microeconomics final exam help
1
IV. Elasticities
A. Show the responsiveness of quantity supplied or quantity demanded to a change in another variable
1. Good´s own price
a) Price elasticity of supply
b) Price elasticity of demand
2. Income-income elasticity of demand
3. Price of a related good (in consumption)-cross elasticity of demand.
4. An elasticity is expressed as a ratio of two percentages
a) Suppose a price increase of 20% leads to a 12% decrease in quantity demanded. The price elasticity of demand is −.12
.20 = −.6
b) Suppose a price decrease of 10% causes a 25% decrease in quantity supplies .25
.10 = 2.5
c) Suppose a 5% increase in income causes a 5% reduction in demand for the good −.05
.05 = −1
(1) What does this say about the type of good?
(2) Inferior good
B. Price elasticity of demand-3 methods to calculate
1. Return to pizza example.
a) 3 of the price quantity combinations
(1) 40 KD 10 pizzas
(2) 30 KD 25 pizzas
(3) 20 KD 50 pizzas
2
b) Use the first two combinations to start-price drops from 40 KD to 30 KD
(1) Percentage change in the quantity of pizza 25−10 25+10( ) /2
= 15 17.5
= 30 35
=.86
(2) Percentage change in the price of pizza 30−40 30+40( ) /2
= − 10 35
= −.29
(3) Price elasticity of demand εd = − .86 .29
= −3
c) Use the second and third-price drops from 30 KD to 20 KD
(1) Percentage change in the quantity of pizza 50−25 50+25( ) /2
= 50 75
=.67
(2) Percentage change in the price of pizza 20−30 20+30( ) /2
= − 10 25
= −.4
(3) Price elasticity of demand εd = − .67 .4
= −1.7
d) Notice that putting the average in the denominator of each percentage change means that the elasticity will be the same whether price falls or price rises.
e) This manner of calculating the elasticity (with the average percentage change in the denominator) is called arc elasticity. Arc because it is between two points.
2. Another way to calculate the price elasticity of demand
a) This manner gives point elasticity, meaning the elasticity at a specific point. Since we need to use the slope of the demand curve in the calculation we will only use this method for a demand schedule that is a straight line.
3
b) ExampleQd = 200−2P
(1) Draw graph showing extreme points.
(2) We can use any two points on the demand to find the line slope. Slope is -½.
(3) Inverse of slope is -2
(4) Now take any P,Q combination that satisfies the demand equation and the elasticity is !
!"!"# ! ! = 𝜀!
(a) Example-1 50 KD, 100 pizzas −𝟐 𝟓𝟎
𝟏𝟎𝟎 = −𝟏
(b) Example-2 75 KD, 50 pizzas −𝟐 𝟕𝟓
𝟓𝟎 = −𝟑
(c) Example-3 25 KD,150 pizzas −𝟐 𝟐𝟓
𝟏𝟓𝟎 = − 𝟏
𝟑
(5) In talking about price elasticity of demand the negative sign is frequently ignored since we all know the actual elasticity must be negative due to the law of demand.
(a) If εd = -1, unit or unitary elasticity of demand (with respect to price). Example 1
(b) If εd < -1, elastic demand. Example 2
(c) If 0 > εd > -1, inelastic demand. Example 3
3. Yet another way
a) If you understand calculus the following form might make more sense to you. Otherwise you need not worry about the following.
b) 𝜺𝒅 = 𝒅𝑸𝒅 𝒅𝑷
𝑷 𝑸
4. Extreme cases
a) Perfectly inelastic demand
4
(1) Demand schedule is a vertical line
(2) 𝜀! = 0
(3) An example might be certain drugs, insulin for example, that must be taken in the prescribed dosage to maintain health. Demand for the drug does not fluctuate with price.
b) Perfectly elastic demand
(1) Demand schedule is a horizontal line
(2) 𝜀! = −∞
(3) We will see this case when we talk about a firm in a perfectly competitive market (to be defined later in the course).
5. Factors affecting the price elasticity of demand
a) Availability of substitutes
(1) A good that has few substitutes tends to have inelastic demand (0 > εd > -1), quantity demanded is not very responsive to price.
(a) Cigarettes
(b) Drug like insulin
(c) Oil
(2) A good that has many substitutes tends to have elastic demand (εd < -1), quantity demanded is very responsive to price.
(a) Pizza
(b) Soft drinks
b) Unimportance of the good in one’s budget
(1) Tend not to respond much to price changes of goods that are a very small share of one’s budget.
(2) That is the good tends to be inelastic.
(3) Examples
5
(a) Salt
(b) Detergent
c) Time
(1) Over short time horizons demand for a good tends to be inelastic. Oil in 1973-price increased
(a) Difficult to quickly adjust driving habits when price rises
(b) Difficult to switch to smaller cars, alternative transport when price rises.
(c) Electricity prices increased.
(2) Over longer time horizons, demand is more elastic.
