Ch. 5 Handouts on Elasticity

Ch. 5 Handouts on Elasticity

Elasticity: measures the responsiveness of one factor due to a change in another factor

• Measures the percentage change in a dependent variable, Y, resulting from a 1% change in the value of an independent variable, X.

• General Form:

• Two different ways to measure elasticity: point elasticity and arc elasticity

• Point elasticity: measures elasticity at one specific point and is commonly used to measure the effect on the dependent variable, Y, of a very small change in X. (typically less than 5% change in X)

• Arc elasticity: measures the average elasticity over a range of a function and is better suited for larger changes in X (more than 5%).

Price Elasticity of Demand (ED or EP): the percentage change in Quantity demanded, Qd or Q, as a result of a percentage change in the product’s own price, P.

• Shows how sensitive consumers are to a change in the price of your product.

• The law of demand says that as prices increases, quantity demanded will fall. Price elasticity will tell you the magnitude of this decrease.

• This will ultimately impact sellers’ decisions regarding increasing or lowering prices to increase total revenue (TR).

• Point Elasticity and Arc Elasticity general form: Ed=
• The difference between the two measures is the information required to calculate each measure and the overall applicability to specific situations.

Point Elasticity Measure of Ed:

• Measures the elasticity at one specific point on the demand curve.

• Point Elasticity: Ed=

• where the second term is the inverse slope. Remember: inverse slope is the “b” term in your demand equation or coefficient for price in regression output:

ex: Qd=100-2P (-2 is inverse slope)

• Point Elasticity example:
• If the current selling price is P=5, and the current Qd=90 then we can estimate the elasticity at that point by the following:

• Ed=

• This means a 1% increase in the price of our product results in a .11% decrease (since negative) in the quantity demanded of our product. Or that a 1% decrease in price results in a .11% increase in Qd.

• This also means that a 3% increase in price would have a 3*.11 = 3.33% decrease in the quantity demanded.

• Advantage of point elasticity: only need the demand equation and one P, Qd combination to get an estimate. Easy to apply with regression output.

• Disadvantage: as we will see later elasticity changes at every point along the demand curve. Therefore, it is only accurate for small changes in prices.

Arc Elasticity Measure of Ed:

• Measures the average elasticity between two points along the demand curve

• Arc formula: *
• Ex:

• Advantage: used to analyze the average sensitivity of demand to price changes over an extended range of prices.

Interpreting and Classifying Ed numbers

• All Ed numbers will be negative in accordance with the law of demand indicating a negative relationship between P and Qd

• Convert all to positive by taking the absolute value.

• We then classify the numbers into one of 5 categories:
• Elastic demand ______

• Inelastic demand ______

• Unit elastic demand ______

• Perfectly elastic demand ______

• Perfectly inelastic demand ______

Elastic Demand:

• Ed > 1 “elastic”

• Ed= to get a number larger than one it must be that the numerator is a larger number than the denominator:

• %Qd > %P meaning that consumers are price sensitive and alter the Qd significantly in response to changes in prices

• this means that for every 1% change in price there is more than a 1% change in Qd

• ex: Ed=-2.5 means a 1% change in price leads to a 2.5% change in the Qd. Consumers have a large reaction to the price change. They are price sensitive or price responsive.

Inelastic Demand:

• 0< Ed < 1 “inelastic”

• Ed= to get a number between zero and one (e.g. 0.5, 0.25) it must be that the numerator is a smaller number than the denominator.

• %Qd < %P meaning consumers are not price sensitive; they may alter the Qd when price changes but it is a small response

• this means that for every 1% change in price there is less than a 1% change in Qd
• ex: Ed=-0.5 means a 1% change in price leads to a 0.5% change in the Qd. Consumers have a relatively small reaction to the price change. They are NOT price sensitive or price responsive.

Unit Elastic:

• Ed = 1 “unit elastic”

• %P = % Qd

• a 1% change in price leads to exactly a 1% change in Qd

a 10% change in price leads to exactly a 10% change in Qd

• occurs when consumers transition from being “elastic” to “inelastic”

Perfectly Elastic Demand:

• special case: Ed =  perfectly elastic (largest positive number)

• when a small change in price results in the consumer altering quantity demanded in an extreme way. Consumers are hypersensitive to prices.

