# econ 503 chp3

**Topics:**Supply and demand, Price elasticity of demand, Elasticity

**Pages:**22 (2261 words)

**Published:**September 27, 2014

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

1 / 19

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.

Advertising elasticity.

Price elasticity of supply.

Dr. Fida Karam

(GUST)

Quantitative Demand Analysis

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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...

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