topic 03 elasticity(4)
TRANSCRIPT
Topic 3
Elasticity and Demand Estimate
(Chapter 3)Ratna K. Shrestha
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Overview
From the time Apple launched iTunes in 2003 through 2009, it charged $0.99 for each song. Music producers wanted Apple to increase price.
How can Apple determine what would happen to its revenue if they increase the price?
It depends on how the number of iTunes downloads would decrease in response to price hike (price elasticity of demand)?
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3.1 Price Elasticity of DemandIt measures the percentage change in the
quantity demanded of a good that results from a one percent change in price.
It is usually a negative numberAs price increases, quantity decreasesAs price decreases, quantity increases
dPdQ
QP
PdPQdQ
PQE D
P
%%
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Price Elasticity of Demand
When EP > 1, the good is price elastic
%Q > % PWhen EP < 1, the good is price inelastic
%Q < % PWhen EP = 1, the good is unit elastic
%Q = % P
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Price Elasticity of Demand
The primary determinant of price elasticity of demand is the availability of substitutes.If many substitute goods are available, then
demand is price elastic. For example, if the price of Pepsi increases, we can easily switch to Coke.
On the other hand, if the price of food increase, one has to buy food to survive. Thus the demand for food is inelastic.
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Price Elasticity of DemandThe availability of substitutes also depends
on how we define the market.Ex: Demand for a car (broad market) vs.
Toyota Corolla (narrowly market). Obviously demand for a Toyota car is more elastic than the demand for a car.
The more inelastic the good, the steeper the demand curve. If the demand is completely elastic, the curve is horizontal.
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Completely Elastic Demand
DP*
Quantity
Price
EP = -
A small increase in price will cause demand to drop off completely.
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Completely Inelastic Demand
Quantity
Price
Q*
D
EP = 0
Even if price increases a lot quantity demanded stays the same at Q*.
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Price Elasticity of Demand: A Case of a Linear Curve
In the case of a linear demand curve, will the price elasticity of demand be same at all points along the curve?
The answer is NO. This is because E = dQ/dP * P/Q and so even if (dQ/dP) is the same at all points, P/Q is not.
As you move downwards along the demand curve, P/Q becomes smaller and hence the demand becomes more inelastic.
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Price Elasticity of Demand: A Case of a Linear Curve
Q
Price4
8
2
4
Ep = -1
Ep = 0
EP = -
Elastic
Inelastic
Computing Point Elasticity
Consider a demand curve: Q = 8 – 2P. At the center of a liner line,
E = dQ/dP * P/Q = - 2* (2/4) = - 1 At P = 0 and Q = 8, E = - 2 * 0/8 = 0 --demand is completely inelastic. At this point the consumer has already consumed the maximum possible. So the consumer will not buy any extra for an infinitesimal change in P.
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Computing Elasticity
Price Elasticityof Demand, ED
Elasticity may be computed for a change from one point on the D curve to another point on the same curve (Arc Elasticity).
% Q =
% P =
(Q2 – Q1)/Q1
(P2 – P1)/P1
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Another approach is to divide the change by the average of two points—(Q1 + Q2)/2 instead of Q1 and (P1 + P2)/2 instead of P1.
Computing Arc Elasticity
Demand forIce Cream
2.20
2.00
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ED =(8 - 10) / 9
($2.2 - $2.0)/$2.1= - 2.33
Demand is Elastic as ED > 1. With this midpoint method, the elasticity value will be the same regardless of the direction of the movement from A to B or B to A.
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A
B
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Other Demand ElasticitiesIncome Elasticity of Demand
Measures how much quantity demanded changes with a change in income.
If it is positive, the good is normal. Suppose Q = 20 – 3P +0.03Y. What is EY
of this good? Is this good a normal or inferior good?
dYQd
QY
Y/YdQ/Qd EY
Other Demand Elasticities
Goods consumers regard as “necessities” tend to be income inelastic...Examples include: food, fuel, clothing,
utilities, & medical services.Goods consumers regard as “luxuries”
tend to be income elastic...Examples include: Sports cars, furs,
and expensive foods.
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Other Demand Elasticities
Cross-Price Elasticity of DemandMeasures the percentage change in the
quantity demanded of one good that results from a one percent change in the price of another good.
m
b
b
m
mm
bbPQ dP
dQQP
PdPQdQE
mb
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Other Demand ElasticitiesComplements:
Cross-price elasticity of demand is negative for complement goods.
