**Economics I**

**Reading 12. Topics in Demand and Supply Analysis**

**Learning Outcome Statements**

a. calculate and interpret price, income, and cross-price elasticities of demand and describe factors that affect each measure;

*CFA Curriculum, 2020, Volume 2*

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### Subject 2. Elasticities of Demand

*how much*the quantity demanded will rise or fall for a given change in price or income.

**Price elasticity of demand**is the percentage change in the quantity of a product demanded divided by the percentage change in the price causing the change in quantity. It indicates the degree of consumer response to variation in price. Specifically, it tells the analyst the percentage change in the quantity demanded for a good caused by a 1% increase in the price of that good.

The change in price is expressed as a percentage of the average price - the average of the initial and new price, and the change in the quantity demanded is expressed as a percentage of the average quantity demanded - the average of the initial and new quantity. Using the average price and average quantity, the same elasticity value is obtained regardless of whether the price rises or falls.

The measure is

*units-free*because it is a ratio of two percentage changes and the percentages cancel each other out. Changing the units of measurement of price or quantity leave the elasticity value the same.

Because a change in price causes the quantity demanded to change in the opposite direction,

*this ratio is always negative*, although economists always ignore the sign and simply use the absolute value. It is the magnitude, or absolute value, of the measure that reveals how responsive the quantity change has been to a price change.

*Example 1*

A Pizza Hut store can sell 50 pizzas per day at $7 each or 70 pizzas per day at $6 each. The price elasticity is: [(50 - 70)/60] / [(7 - 6) / 6.5] = -2.17.

**Own-Price Elasticity of Demand**

Demand can be inelastic, unit elastic, or elastic, and can range from zero to infinity. (Note: the negative sign is ignored.)

- If the elasticity coefficient is greater than 1, demand is
**elastic**. A small price change leads to a large change in the quantity demanded. The more elastic the demand, the flatter the demand curve over any specific range. Demands for goods with many substitutes (e.g., juice) are relatively elastic. If the demand curve of a good is completely horizontal, the demand is**perfectly elastic**. Consumers will buy all of that good at the market price. - When the elasticity coefficient is less than 1, demand is
**inelastic**. The more inelastic the demand, the steeper the demand curve. Demands for goods with few substitutes (e.g., cigarettes) are relatively inelastic. - When the elasticity coefficient is equal to 1, demand is said to be
**unitary elastic**.

Because elasticity is a relative concept, the elasticity of a straight-line demand curve will differ at each point along the demand curve. Specifically, a straight-line demand curve is more elastic when price is high. Note that the elasticity is not the slope of the demand curve. Elasticity is used since it is independent of the units of measure.

*Example 2*

Refer to the graph below. Which of the following is true?

A. Areas C and E are smaller than area A, so demand must be elastic between $10 and $30.

B. Areas C and E are smaller than area A, so demand must be inelastic between $10 and $30.

C. Area F is smaller than areas B and C, so demand must be inelastic between $10 and $30.

Answer: C. Since at $30 the demand is unit elastic, at prices below $30 demand is inelastic. This is because when price rises from $10 to $30, the revenue gained is greater than the revenue lost.

**The Factors that Influence the Elasticity of Demand**

The elasticity of demand among products varies substantially. The determinants of price and income elasticity of demand are:

**The closeness of substitutes.**The most important determinant is the availability of substitutes. The closer the substitutes for a good or service, the more elastic the demand for it.- Necessities, such as food or housing, generally have inelastic demand.
- Luxuries, such as exotic vacations, generally have elastic demand.

**The proportion of income spent on the good.**If expenditures on a product are quite small relative to a consumer's budget, the income effect will be small even if there is a substantial increase in the price of the product. This will make the demand less elastic. For example, if the price of matches triples, consumers would not bother to find substitutes, since they only spend a few bucks on matches each year.**The time elapsed since a price change.**The more time consumers have to adjust to a price change, or the longer a good can be stored without losing its value, the more elastic the demand for that good. In general, when the price of a product increases, consumers will reduce their consumption by a larger amount in the long run than in the short-run. Therefore, the demand for most products will be more elastic in the long run than in the short run.

The price elasticity of demand tends to increase in the long run.

As changing market conditions raise or lower the price of a product, both consumers and producers will respond. However, their response will not be instantaneous, and it is likely to become larger over time. In general, when the price of a product increases, consumers will reduce their consumption by a larger amount in the long run than in the short run. Thus, the demand for most products will be more elastic in the long run than in the short run. This relationship between the elasticity coefficient and the length of the adjustment period is referred to as

**the second law of demand**.

**Impact on Total Expenditure**

Consumers' total expenditure is the same as total revenues from the suppliers' point of view. One of the most important applications of price elasticity is determining how total consumer expenditure on a product changes when the price changes.

**Total Revenues = Total Expenditures = Price x Quantity**

According to the law of demand, price and quantity move in opposite directions. When the price changes, total revenue also changes. But a rise in price doesn't always increase total revenue. The change in total expenditures depends on whether the effect of the changes in price or the effect of the changes in quantity is greater.

- When demand is inelastic, a change in price will cause total expenditures to change in the same direction.
- When demand is elastic, a change in price will cause total expenditures to move in the opposite direction.
- When demand elasticity is unitary, total expenditures will remain unchanged as price changes.

Because of the relationship between price and quantity sold, a firm's total revenue can rise, fall or stay the same in response to a change in price. The outcome is determined by the price elasticity of demand. This conclusion is similar to that of total expenditures.

