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Unformatted text preview: Which of the following seem more Elasticity: Percentage Change serious: Percentage changes are often more – An increase of 50 cents or an increase of 50% in the price of a hamburger – An increase of $100 or an increase of 1% in the price of a new car – Therefore economists often use elasticities to examine percentage change or responsiveness
1 important than the amount of change Price Elasticity of Demand
Price Elasticity of Demand (E ) 2 Impact of a Change in Supply & Therefore Price on the Quantity Demanded
Price (dollars per pizza) 40.00 … a 30.00 20.00 10.00 5.00 0 5
large fall in price... S0
An increase in supply brings ... S1 Large price change and small quantity change … and a small increase in quantity 10 13 15 Da 20 25
3 Quantity (pizzas per hour) Impact of a Change in Supply…
Price (dollars per pizza) 40.00 30.00 … a small 20.00 15.00 10.00
fall in price... An increase in supply S0 brings ... S1 Small price change and large quantity change Db
… and a large increase in quantity 0 5 10 25 15 17 20 Quantity (pizzas per hour) 4 Solution: Price Elasticity of Demand Price Elasticity of Demand
ЄQ,P=
Percentage change in quantity demanded Percentage change in price %∆Qd ∈Q,P = %∆P
The ratio of the two percentages is a number without units. 5 Example Price Elasticity – Price of oil increases 10% – Quantity demanded decreases 1%  1% ∈Q,P = = −.1 + 10%
When calculating the price elasticity of When demand, we ignore the minus sign for % change in Q. 6 TYPES OF ELASTICITY Hypothetical Demand TYPES Elasticities Elasticities
Product % Change in price (% P) ∆ % Change in quantity demanded (% QD) ∆ 0% Elasticity (% QD/% P) ∆ ∆ Insulin + 10% 0 Perfectly inelastic Basic Telephone service + 10% > 1% .1 Inelastic Beef + 10% = 10% 1.0 Unitarily elastic Bananas + 10% < 30% 3.0Elastic
7 Price Elasticity Ranges: Extreme Price Elasticities Perfect elasticity,
D
P1 Perfect inelasticity, zero elasticity, no matter how much Price changes, Quantity stays the same; insulin infinite elasticity, the slightest increase in price will lead to zero sales. P1 Price 30 Price P0 D 0 Quantity Demanded per Year
(millions of units) 8 0 Quantity Demanded per Year (millions of units) 8 Price Elasticity Ranges
Summary from Table Elastic Demand %∆ >%∆ ; ∈ P > Q P 1 Q, Unit Elastic %∆ =%∆ ; ∈ P =1 Q P Q, Inelastic Demand %∆ <%∆ ; ∈ P <1 Q P Q,
9 Elasticity of Demand Calculating elasticity
ЄQ,= Sum of quantities/2 P Change in Q Change in P Sum of prices/2 or
u se ways oint Al idp the m la fo rm u ЄQ,P = Change in Q (Q1 + Q2 )/2 Change in P (P1 + P2 )/2 ∆P Avg. P
10 10 or ∆Q = ЄQ,P Avg. Q Calculating the Elasticity of Demand
Price (dollars/pizza) 20.50 Original point 2/10 ∆ Q /Q Elasticity = =4 = ∆ P/P 1/20
ave ave ΔP=1 20.00 19.50 New point D Q P =1/2(11+9)=10 =1/2(20.50+19.50)=20 9 10 11
Quantity (pizzas/hour)
11 11 ΔQ=2 Elasticity of Demand (midpoint)
∆ Q =2 %∆ Q =20%
ЄQ,P X 100 Q1 + Q2 (9 + 11) 2 ∆ P = $1.00 = 10 20% 5% =
X 100 = = ЄQ,P = 4 %∆ P =5% P1 + P2 ($20.50 + $19.50) 2 = $20
12 12 Always use the midpoint formula for calculating elasticity Elasticity: Example You are the consulting economist to the Guelph transportation commission, The current fare is $.80 There are 25,000 riders per day For each $.01 increase (decrease) in the fare, rider ship decreases (increases) by 500 riders per day. What is the price elasticity of demand at the current fare? Should fares be raised or lowered? What fare will maximize revenue? 13 13 Total Revenue and Elasticity
Total Revenue
= Price Per Good
X # of Goods Sold TR = P X Q Assumption : Costs are constant
14 14 1.10 Elastic demand Unit elastic Inelastic demand Ela sticity and Total Reven ue Price .80
.55 0 55 55 Total Revenue 3.00 (dollars) 110 Maximum total revenue Quantity When demand is elastic, price cut increases total revenue When demand is inelastic, price cut decreases total revenue Quantity 0 55 110 15 15 Relationship Between Price Elasticity of Demand and Total Revenues
Price Elasticity of Demand Effect of Price Change on Total Revenues (TR) Price Decrease Price Increase Inelastic (ЄQ,P < 1) TR ↓ TR ↑ Unitelastic (ЄQ,P = 1) No change No change No change Elastic (ЄQ,P > 1) TR ↑ TR ↓ Note: It is possible to classify elasticity by observing the change in revenue from a price change
16 16 Question
• • • • • 2 drivers Tom & Jerry each drive to to a gas station. Before looking at the price, each places an order. Tom says, “I’d like 10 litres of gas”. Jerry says, “I’d like $10 of gas”. What is each driver’s price elasticity of demand?
