13 February 2006 Reading Baye, Ch 3. pp 73-82
Collect Handout Problem #4
Lecture 12
REVIEW______:
II. Chapter Market Forces: Demand and Supply
D. Equilibrium. Putting Supply and Demand Together
Equilibrium is
1. Stable
2. Socially desirable
E. Comparative Statics.
1. Single market changes.
2. Multiple Market Changes
Preview______
III. Quantitative Demand Analysis
A. Price Elasticity of Demand
1. Motivation
2. Calculation
a. Arc price elasticity of demand:
b. Point price elasticity of demand
c. Percentage Changes
Lecture ______
III. Chapter 3. Quantitative Demand Analysis
Introduction: In the preceding chapter we reviewed the basic supply and demand model used to predict price and quantity outcomes. This model is an extremely useful device for making qualitative predictions. An important limitation of the model as it has been presented, however, is that it does not allow quantitative predictions. For quantitative predictions, it is necessary to more fully characterize the arguments in the demand and supply functions.
We start with demand in this chapter. The presentation is divided into two parts. The first will deal with the quantitative conclusions that may be fairly limited elasticity information. In the second part, we turn more comprehensive analysis of demand estimation via the use of regression.
A. Price Elasticity of Demand
1. Motivation: Elasticity this is a tool for estimating responsiveness of some dependent variable to a change in a dependent variable, based on very little information.
Definition: Elasticity: The percentage change in an independent variable brought about by a 1% change in an independent variable.
Intuitively, elasticity may be regarded as a measure of sensitivity. If people are sensitive, we will say that they are elastic. If they are insensitive, we will regard them as inelastic.
For concreteness, we will focus initially on price elasticity of demand (change definition accordingly)
Price Elasticity of Demand: The percentage change in Quantity Demanded brought about by a 1% change in the price of a good, or
h = %DQd/%DP = DQ/Q = DQP
DP/P DPQ
2. Calculating Elasticity of Demand. There are three ways to calculate price elasticity of demand: arc price elasticity, point price elasticity, and direct percentage changes. The method that is appropriate in any particular context depends on the information provided.
a. Arc Price Elasticity. Applies to a discrete change. For example, consider the demand curve implied by the following table:
P Q
4 40
5 10
P5
4 / D
10 40 Q
Notice DQ may be calculated as Q1-Q0, and
DP = P1-P0. Then h = (Q1-Q0)P/(P1-P0)Q
But it makes a big difference if you use (P0,Q0) as your divisor, or (P1,Q1).
For example:
(40-10) (4) = 30(4) = -3.00
(4-5) (40) -1(40)
(40-10) (5) = 30(5) = -15.00
(4-5) (10) -1(10)
Neither of these points is inherently more correct. As a convention, we calculate the arc price elasticity of demand using the average of the distance between the 2 points:
h = (Q1-Q0)(P1+P0)/2
(P1-P0)(Q1+Q0)/2.
In this case
= (40-10) (4+5)/2 = 30(4.5) = -5.4
(4-5) (40+10)/2 -1(25)
Arc Price elasticity is interpreted as follows: Over the range of prices between $4 and $5 on average, a 1% reduction in price increases quantity demanded by 5.4 %.
b. Point price elasticity: When you are given a slope, and a point.
Insight h = (dQ/dP)(P/Q)
Example: Suppose a demand curve is
Q = 30 - 10P
Then, if P = 2, then Q=10 and elasticity is
-10 ( 2/10) = -2.
Uses: Mostly when given a demand function.
Point Price elasticity is interpreted as follows: At a price of $2 a 1% reduction in price increases quantity demanded by 2 %.
c. Percentage changes. For rough policy purposes.
Insight h = (%DQ)/(%DP)
Example. Suppose that beer sales at Joe's Inn increased 20% in response to a “half price” (50% off night). What is the implied elasticity of demand?
-20/ 50 = -.4
Example: Suppose that Joe sells 400 beers per day. What would be the effect of a 10% increase in beer prices on his sales?
-.4 = %DQ/10 implies 4 % decrease, or a decrease of .04(400) = 16 beers per day.