Note that firms attempt to maximize profit (total revenue minus total cost), not revenue.

**Income Elasticity of Demand: Normal and Inferior Goods**

Definition: The percentage change in the quantity of a product demanded divided by the percentage change in consumer income causing the change in quantity demanded.

Since increases in consumer income will increase the demand for most goods, income elasticity measures the responsiveness of a demand for a good to a change in income. Specifically, it tells the analyst the percentage change in the quantity demanded for a good caused by a 1% increase in consumer income.

Calculation:

The type of product is the primary determinant of income elasticity of demand.

- Most products have positive income elasticity;
**normal goods**have positive income elasticity.- Necessities have low income elasticities (between 0 and 1); when income rises by 1%, the quantity demanded for necessities will increase by less than 1%.
- Luxuries have high income elasticities (greater than 1).

- A few commodities (
**inferior goods**) have negative income elasticity; as income expands, the demand for them will decline. Examples of inferior goods are margarine, junk food, etc.

**Cross-Price Elasticity of Demand: Substitutes and Complements**

The cross elasticity of demand is a measure of the responsiveness of demand for a good to a change in the price of a substitute or a complement, other factors remaining the same. The formula for calculating the cross elasticity is:

- The cross elasticity of demand for a substitute is positive.
- The cross elasticity of demand for a complement is negative.

The following figure shows the increase in the quantity of pizza demanded when the price of a burger (a substitute for pizza) rises. The figure also shows the decrease in the quantity of pizza demanded when the price of a soft drink (a complement of pizza) rises.

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**User Contributed Comments**
19

You need to log in first to add your comment. ###### Nathan

Elasticity coefficient = (% change in quantity demanded) / (% change in price)

###### Nathan

note that "% change ..." = change in value / average value, thus if Q1 = 10 and Q0 = 11 then the correct way to determine the %change in quantity demanded is (11 - 10)/[(11 + 10)/2]. This reduces to 1 / 1.5 = 0.666.

It's also important that you not be misled by the way that the variables were indexed in the text above. That equation only holds if we reverse the conventional assumption that higher subscripted variables in a time-series are later in time. I don't think it will matter as long as you're consistent with numerator and denominator. Am I right about that?

###### Nathan

No. I'm incorrect! These are two approaches to the same result and I would suggest the approach given in the notes as it cuts out the step of dividing numerator and denominator by 2.

###### salvo15

At a price of R20 the Quantity demanded is 10 and the elasticity = 4.

For a 1% change in price we can expect a 4 % change in quantity

THERFORE AT A ELASTICTY OF 4:

For a 2.5% change in price we can expect a 10% change in quantity. 10% = 2.5*4

Thus: If the price increase by 2.5% to R20.5 the quantity demanded will be 9 [10 - (10*10%) ]

###### soarer1

Can someone please explain how to read the areas represented in the graph above?

###### aakash1108

@soarer1

The areas are LxB.

For A, L = 10 and B = 10. Therefore, Area = 100

For B, L = 20 and B = 10. Therefore, Area = 200

For C, L = 20 and B = 5. Therefore, Area = 100

For D, L = 10 and B = 10. Therefore, Area = 100

For E, L = 10 and B = 5. Therefore, Area = 50

For F, L = 10 and B = 10. Therefore, Area = 100.

###### azratowfiq

can someone please let me know how the annlysis for d arrives?

###### Sailor85

Aratowfig: Note that although the line as a constant slope on the graph, if you calculate the slope for each line section you will see that the slope varies. It didn't make sense to me at first either.

###### veeyeung

when the price is at $10, revenue= areas D,E,F. when the price is at $30, revenue= areas D,E,B,C

therefore, when the price rises from $10 to $30, revenue lost= F, and revenue gained= B,C

we know F=100 and B=200,C=100, so revenue gained is larger than revenue lost.

###### endlessfin1te

CFA uses the "arc" elasticity of demand, where price and quantity demanded changes are calculated by dividing the change with "average of original and new value", instead of "original value". This is called the midpoint method.

###### Allen88

normal good- ramen noodle.

jk guys.... its a superior good :)

###### breakman

I laughed

###### GamePlayer

RESPONSIVENESS

###### duzhnikov

How did they get "at 30 the demand is unit elastic" - I'm getting -0.5 so the demand is inelastic.

((15-25)/((15+25)/2)) / ((30-10)/((30+10)/2)) = -.50

###### Creep

@Duzhnikov, from $10 to $30, the revenue goes up from $10 x 25 = $250 to $30 * 15 = $450, so it's inelastic. from $30 to $40 the revenue goes down from $450 to $40 x 10 = $400, so it is elastic. That's why at $30 it is unit elastic.

###### padasalasunil

i did not understand how the elasticity can vary when the demand curve is a stragiht line. The elasticity is measured by taking the inverse of the gradient of the line right? In that case, shouldn't the gradient be constant for a straight line?

###### Thediceman

this chapter is very confusing, should demand curve be inverse slope? So I think elasticity coefficient should be recognized as negative......

###### tangyjab

For example 2: "Since at $30, the demand is unit elastic, at prices below $30, demand is inelastic: this is because when price rises from $10 to $30 the revenue gained is greater than revenue lost" - how is demand unit elastic at $30, when qty demanded is 15? Shouldn't demand be inelastic when price is below $20 and not $30, since it's at $20 when demand is unit elastic?

###### rafeeul

In example 1, should it be: ((70-50)/50) / ((6-7)/7) = 2.86. I've never seen anyone use average prices.