Download Elasticity Part 1

Elasticity Part 1
Microeconomic Theory
Associate Professor Lisa Giddings
Objectives
– Answers to last MiniQuiz
– A bit more practice and….
– Elasticity!
Note: Still Chapter 3 of Goolsbee
We are building up to LO #1!
• ECO308 LEARNING OUTCOMES
• 1. Students will be able to construct
and use supply and demand models
to determine the impact of a
microeconomic policy on equilibrium
price and output.
Last Powerpoint’s MiniQuiz
• Using the equations for processed pork, solve for the
equilibrium price and quantity in terms of consumer income.
How does equilibrium P & Q change with consumer income?
• Qd = 171 – 20p + 20pb + 3Pc + 2Y
• Qs = 178 + 40p – 60Ph
• Pb=4, Pc=3.33, Y=12.5 and ph = 1.50
• What happens if income increases by 10% (an increase of 1.25
in thousands)?
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Quick MiniQuiz to Finish Up our
S&D Model
Recall the following:
Qd = 171 – 20P + 20Pb + 3Pc + 2Y
Qs = Qs = 178 + 40p – 60Ph
With typical values: Pb=4, Pc=3.33, Y=12.5 and ph = 1.50
What is the difference between the following two
derivatives:
DQd/DPc = 3 and DQ*/DPc = 2
Can you explain what each one means?
Question from Practice Problems
• The demand function for roses is Q = a –
bP and the supply function is Q = c + eP +
ft
• Where a, b, c, e, and f are positive
constants and t is the average
temperature in a month. Show how the
equilibrium quantity and price vary with
temperature.
The Shapes of the S & D Curves
• Ok, so now we know HOW exogenous variables affect
equilibrium…. If income, for example, increases, then we
expect the demand curve to shift out, and price and
quantity to rise in equilibrium.
• We have explored this both graphically and
algebraically.
• If we have a model that describes demand and supply
explicitly, we can predict what will happen for ALL
exogenous changes fairly EXACTLY…
• Now we are going to explore how the SHAPE of demand
and supply curves matter.
Elasticity
• Elasticity is the most commonly used
measure of the sensitivity of one variable,
such as the quantity demanded, to
another variable, such as the price.
• Elasticity is a percentage change in one
variable in response to a given
percentage change of another variable
Price Elasticity of Demand
• The percentage change in the quantity
demanded, Q, in response to a given
percentage change in the price, P
• ε = (∆Q/Q )/(∆P/P)
• Range of ε: 0 > ε < ∞
• Note: Because demand curves slope downward,
the elasticity of demand is a negative number.
Realizing that, some economists ignore the
negative sign when reporting a demand
elasticity.
Interpretation of ε
• If ε < 1: Inelastic (Steep Demand Curve)
• If ε = 1: Unitary Elastic
• If ε > 1: Elastic (Flat Demand Curve)
If ε = ∞: Perfectly Elastic (Horizontal Demand
Curve)
If ε = 0: Perfectly Inelastic (Vertical Demand
Curve)
Factors that Affect ε
• The availability of substitutes
Glenn and Sara Ellison looked at the markets for different
CPUs and memory chips on a price search ending Web site.
This makes it very easy to compare multiple suppliers’ prices
for certain products. Because the product is so standardized,
little distinguishes one chip from another, so price is the
determining factor for most consumers.
Ellison and Ellison found that the price elasticity of demand
for any single chip was about -25… If the supplier raises its
price just 1% higher than that of its competitors it can expect
sales to fall by 25%.
More Factors Affecting ε
• Time Horizons
– Short Run: limited ability to change
consumption patterns
– Long Run
– Example: Gasoline
Elasticity and Linear Demand
Curves
Elasticity is NOT Slope
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So, you can see that elasticity and slope are not the same.
Let’s go back to our Tomato Market
Qd = 1,000 – 200P
The slope of this demand curve is found by looking at the inverse demand curve:
P = 5 – 0.005Qd
The coefficient on P (in the first equation - ∆Q/∆P) and on Qd (in the second equation ∆P/∆Q) tells us some things… Like The
quantity demanded falls by 200 pounds for every dollar per pound increase in price. That coefficient is
But there are problems with this:
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1. slopes depend completely on the units of measurement we choose. Suppose we measured tomato prices P in cents per pound
rather than in dollars. Now the demand curve would be Qd = 1,000 – 2P because the quantity of tomatoes demanded would fall by
2 pounds for every 1 cent increase in price. But the fact that the coefficient on P is now 2 instead of 200 doesn’t mean that
consumers are 1/100 as price sensitive as before. Actually nothing has changed about price sensitivity.
