Elasticity of demand:
Elasticity of demand is a measure of how much the demand of a good responds to a change in the price of that good, computed as the percentage change in quantity demanded divided by the percentage change in price
Given that price changes from P1 to P2 (Ã?Â?P = P1 – P2), quantity demanded changes correspondingly from Q1 to Q2 (Ã?Â?Q = Q1 – Q2). Define the following quantity
Then, elasticity of demand is defined as , that is, the absolute value of .
Absolute value means the value without the sign, for example, if , then , if then .
Types of demand curves:
ELASTIC: If or , demand is called elastic.
INELASTIC: If or , demand is called inelastic
UNITARY ELASTIC: If or , demand is called unitary elastic
(1) Elasticity indicates % change in demand caused by 1 % change in the price.
(2) The elasticity of demand is a dimensionless number, because we use
percentage change in price and quantity.
(1) Calculate the elasticity when price changes from $4 to $5:
(ii) Calculate the elasticity when price changes from $5 to $6:
The elasticity of demand is a measure of sensitivity of demand.
The greater it is, more sensitive the demand is to a price change
Q Which demand curve is more elastic (i.e., which demand curve has higher elasticity) at price P1 ?
(A) Steep demand curve (B) Flat demand curve
A: (B) is more elastic because the same amount of change in price leads to
larger change in the demand.
In general, the flatter is the demand curve that passes through a given point, the more elastic the demand is. Intuitively this is because when the demand curve is flat, even a small price change causes a large change in quantity demanded
Q: Which demand curve is more elastic at price P1 ?
(A) Demand curve before a shift (B) Demand curve after a shift
A: (A) is more elastic.
Suppose that price changes from P1 to P2 by Ã?Â?P (and the quantity demanded also changes accordingly.) The elasticity of demand of (A) is the absolute value of and that of (B) is the absolute value of .
In both cases, the denominators ( P /P1) are the same. However the numerators are different. Because both demand curves have the same shape, the changes in quantity demands ( Q) are the same. However, Q2 is greater than Q1, which implies that the numerator of (=Ã?Â?Q/ Q1) is greater than that of (=Ã?Â?Q/Q2). This means that the elasticity of demand for demand curve (A) is greater than that for demand curve (B) at price P1
In general if demand curve shifts toward right, then the elasticity of demand becomes smaller at given price level
This is because the elasticity of demand is defined in terms of percent change in quantity demanded. For example, when the price becomes higher by $1 and the quantity demanded decreased by 1 unit. When we consider the impact of this price change we also need to consider the level of the quantity demanded before the price change because it is more reasonable to think that the impact of change from 10 to 9 (units) is greater than the impact of change from 10000 to 9999 (units) even though the same amount of change (1 unite) occurs.
The above definition of elasticity requires two points, (Q1, P1) and (P2, Q2) on the demand curve, for its calculation. We often ask like “what is the elasticity at price P1?” This value obtained by taking the limit of in which , and . However, it is shown that when the demand curve is linear, i.e., straight line (we use this approximation quite often) then the value of elasticity at (Q1, P1) does not depend on (P2, Q2), i.e., given a point (Q1, P1), then we can calculate the elasticity of demand at P1 without knowing (P2, Q2).
Elasticity of Linear Demand
The definition of elasticity is . The definition of elasticity above requires two points to calculate it, but if the demand curve is linear, the elasticity is determined by only the value of intercept and the price level.
Suppose that price changes from P1 to P2
What is the elasticity at price P1 ? From the definition of elasticity
What is ? It is equal to . So . Notice that this depends on neither nor . If we know P1 (and the intercept A), then we can calculate the elasticity of demand at P1
Now, we obtain a convenient formula for calculating the elasticity of demand for a linear demand curve at given price P1:
For a linear demand curve, the elasticity of demand whose intercept is A at a given price P1 is . This formula is very convenient when the demand curve is linear (or is approximated by a linear demand curve.)
Furthermore you can show that when ,i.e., the demand is inelastic; when ,i.e., the demand is elastic.
The above results are summarized in the following diagram.