• Realistically occurs only in rare circumstances when consumers can buy the exact same product from different vendors and always select solely on the basis of lowest price.

• occurs with a horizontal demand curve (show graph)

Perfectly Inelastic Demand:

• special case: Ed = 0 perfectly inelastic

• when any change in price results in the consumer buying the exact quantity they were already purchasing. Consumers do NOT change their Qd at all.

• Realistically occurs only in rare circumstances when consumers must buy a product in fixed quantities and cannot store products (so they don’t buy extra units when prices are low).

• Ex: insulin for diabetics. Use the same amount of prescription medication. You don’t buy more when prices fall; and you can’t really buy less for health reasons.

• Vertical demand curve

Factors that Influence Price Elasticity of Demand

1. degree of substitutability

• All beverages (soda, water, alcohol, juice, etc).
• With lots of choice price plays an important role in decision making

• Gasoline for your car—there is no good substitute
• With little or no choice price plays less of a role

2. Product Definition

• Ex: milk (not any good substitutes for milk)

Ex: many substitutes within brands or types of milk such as 1% milk, 2% milk, ½% milk, whole milk etc.

3. Time horizon before purchase

Ex: airlines, last minute willing to pay more

Ex: last minute gifts

Ex: vacation next year: time to search for alternatives

4. Proportion of budget spent on the good

Ex: expensive items such as cars, jewelry, computers

A 5% change in the price of an expensive good can have a large effect on your budget. You will be more price sensitive.

Ex: inexpensive items such as pencils, pop.

A 5% change in price has little or no effect on budget. You will not alter the Qd by very much.

Calculating Price Elasticity from Sales Data

• To determine the price elasticity of demand for sports watches we will estimate the change in sales of sports watches resulting from changes in its own price.

• Arc formula: Ed= *
• Ed=

• Ed=

• For every 1% of a price change sales will change by 5%.

• If expect prices to decrease by 6% then sales will increase by 6*5=30%.

Elasticity changes as you move along a Linear Demand Curve:

Since the relative expense of the product influences elasticity, this means that you will not be able to categorize demand for a good as always being elastic or inelastic it depends on where you are located on the demand curve.

Plot on graph:

• Demand equation: P=4-1/2 Qd
• Inverse demand equation:2P=8-Qd

Qd=8-2P (x-intercept is 8; inverse slope Qd/P=-2)

• Calculate point elasticity Ed at various points

A: P/Q * Qd/P =

B: P/Q * Qd/P =

C: P/Q * Qd/P=

D: P/Q * Qd/P =

Hence, given regression output you should be able to determine elasticity by using the coefficient for price as Qd/P .

• Example: Q=10,000 -200P+ ……………….

Total Revenue (TR) and Elasticity of Demand

• TR= P * Q

• Ed deals with percentage changes so want total revenue expression in percentage terms

If elastic, then %P < % Qd.

• %TR= %P + % Qd

ex: ED=-2

• If increase price, Qd falls by more than P so TR falls
• If decrease price, Qd increases by more than P so TR increases
• If demand is price elastic, reduce prices to increase revenues.
• Ex: discounts, coupons, specials

If inelastic, then %P >% Qd.

• %TR= %P + % Qd

• ex: ED=-.25

• If increase price, Qd falls by less than P so TR increases
• If decrease price, Qd increases by less than P so TR decreases
• If demand is price inelastic, increase prices to increase revenues.
• Ex: taxes on cigarettes, alcohol, prescription drugs

If unit elastic then Ed=1

For a 10% increase in Price, Qd will decrease by 10%

%TR= %P + % Q

= 10 -10

=0

price changes have no effect on TR with unit elastic demand

Total revenue is maximized at this point.

Show Graph of Linear Demand Curve and ranges of Ed (TOP)

Graph of TR (BOTTOM)

Starting at the reservation price:

Elastic range of the curve: Ed > 1

Unit Elastic point on curve: Ed = 1

Inelastic range of the curve: 0< Ed < 1

Optimal Price Formula for Firms:

• Pricing depends on your marginal cost of production as well as demand

• Specifically, on the demand side you can charge higher prices when demand is inelastic to make more money, and charge lower prices when demand is elastic to make more money.