17 17 Determinants of Price Elasticity of Demand Existence of substitutes Share of budget – Goods are more price elastic if substitutes exist – Goods are more price elastic when a consumer’s expenditure on the good is large (absolutely or relatively) – Goods are less price elastic when seen as a necessity Necessity 18 18 Market and Brand Elasticities Market and Brand Elasticities are not equal – Although a water addict is very price inelastic to the price of bottled water in general, he/she would quickly switch to another brand if only 1 brand of water increased in price – GENERALLY, Brand price elasticity of demand is higher than market price elasticity of demand
19 19 Qd = a – bp a,b are positive constants p is price •b is the slope •a/b is the choke price (price at which nothing is sold) 20 20 •the elasticity is ε Q,P = (∆ Q/∆ p)(p/Q) …definition… = b[p/(abp)] Since the slope of the graph is b so…elasticity falls from 0 to ∞ along the linear demand curve, but slope is constant. •if Qd = 400 – 10p, and p = 30, ε Q,P = (10)(30)/(100) = 3 "elastic"
21 21 Changes in Elasticity Along a Linear Demand
1.10 1.00 .90
Price per Minute ($) Elastic (ЄQ,P > 1) Unitelastic (ЄQ,P = 1) Inelastic (ЄQ,P < 1) Demand, or average revenue curve D
1 2 3 4 5 6 7 8 9 10 11
22 22 .80 .70 .60 .50 .40 .30 .20 .10 0 Quantity per Period (billions of minutes) The Relationship Between Price Elasticity of Demand and Total Revenues for Cellular Phone Service
Price $1.10 1.00 .90 .80 .70 .60 .50 .40 .30 .20 .10 Quantity Demanded 0 1 2 3 4 5 6 7 8 9 Total Revenue 0 1.0 1.8 2.4 2.8 3.0 3.0 2.8 2.4 1.8 1.0 Elasticity
ЄQ,P 21.000 6.333 3.400 2.143 1.144 1.000 Unitelastic .692 .467 .294 .158 Inelastic
23 23 Elastic 10 Qd = Apε ε = elasticity of demand and is negative p = price A = constant •Elasticity is constant, but the slope of demand falls from 0 to ∞ . In another form, if Ln(Qd)=μLN(P), μ= Price Elasticity of Demand
24 24 Price Example: A Constant Elasticity versus a Linear Demand Curve P •
0 Q Observed price and quantity Constant elasticity demand curve Linear demand curve Quantity
25 25 Elasticity of Supply Calculating elasticity
= ЄQs,P Change in Q Sum of quantities/2 Change in P Sum of prices/2 or
se ays u int Alw o midp the la ormu f Change in Q = ЄQs,P (Q1 + Q2 )/2 Change in P (P1 + P2 )/2 ∆P Avg. P
26 26 or ∆Q ЄQs,P = Avg. Q How a Change in Demand Changes How Price and Quantity Price
Price (dollars per pizza) 40.00 30.00 20.00 An increase in demand brings ... Sa Large price change and small quantity change … a large price rise... 10.00
… and a small quantity increase D1 D0 20 25 0 5 10 13 15 Quantity (pizzas per hour) 27 27 How a Change in Demand Changes Price and How Quantity Quantity
Price (dollars per pizza) 40.00 30.00 21.00 20.00 10.00 An increase in demand brings ... Small price change and large quantity change
Sb … a small price rise... … and a large quantity increase D1 D0 0 5 10 15 20 25 Quantity (pizzas per hour) 28 28 Elasticity of Supply Elasticity of supply ranges – (from) Perfectly Elastic Supply – (to) Perfectly Inelastic Supply Quantity supplied falls to 0 when there is any decrease in price Quantity supplied is constant no matter what happens to price Notice: There is no total revenue test for supply since price and quantity are directly related
29 29 Price supply = 0 Price Supply Elasticity Ranges S Elasticity of
Elasticity of supply = ∞
S Quantity supplied is the same for any price! Suppliers will offer ANY quantity at this price 0 Quantity
30 30 0 Quantity Elasticity of Supply: Depends On:
1. Resource substitution possibilities, The more unique the resource, the more inelastic the supply. 2. Time frame for the supply decision,
Momentary supply Longrun supply Shortrun supply  The longer producers have to adjust to a price change, the more elastic is supply.