Factors affecting the elasticity of demand:
(1) Availability of close substitute: Goods with close substitutes tend to have more elastic demand.
Ex) Demand of coca cola would be very elastic because we can easily switch to pepsi cola while demand of addictive goods such as cocaine and marihuana would be inelastic.
(2) Necessities vs. Luxuries: Necessities tend to have inelastic demands, whereas luxuries have elastic demands
Ex) Demand of oil and gas would be inelastic because it is difficult to reduce the consumption (at least in a short run.)
Implication of Elasticity
There are two important implications from the value of elasticity
(1) When the demand is elastic, the total expenditure decreases as the price
(2) When the demand is inelastic, the total expenditure increases as the price
Here total expenditure is defined as: Total Expenditure (TE): P Ã?Â? Q
Case (1) : When the demand is elastic (demand curve is relatively flat), 1 % price change will lead to more than 1 % demand change. Total expenditure decreases as the price goes up
Case (2): When the demand is inelastic (demand curve is steep), 1 % price change will lead to less than 1 % demand change. Total expenditure increase as the price goes up (See below)
Elasticity Effect on TE if P increases Effect on TE if P decreases Example
Elastic Decrease Increase Perfume
Unitary elastic Same Same
Inelastic Increase Decrease Medicine
Q: Will sellers always get more revenue if they increase the price of their products?
A. It depends on elasticity of demand at the initial price
Ex) If you are the boss of the metro, should you raise up the bus fare?
? It will depends on the demand for the metro bus
? Analyst would collect the historical data to see how the quantity demanded change with any change in price.
Sample question for quiz 2.
Assume the demand curve for a typical consumer for Metro bus
rides per week is:
P: $4 $3.50 $3.00 $2.50 $2.00 $1.50 $1.00 $.50
Q: 1 2 3 4 5 6 7 8
(1) The current price of a bus ride is $1.00. Suppose the price increases to $1.50. Calculate the demand elasticity at this price. Is the demand elastic or inelastic at this price?
(2) Suppose you are a consultant to Metro, which finds that its revenues are not meeting cost. They plan on raising the fare by $.50. Will this improve their profit situation?
(3) Would your answer to part b. be the same if the current price were $3.00? What general rule about elasticity applies?
INCOME AND CROSS ELASTICITY
Income Elasticity of demand
Income Elasticity is a measure of how much the quantity demanded of a good responds to a change in consumers’ income, computed as the percentage change in quantity demanded divided by the percentage change in income
Definition: Let M denote consumer’s income. When income increased by and, as a result, the quantity demanded changes by , then Income elasticity is defined as
where and are the original quantity demanded and income.
Normal goods: income elasticity of demand is positive or negative?
Inferior goods: income elasticity of demand is positive or negative?
Ex) If Tom’s income goes up from $20000 to $22000, and the quantity demanded of beers he buys each week falls from 6 to 10 bottles. What is the income elasticity of demand for beer?
The Cross Elasticity of Demand
Cross elasticity is a measure of how much the quantity demanded of one good responds to a change in the price of another good, computed as the percentage change in quantity demanded of the first good divided by the percentage change in the price of the second good
Definition: Suppose there are two goods, X and Y (these two goods may be substitutes or complements.) Let PY denote the price of good Y and Qx denote the quantity demanded of good X. When the price of Y changes by and, as a result, the quantity demanded of good X changes by , then cross elasticity, denoted by , is defined as
When these two goods are substitute, cross elasticity of demand is positive or negative?
When these two goods are complement, cross elasticity of demand is positive or negative?
Ex) The price of coffee goes up from $2 to $2.5, the quantity demanded of tea will go up from 100 to 150. What is the cross-price elasticity of demand of tea?
THE ELASCITY OF SUPPLY
Elasticity of supply is a measure of how much the quantity supplied of a good responds to a change in the price of that good, computed as the percentage change in quantity supplied divided by the percentage change in price
Definition: Suppose that price changes by Ã?Â?P, and as result, quantity supplied changes by Ã?Â?S. Supply elasticity is defined as
where P1 and S1 are the original price and quantity supplied.