For example: when the price of cars (PC) increases, quantity demanded of tires decreases.
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Other Demand Elasticities
Substitutes: Butter and MargarineCross-price elasticity of
demand is positive for substitute goods.
When price of butter increases, quantity of margarine demand rises.
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Other Demand Elasticities
In the wake of an increasing price of gasoline, the demand for fuel efficient cars has been increasing recently. Why?
Consider demand for tires
Q = 50 - 4PT – 2PC.
Find the cross price elasticity of tire demand.
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Price Elasticity of Supply
Measures the percentage change in quantity supplied resulting from a 1 percent change in price.
PQE
SSP
%%
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Demand Elasticity Over time
In general, demand is much more price elastic in the long runConsumers take time to adjust
consumption habits.Demand might be linked to another good
that changes slowly.More substitutes are usually available in
the long run.
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Demand Elasticity over Time: Gasoline
DSR
DLR
In the long run, people tend to drive smaller and more fuel efficient cars. Alternative energy cars (e.g., battery operated) may also be available.
Quantity of Gas
Price
3.2 Regression AnalysisTable 3.1 Data Used to Estimate Cod Demand at the Portland Fish Exchange
Price in $ per lb. Thousands of lbs
1.90 1.5
1.35 2.2
1.25 4.4
1.20 5.9
0.95 6.5
0.85 7.0
0.73 8.8
0.25 10.1
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Cod Data in a Diagram
We can estimate a demand curve by drawing a line or curve through these points.
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Using Regression to Estimate Demand
We want to find the “best possible” line or curve that represents this data.
We think of price as the explanatory variable and quantity as the dependent variable.
Fishing boats catch as much as they can and bring that to market. Price adjusts to clear the market.
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Inverse Demand
If we start with a standard demand curve of the form Q = a + bp (where b is negative), we can rearrange this expression to obtain p = -a/b + Q/b.
We can rewrite this as p = g + hQ where g = -a/b and h = 1/b.
This (p = -a/b + Q/b) is the inverse demand curve. It expresses the same information as the standard demand curve.
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Random ErrorWhen we observe actual data it would not
normally lie on straight line. However, we can write: p = g + hQ + e
where e is an “error”. The “error” shows the difference between the proposed linear relationship and the actual observation.
The error might be due to non-price factors that we cannot hold fixed (such as random variations in the number of buyers who show up on a particular day) .
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An Estimated Demand Curve
The observed points do not lie on the estimated line precisely, because of the random error.
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Ordinary Least Squares
The “residual” is the vertical distance between the actual price and the “predicted” price obtained from the regression line. We get our estimate of the demand curve by making the residuals small.
An “ordinary least squares (OLS)” method makes the sum of squared residuals as small as possible. This is normally done using computer programs such as Excel.
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Regression Using Excel
Carry out the following steps.
1.Put the Cod data in an Excel spreadsheet. Put Quantity in column A and Price in Column B.
2.Select the two columns of data.
3.Click on <Insert>, <Scatter>, and select the first type of scatter plot. You should see a scatter plot like Figure 3.3.
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Regression Using Excel
4. Click on Layout, then Trendline and select Linear Trendline. The estimated demand curve will appear.
5. Right Click on the line and then Format Trendline. Select Display Equation, and Display R-squared.
6. Click on and then delete the legend that appears at the right.
7. Excel uses Ordinary Least Squares Regression to get this line.
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Trendline
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Question: Effect of Changing Price
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The R2 number shows how well the estimated regression line fits the data. Thus the R2 statistic measures the goodness of fit.
If R2 = 1, then all the observed points lie on the estimated line and hence the estimated regression line perfectly fits the data.
On the other hand if the regression explains none of the variation in the dependent variable, then R2 =0.
Goodness of Fit and R2 Statistics
0
5
10
15
0 10 20 30 40
Q, Pies per day
p, $
per
pie
0
5
10
15
0 10 20 30 40
Quantity of Pies SoldP
rice
(a) R2 = 0.98 (b) R2 = 0.54
R2 = 0.54 on the right panel shows that 46% of the variation in demand is due to random errors.
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Do We Have the Right Functional Form? – Advertising and Demand
0
5
10
-4 1 6 11 16
A, Commercials per week
0
5
10
0 2 4 6 8 10 12 14 16A, Commercials per week
(a) Linear (b) Quadratic
Using a linear regression would be a mistake in this case. The actual relationship is more like a quadratic function.
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