31 31 Elasticity can vary in the short run Elasticity (when major changes cannot be made) and the long run. and For most goods, elasticity is greater in For the long run (curves are “flatter) the People and firms are more able to adjust People to changes over time to For essential durable goods (ie: Cars), For elasticity is less in the long run (curves are “steeper” are People can change their purchases or People 32 32 Elasticity in the Long Run Supply Elasticity and the Long Run (most nondurable, nonessential goods)
S1 Price per Unit S2
S3 P1 Pe As time passes, the supply curve rotates to S2 and then to S3 and quantity supplied rises first to Q1 and then to Q2 Qe Q1 Q2 Quantity Supplied per Period 33 33 There is no set amount of time that puts a There market into the long run market
– The long run could be a week or a year How Long is the Long Run? The long run is how long a consumer or The firm takes to fully adjust to a price change firm
– Time required to make major changes Time – Ie) Give up Pepsi Vanilla, Build more cost Ie) efficient Pepsi factory, secure a US Pepsi Vanilla supplier Vanilla The short run is anything shorter than the The long run long
34 34 Cross Price Elasticity of Demand We’ve seen already that demand is We’ve affected by the price of substitutes and compliments and
– An increase in the price of a substitute An increases demand increases – An increase in the price of a complement An decrease demand decrease This effect can be measured using This cross price elasticity cross If the cross price elasticity is zero, the If 35 35 Cross Price Elasticity of Demand
Є
Qi,Pj = Percentage change in quantity demanded of X Percentage change in price of Y Є Qi,Pj = Change in X  / Change in Price of Y  Substitutes – Positive Cross Price Elasticity Compliments – Negative Cross Price Elasticity
36 36 Cross Price Elasticity of Demand Example “Recent cat attacks have Recent prompted cat owners to buy guns for selfdefense” for
Originally, Originally, 2 Econ students owned a cat. After the price of guns went from $100 to $200, only 1 Econ student owned a cat. $200, Calculate the crossprice elasticity of Calculate
37 37 CrossPrice Elasticity
∆ Q = 1 %∆ Q i =66%
ЄQ,P X 100 Q1 + Q2 (2 + 1) 2 ∆ P = $100 = 1.5 = = ЄQi,Pj = 66% 66% = 1 %∆ P J =66% P1 + P2 ($100 + $200) 2 X 100 = $150
38 38 Are cats and guns substitutes or compliments? Income Elasticity of Demand
Income Elasticity of demand refers to a HORIZONTAL SHIFT in the demand curve resulting from an income change Price elasticity of demand refers to a MOVEMENT ALONG THE DEMAND CURVE in response to a price change 39 39 Income Elasticity of Demand
Є
Q,I = Percentage change in quantity demanded Percentage change in income / Change in M  Normal Good – Positive Shift/Elasticity Inferior Good – Negative Shift/Elasticity 40 40 In New Zealand, the average family will In own 4 Toyotas in their lifetime. own If average Kiwi family income rose from If $140K to $160K a year, the average Kiwi family would own 2 Toyotas over their lifetime lifetime Income Elasticity of Demand Example Calculate Income Elasticity of Demand Calculate for Toyotas in New Zealand. for Are Toyotas normal or inferior goods in Are 41 41 Income Elasticity of Demand
∆ Q = 2 %∆ Q =66%
ЄQ,P X 100 Q1 + Q2 (4 + 2) 2 ∆ I = $20K =3 = = ЄQi,Pj = 66% 13.3% = 5
X 100 %∆ I =13.3 % I1 + I2 ($140K + $160K) 2 = $150K
42 42 In New Zealand, are Toyotas normal or inferior goods? Guess which brand is the luxury car. ...
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This note was uploaded on 03/14/2009 for the course ECON ECON 281 taught by Professor Priemaza during the Fall '08 term at University of Alberta.
 Fall '08
 Priemaza
 Economics

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