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2. You can’t compare the slopes across different products. Does the fact that consumers demand 100 fewer celery hearts for every
10 cent per celery heart increase in the price mean that consumers are more or less price elastic in the celery market than i n the
tomato market?
Using Elasticities to express responsiveness avoids these tricky issues.
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But… Elasticity is RELATED to
Slope
ε = (∆Q/Q )/(∆P/P)
Now, let’s rearrange:
(∆Q/Q )/(∆P/P) = (∆Q/Q )*(P/∆P) =
(∆Q/ ∆P)*(P/Q)
This equation should look a little more familiar. What is (∆Q/ ∆P)?
Well this LOOKS like the inverse of slope.
Remember a slope is just rise/run or ∆Y/ ∆X.
In economics terms, we have ∆P/ ∆Q,
So, ∆Q/P is just the inverse of this. ….. And isn’t that just what we have when we
are given a demand curve in the form of the following:
Q = a – bP
So ∆Q/ ∆P is just b
So…
• ε = (∆Q/ ∆P)*(P/Q)
For any given demand curve of the
following form: Qd = a – bP
Then, ε = -b(P/Q)
Where P and Q are the price and
quantity at equilibrium!
Example:
• Find the price elasticity of demand for
Tomatoes in the following market:
• Qd = 1,000 – 200P
• Qs = 200P – 200
• P* = 3 and Q* = 400
• ε = (∆Q/ ∆P)*(P/Q) = -200(3/400) = 1.5
• Are tomatoes elastic or inelastic?
MiniQuiz
• Find the price elasticity of demand for
pulled pork:
• Qd = 171 – 20p + 20pb + 3Pc + 2Y
• Qs = 178 + 40p – 60Ph
• Pb=4, Pc=3.33, Y=12.5 and ph = 1.50
ε and Expenditures and Revenue
• Interesting and Useful Relationship
between Consumer expenditures and ε :
Consumer expenditures rise with prices if
demand is inelastic, but decrease with
prices if demand is elastic.
• Why should we care?
• Total expenditure = Total Revenue = P * Q
ε and TR
ε = %∆Q/%∆P TR = P * Q
So… Check this out:
ε>1
ε <1
Increase
Price
Large decrease in Qd so
%∆Q > %∆P and TR falls
Small decrease in Qd
So %∆Q < %∆P and TR
increases
Decrease
Price
Large Increase in Qd
So %∆Q > %∆P and TR
increases
Small increase in Qd
So %∆Q < %∆P so TR falls
Revenues along a Linear
Demand
• See graph on page 52
Test this
• The demand for movie tickets in a small town is given as:
• Qd = 1000 – 50P
– 1. Calculate the price elasticity of demand when the price of
tickets is $5.
– 2. Calculate the price elasticity of demand when the price of
tickets is $12.
– 3. At what price is the price elasticity of demand “unit elastic”?
– 4. What happens to the price elasticity of demand as you move
down the demand curve?
– 5. What happens to the revenue as you move down the demand
curve?
Other Elasticities
• Income Elasticity of Demand
– Ey = (%∆Qd/%∆Y) = ∆Qd/∆y * Y/Q
– The percentage change in quantity demanded associated with
a 1% change in consumer income
– Inferior Goods: Goods that have an income elasticity that is
negative, meaning consumers demand a lower quantity of the
good when their income rises
– Normal Goods: goods with positive income elasticities
(consumers’ quantity demanded rises with their income)
– Luxury Goods: the subcategory of normal goods with income
elasticities above 1. Having an income elasticity greater than 1
means the quantity demanded of these products rises at a faster
rate than income.
Cross-Price Elasticity of Demand
• Ex = (%∆Qd1/%∆P2) = ∆Qd1/∆P2 * Ps/Qd1
• The percentage change in quantity demanded of one good
associated with a 1% change in the price of another good
– Complement Goods: Goods that have a cross price
elasticity that is negative, meaning consumers demand a
lower quantity of the good when the price of the other
good rises
– Substitute Goods: Goods that have a cross price elasticity
that is positive, meaning consumers demand a lower
quantity of the good when the price of the other good
declines
Price Elasticity of Supply
• η = (∆Qs/Qs )/(∆P/P)
• How responsive is Quantity Supplied to
changes in prices?
MiniQuiz
• Suppose that the price elasticity of
demand for cereal is -0.75 and the crossprice elasticity of demand between
cereal and the price of milk is -0.9. If the
price of milk rises by 10%, what would
have to happen to the price of cereal to
exactly offset the rise in the price of milk
and leave the quantity of cereal
demanded unchanged?