(a) Adjust driving habits
(b) Switch to smaller and more fuel efficient vehicles
(c) Replace older appliances with those that use less electricity
C. Price elasticity of supply
1. Return to pizza example
a) 3 of the price quantity combinations
(1) 40 KD 80 pizzas
(2) 30 KD 70 pizzas
(3) 20 KD 50 pizzas
b) Use the first two to start-price drops from 40 KD to 30 KD
(1) Percentage change in the quantity of pizza 70−80 70+80( ) /2
= − 10 75
= − 2 15
= −.13
(2) Percentage change in the price of pizza 30−40 30+40( ) /2
= − 10 35
= −.29
6
(3) Price elasticity of supply 𝜀! = .!" .!" = .45
c) Use the second and third-price drops from 30 KD to 20 KD
(1) Percentage change in the quantity of pizza 50−70 50+70( ) /2
= − 20 60
= −.33
(2) Percentage change in the price of pizza 20−30 20+30( ) /2
= − 10 25
= −.4
(3) Price elasticity of supply 𝜀! = .!! .! = .83
d) Notice that putting the average in the denominator of each percentage change means that the elasticity will be the same whether price falls or price rises.
e) Again, an elasticity calculated in this manner (with the average in the denominator) is called arc elasticity. Arc because it is between two points.
2. Another way to calculate elasticity if we have a straight line supply schedule.
a) This manner gives point elasticity, elasticity at a specific point.
b) Straight line like 𝑸𝒔 = 𝟓𝑷 − 𝟖𝟎
(1) Graph showing vertical axis intercept at 16 KD
(2) Slope is ! ! . Inverse of the slope is 5
(3) Take any P,Q combination that satisfies the equation then elasticity is
! !"#$%
! ! = 𝜀!
(a) Example-1 20 KD, 20
𝟓𝟐𝟎 𝟐𝟎 = 𝟓
(b) Example-2 40 KD, 120
7
𝟓 𝟒𝟎 𝟏𝟐𝟎
= 𝟓 𝟑 = 𝟏.𝟔𝟔
(c) Example-3 100 KD, 420
𝟓𝟏𝟎𝟎 𝟒𝟐𝟎
= 𝟏.𝟐
(4) Size of the price elasticity of supply
(a) If εs = 1, unit or unitary elasticity of supply (with respect to price)
(b) If εs > 1, elastic supply
(c) If εs < 1, inelastic supply
3. Yet another way
a) If you understand calculus
b) εs = dQs dP
P Q
4. Extreme cases
a) Perfectly inelastic supply
(1) Supply schedule is a vertical line
(2) 𝜀! = 0
(3) Example would be a good for which supply cannot be changed in the short run. Supply of fish in the market cannot vary day to day. Supply of apartments cannot be changed over the short run.
b) Perfectly elastic supply
(1) Supply schedule is a horizontal line
(2) 𝜀! = +∞
D. Income elasticity of demand
1. Measure of the responsiveness of demand for a good to changes in income.
2. Ratio of two percentages
8
a) Suppose income increases 5% and demand increases 12% then εy =
12 5 = 2.4 Note this must be a
normal good
b) Suppose income decreases 10% and demand increases 6% then εy = −
6 10
= −.6 Note this must be an
inferior good.
3. Again we use an arc elasticity measure.
a) Suppose income in the United States as measured by gross domestic product increases from 9.5 trillion to 10.5 trillion. By the arc measure, the percent change in income is 10.5−9.5
10.5+9.5( ) /2 =.1 or 10%.
b) Suppose that the quantity demanded of cars goes from 4.5 million to 5.5 million 5.5−4.5
5.5+4.5( ) /2 =.2 or
20%
c) Income elasticity of demand is .2 .1 = 2 . Why can
we conclude that cars are a normal good?
(1) A normal good is one whose demand increases (D shifts right) when income increases and vice versa. . Thus 𝜀! > 0
(a) Thus either demand rises (positive percentage change) when income rises (positive percentage change) or
(b) demand falls (negative percentage change) when income falls (negative percentage change)
(c) The income elasticity of demand is either the ratio of two positive percentage changes or two negative percentage changes thus always positive for a normal good.
(2) An inferior good is one whose demand increases (D shifts right) when income decreases and vice versa. Thus 𝜀! < 0
9
(a) Thus either demand rises (positive percentage change) when income falls (negative percentage change) or
(b) demand falls (negative percentage change) when income rises (positive percentage change)
(c) The income elasticity of demand is the ratio of a positive percentage changes and a negative percentage change thus always negative for an inferior good.
E. Cross elasticity of demand
1. Ratio of the percentage change in the quantity demanded caused by a percentage change in the price of another good. Goods A and B 𝜀! =
%!!! !
%!!!
2. Cross elasticity values
a) εc = 0
(1) Goods must be unrelated.
(2) A price change in one has no effect on the quantity demanded of the other.
b) εc > 0
(1) A price increase (decrease) in one increases (decreases) the quantity demanded of the other.
(2) The goods are substitutes
(3) Example: the price of tea increases causing the demand for coffee to increase.
c) εc < 0
(1) A price increase (decrease) in one decreases (increases) the quantity demanded of the other.
(2) The goods are complements
(3) Example: the price of tea increases causing the demand for sugar to decrease.