Topic 4 – Elasticity of Demand
(Week 3-4 Sep 29 – Oct 4 )
You own the only spring in town, which produces sparkling water that you sell for $10 a bottle;
You have no costs, so that your profit equals your total revenue (price X quantity sold);
Q1. If you want to increase your revenue, should you raise your price above $10/bottle?
Q2. Would your answer change if these were other springs to town that also sold sparkling water?
Q1: If you raise your price:
a. consumer who continues to buy your water would pay more; you earns more money per bottle;
b. there will be fewer customer due to the “law of downward-sloping demand.”
Revenue = price X quantity; price goes up while quantity sold goes down. Should you raise your price?
Thus introduced the concept of “Price Elasticity of Demand”.
Price Elasticity of Demand
Elasticity of Demand measures the responsiveness of quantity demanded to a change in price.
Formula: Elasticity of demand = % Change in quantity demanded = %△Q D
% Change in price %△P
(Due to the law of downward-sloping demand, the elasticity will be negative; just ignore the negative sign.)
1. Mid-Point Convention (calculating %change)
%△Q = △Q D (change in quantity demanded over average quantity demanded);
%△P = △P (change in price over average price)
Insight: percentage change is the same with going up from A to B or going down from B to A on the curve.
e.g.1 – calculating percentage change
Situation Price Quantity Demanded %△ Q = 200 20%;
A 0.90 1,100 1000
%△ P = 0.2 = 20%
B 1.10 900
Perfectly inelastic e=0 Q doesn’t change no matter how price changes
Inelastic 0 < e < 1 Q is not very responsive to a change in price;
Unit elastic e=1 Q Dhanges at the same pace as the price;
Elastic 1 < e < ∞ Q is very responsive to a change in price;
Perfectly elastic e=∞ Q is unlimited at certain price; and zero if price
ECO100Y1-Pesando-Notes edited by Eva Wu 3. Why do elasticity differ: More/better substitutes = higher elasticity;
a) longer time elapsed since price change (long run vs. short run);
-- higher elasticity (closer substitutes) as time passes;
-- e.g. price of gas goes up.
As there are no close substitutes with cars (public transit and walking are not), therefore people drive
less, and elasticity of demand for cars is relatively low; as time goes by, fuel efficient cars are invented as
close substitutes with regular cars, and the elasticity goes up;
-- insight: lower elasticity in the short run; higher elasticity in the long run;
b) Definition of market
-- narrow (market of Colgate toothpaste) – higher elasticity because there are many substitutes
-- broad (market of toothpaste) – lower elasticity because toothpaste has few substitutes;
-- Margarine & Butter (close substitutes) = higher price elasticity of demand;
-- Tobacco has few close substitute = lower price elasticity of demand;
e.g.2. Will the price elasticity of demand for Ford SUV increase, decrease, or remain the same when each
of the flowing events happen?
a) Other car manufacturers decide to make and sell SUVs:
e goes up because there are more close substitutes for Ford SUV;
b) SUVs produces in foreign countries are banned from Canadian market;
e goes down because there are fewer substitutes now;
c) Due to an ad campaign, Canadian believe that SUVs are much safer than ordinary cars;
e goes down because there are fewer substitutes now.
4. Special Case
a) Perfectly elastic demand: A straight line.
Consumer demanded unlimited quantity at Price P,
ee and zero if price exceeds P.
PPrice Since seller can sell unlimited quantity at P, there is no
ee incentive for the seller to lower the price.
e.g.3 Purple Tennis Balls;
-- Assume tennis balls in all colors, available at $5 each, and the seller is able to sell as many tennis balls as
he wants; players are indifferent to the color of tennis balls.
-- If the price of all purple tennis balls rises to $5.1, all buyers will by other colors tennis balls and the
quantity demanded for purple tennis ball is zero.
-- Since sellers can sell unlimited tennis balls at $5, there is no incentive for the seller to lower the price.
Therefore the purple tennis ball is an example of perfectly elastic demand.
ECO100Y1-Pesando-Notes edited by Eva Wu b) Perfectly inelastic demand
PPrice A Vertical Line;
Consumer demand Q regardless of price;
Example includes insulin;
Q Quantity demanded
5. Elasticity varies along a linear demand curve
e.g. 4 D
Price Quantity Given linear demand curve: Q = 20 – 0.4P
50 0 1. if price declines from 50 – 40:
E = (4 - 0)/2 = 18 ---- elastic
25 10 (40 – 50)/45
10 16 2. if price declines from 10 to 0:
E = (20 - 10)/18 = 0.28 ------ inelastic
(0 – 10)/5
a) -- when price is high, quantity demanded is low; price
-- %△Q is high (smaller denominator ),
-- %△P is low (larger denominator) ee elastic
-- high elasticity;
-- DD “starts out” with high elasticity of demand;
b) – when price is low, quantity demanded is high;
D Quantity demanded
-- %△Q is low (larger denominator)
-- %△P is high (smaller denominator)
-- low elasticity;
-- DD “ends up” with low elasticity of demand;
c) Elasticity is not the slope of demand!!! It’s changing along the linear demand!
e.g. demand curve A