand over this region of the demand curve? Is demand elastic or inelastic? Solution

D = −4.625. Thus, over the range of price between \$18 and \$19, the quantity demanded falls at a rate of 4.625 percent for every 1 percent increase in price. The demand is elastic over this price range.

Dr. Fida Karam

(GUST)

Quantitative Demand Analysis

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Price Elasticity of Demand
Point Price...