• If you can divide up your markets into segments, the optimal price strategy would be to charge different prices to different customers (price discrimination: review later)

• If you plan to charge one price across a given population, then determining the optimal price is a function of marginal cost and the average Ed.

• Firm’s maximize profit by producing the Q where MR=MC and then set their price accordingly. We will translate the MR equation to be a function of Ed.

• MR=∆TR/∆Q and TR=P*Q. You can then algebraically substitute and simply to obtain the following

where Ed is not in absolute value so it is a negative number

• If you set MR=MC and solve you arrive at the optimal pricing formula called the “inverse elasticity rule”

• Ex: If MC=20 and Ed=-2.5

• Because of the nature of TR and costs, firms will always end up charging a price in the elastic portion of the demand curve in order to maximize profits (We will see this later in the course when we draw out cost curves)

• Thus, this rule works only with prices in the elastic portion of the demand curve

• Note: This may appear that the rule then only works for “elastic goods” but this is absolutely false. All products even if they are typically more inelastic in nature will still have prices at which people are price elastic, unit elastic, and inelastic. Remember elasticity changes as you move along the demand curve so all products effectively span the entire range of Ed.

Income Elasticity (EI)

• Measures how buyers change the quantity they purchase when income changes.

• This is particularly useful for firms in forecasting changes in demand when the overall economy, or local economy, is headed toward a recession or expansion.

• Income elasticity will not only tell you if people will buy more or less of your product as income changes, but how much more or less for each one percentage change in income.

• There are two major classifications of income elasticity: normal goods and inferior goods.

Normal Goods:

• if EI > 0 (any positive number) then the product is considered a normal good.

• This means that there is a positive relationship between Income and Demand so that as income increases, demand increases and as income decreases demand decreases (I, D; ifI D)

• Ex: EI= 0.35, 1.6, 2.5, etc.

• EI=0.35 means a 1% increase in income leads to a .35% increase in demand. Or a 10% increase in income leads to a .35(10)=3.5% increase in demand.

• This means with normal goods an increase in income will shift demand to the right

• This means with normal goods a decrease in income will shift demand to the left.

There are two subcategories for normal goods: luxury goods (also called cyclical normal goods) and necessities (also called noncyclical normal goods)

• Luxury goods or cyclical goods:

• Ex: automobiles, entertainment, jewelry, food items,

• Ex: EI=3.5 means that for every 1% increase in income, you will increase demand by 3.5%. This is typically true of luxury goods. The more money you have, the more of these goods you buy.

• They are considered “cyclical goods” because demand is highly influenced by the state of the economy (recession vs. expansion: where the economy is in terms of the business cycle). When the economy is strong (and incomes rise), demand increases dramatically. When the economy is weak (and incomes fall) demand decreases dramatically.

• Necessities or Non-cyclical Goods:

• Ex: toiletries, movies, liquor, cigarettes

• Ex: EI=.25 means that for every 1% increase in income, you will increase demand by .25%. This is typically true of necessities. Even when you have more income you still buy about the same amount of those basic goods.

• They are considered “non-cyclical goods” because demand is relatively unaffected by the state of the economy. You don’t alter consumption very much as income changes.

Inferior Goods or Countercyclical Goods

• if EI < 0 (any negative number) then the product is considered an inferior good.

• This means that there is a negative relationship between Income and Demand so that as income increases, demand decreases and as income decreases demand increases (I, D; ifI D)

• Examples: public transportation (buses), generic products. Goods that you will buy less of if you have more income. And when your income really falls, goods you will buy more of often because they are less expensive.

• Ex: EI=-0.15, -1.3,

• EI=-0.15 means a 1% increase in income leads to a .15% decrease in demand. Or a 10% increase in income leads to a -.15(10)=-1.5% decrease in demand.