Relationship between slope of supply curve and supply elasticity
Similarly to the demand curve, in general,
(1) the flatter the supply curve that passes through a given point, the more elastic is the supply
(2) when supply curve shift toward right, elasticity of supply at a given point will decrease.
Factors affecting price elasticity of supply
(1) Flexibility of sellers: goods that are somewhat fixed in supply (beachfront property) have inelastic supplies.
(2) Time horizon: supply is usually more inelastic in the short run than in the long
Suppose that Crusoe and Friday live together in an island.
They survive only by gathering coconuts and fishing.
Production Possibility Frontiers (PPF) of Crusoe and Friday:
Crusoe can produce 3 fish or 3 coconuts a day or any combination of fish and coconut.
Friday can produce 4 fish or 8 coconuts a day or any combination of fish and coconut.
(1) Production Possibility Frontier for Crusoe
(2) Production Possibility Frontier for Friday
? With the same amount of time devoted to producing one good, who can
? The person whose cost of producing one unit of goods in terms of time (or
inputs) is lower is said to have absolute advantage toward that good.
Friday is more productive in both goods.
Ã¢Â?Â?Friday has absolute advantage in both goods.
? The person, whose cost of producing one good in terms of another good
(marginal cost measured by other goods) is lower than another person, is said
to have comparative advantage in it.
What are the marginal costs of these goods for Crusoe and Friday?
Marginal cost of one coconut is one fish.
Marginal cost of one fish is one coconut.
Marginal cost of one coconut is 0.5 fish
Marginal cost of one fish is two coconuts.
Crusoe has lower marginal cost in catching fish than Friday.
Ã¢Â?Â? Crusoe has comparative advantage in catching fish
(Note that this implies that Friday has comparative advantage in gathering coconuts as you can easily see. In general, if there are only two goods, then Crusoe has CA in one good automatically implies that Friday has comparative advantage another good.)
As we saw,
Crusoe has comparative advantage in FISH
Friday has comparative advantage in COCONUTS
What if Crusoe specialized in catching fish and Friday specialized in gathering coconuts?
Consider the cases:
(1) When trade is impossible,
Crusoe produces (coconuts, fish) = (2, 1) and Friday produces (coconuts, fish) = (4, 2) (these were determined according to their preference, but how it will be determined? Hint: marginal value.) Therefore, they can produce/consume (coconuts, fish) = (2+4, 1+2) = (6, 3) in total.
(2) If they can trade,
by specializing in producing fish, Crusoe can produce 3 fish, and Friday can produce 8 coconuts. Now they can produce/consume (coconuts, fish) = (8, 3)
They both can consume more coconuts by sharing coconuts (8 coconuts) they produced.
Ã¢Â?Â? Specialize in producing one good in which you have comparative advantage.
Ã¢Â?Â? We can gain by producing at lower cost.
(1) To see who has comparative advantage in a good, compare their marginal
(2) A person who has lower marginal cost in producing one good should specialize in producing that good.
Implication of Joint Production Possibility Frontier
By summing up their production possibility frontiers, we can get joint production possibility frontier
PPF for Crusoe PPF for Friday Joint PPF
Note that the joint PPF shifts to right. It is concave to the original, not a straight line. Marginal cost of coconuts is no longer constant but change from 0.5 fish (at coconuts =0~8) to 1 fish (at coconuts = 8~11.); it increases as we produce coconuts more.
What if there are more producers in this economy?
? PPF becomes more concave like:
? PPF for the entire economy exhibits increasing marginal cost when it produces more of one good. Graphically, it is concave to the origin, but not a straight line.
Ex): Rancher vs. Farmer (Sample Questions for Quiz 2)
Minutes Needed to Make 1 Ounce of:
Amount Produced in 8 Hours
1 Which has absolute and comparative advantage in which good?
2 What is the marginal costs for them for these goods
3 What would be the price range of each good, in terms of another good, if they trade?
Applications of Comparative Advantage
Answer to the following question using the concept of comparative advantage.
1. Should Tiger Woods Mw His Own Lawn ?