• This means with inferior goods an increase in income will shift demand to the left (decrease demand)

• This means with inferior goods a decrease in income will shift demand to the right (increase demand)

Determining if goods are Normal or Inferior using basic sales data:

Calculating EI whether goods are normal or inferior:

• EI=
• Point Elasticity formula:
• Arc Elasticity formula:Simplify to: *
• Typically use arc since it is applicable to wider swings in income.

• If you have actual income level as data then you may plug in actual changes in income and changes in sales to calculate income elasticity.

• Otherwise, given the table of data above we only have percentage changes in income and percentages in sales data:

• Example: from December to January income decreased by -0.4%

• You may also calculate income elasticity using regression output: if Q=10,000 -200P +1.5I

• Ex:suppose current price =10; income=30,000

• If median income is expected to increase to 32,000 then estimate sales:

Cross Price Elasticity (EXY or EPX):

• Tells us the relationship between goods
• Are x and y substitutes (consume one or the other)
• Are x and y complements (consume together)
• Are x and y unrelated

• Measures how the quantity demanded of one good (X) changes as a result of a price change of another good (Y).

• EXY =

• EXY = EXY Point Elasticity Formulation

• EXY = * EXY Arc Elasticity Formulation

• Ex: Y=McDonald’s hamburger and X=Wendy’s hamburger

Py=$1.00, Qx=2000.

Py=$.80, Qx=1800.

• EXY = * EXY Arc Elasticity Formulation

• EXY =

• EXY =

• For a 1% change in the price of McDonald’s hamburgers we would expect a .47% change in Wendy’s hamburgers. Since the number is positive: a 1% increase in price of McDonald’s hamburgers leads to a .47% increase in the quantity or demand for Wendy’s hamburgers.

Interpreting and Classifying EXY numbers:

• Substitute Goods:
• If EXY is positive > 0 then Goods X and Y are substitutes

• A positive number suggests a positive relationship between the Price of Y (PY) and the Quantity purchased of X (QX).

• This means that an increase in the price of y results in an increase the the quantity purchased of X.

• Ex: Y=coke; X=pepsi

• If the price of Y, coke, increases we know that people will buy less coke. They will increase the quantity of pepsi, X.

• Ex: EXY= 2.1 means that a 1% increase in the price of coke leads to a 2.1% increase in the quantity of pepsi. Or a 1% decrease in the price of coke leads to a 2.1% decrease in the quantity of pepsi. Or a 4% decrease in the price of coke leads to a 4(2.1)=8.5% decrease in the demand for pepsi.

• Since changes in the price of a substitute will shift the demand curve we know that with a positive EXY an increase in the price of coke will result in an increase in the demand for pepsi (demand shifts to the right for pepsi). Show example:

• Complements:
• If EXY is negative < 0 then Goods X and Y are complements

• A negative number suggests a negative relationship between the Price of Y (PY) and the Quantity purchased of X (QX).

• This means that an increase in the price of y results in a decrease the the quantity purchased of X.

• Ex: Y=camera; X=film

• If the price of Y, camera, increases we know that people will buy less cameras. Thus, less film will be needed so we see a decrease the quantity of film, X.

• Ex: EXY= -0.15 means that a 1% increase in the price of camera leads to a 0.15% decrease in the quantity of film. Or a 1% decrease in the price of film leads to a 0.15% increase in the quantity of film. Or a 4% decrease in the price of camera leads to a 4(0.15)=.60% increase in the demand for film.

• Since changes in the price of a complement will shift the demand curve we know that with a negative EXY an increase in the price of a camera will result in an decrease in the quantity of film (demand shifts to the left for film). Show example:

• Unrelated Goods:

• if EXY =0 then X and Y are unrelated

• If you estimate the impact of a change in the price of pizza on the quantity of cars purchased you would calculate a zero.

• There is no conceivably predictable relationship between pizza and cars.

Applications of EXY:

1. Understanding basic relationships between goods and predicting sales:

• If Exy for McDonald’s burger (X) relative to BK burger prices (Y)=2.75 and BK plans to lower prices by 10% then determine impact on McDonald’s sales:
• Exy =

2. Determining your strongest competition in a market:

• Stronger competition means the two goods are stronger substitutes

• If you know the EXY for each related pair you can rank your competition:

Ex: McDonald’s Hamburgers