Elasticity
Elasticity and slope of demande curve
Elasticity of Demand
Part a
1. There are several ways of finding out the price elasticity of demand () , depending on the type of data.
(a) Percentage change:
i. What is the formula?
ii. Suppose P increased from 100 to 120 and QD went down from 250 to 200. Using this method, find out || .
iii. Suppose P decreased from 120 to 100 and QD increased from 200 to 250. Using this method, find out || .
(b) Mid-point:
i. What is the formula?
ii. Suppose P increased from 100 to 120 and QD went down from 250 to 200. Using this method, find out || .
(c) Slope of demand:
i. What is the relationship between and the slope of a demand curve?
ii. Find out using this method for the following demand curves at P = 50.
A. P = 901.25Q
B. Q = 9000.5P 0.25P2
C. Q = 50+ 7500
P
(d) Slope of the demand after (natural) logarithmic transformation:
i. What is the relationship between and the slope of a demand curve after (natural) logarithmic transformation(
d(lnQ)
d(lnP)
)
?
ii. Find out using this method for the following demand curve at P = 10 : lnQ = 112lnP
(e) Marginal revenue:
i. What is the relationship between || and marginal revenue?
ii. When TR is maximized, how much is MR and hence how much is ||?
iii. If P = 30 and MR = 24, then how much is ||?
Part b
2. Linear demand
(a) Prove mathematically that along a linear demand, || decreases as P decreases.
(b) Suppose the vertical intercept of a linear demand is 78. What can you say about || at P = 52?
(c) Suppose the horizontal intercept of a linear demand is 40. What can you say about || at Q = 16?
(d) Suppose two linear demand curves D1 and D2 have the same vertical intercept and D1 is steeper than D2.
i. At any given P , which demand is more elastic?
ii. At any given Q, which demand is more elastic?
(e) Suppose two linear demand curves D1 and D2 are parallel to each other and D1 is higher than D2.
i. At any given P , which demand is more elastic?
ii. At any given Q, which demand is more elastic?
3. What is the difference between a “constant slope” demand curve and a “constant elasticity” demand curve? Give
examples for each one of them.
4. Data analysis
Go to the excel sheet titled Elasticity Data.xlsx in the modules section. In that file, you can find 3 columns for Q,P
and I. First, use natural log transformation (using the function LN in excel to transform the entire data set to create
3 new columns for lnQ, lnP and lnI. Then run a regression analysis with lnQ being the Y or dependent variable
and lnP, lnI being the X or independent variable. (Make sure your data analysis package in excel is active, you can
check that by going to the Options under Files tab in excel; if you need help with this regression, google it or set up an
appointment with me.) Once you are done with the regression, interpret the coeffi cients in terms of elasticities. Data for IN
Quantity Price Income
83 30.85 31.9
83 31.94 31.77
97 30.69 36.86
103 32.27 40.79
101 32.39 37.06
88 30.01 34.03
81 30.35 33.52
99 30.58 32.78
98 30.1 37.02
103 27.43 35.88
102 27.02 36.01
88 30.24 32.55
105 28.84 37.14
98 29.57 33.84
93 31.17 35.82
88 32.17 35.68
92 32.21 36.24
92 29.43 33.66
86 34.07 34.85
93 29.79 32.51
86 35.54 34.97
87 30.13 33.81
108 26.26 35.24
88 33.13 37
98 30.3 38.6
92 27.94 30.02
93 32.07 36.88
99 30.51 36.15
105 27.23 36.09
88 33.37 36.44
97 29.75 34.99
93 29.44 31.71
101 28.6 34.46
90 30.71 32.6
106 32.35 40.61
87 32.57 36.37
98 31.61 37.34
89 30.08 32.81
83 34.49 34.1
104 27.52 32.3
97 30.08 35.26
76 34.35 32.25
98 28.59 33.53
82 34.75 34.15
94 29.51 33.95
99 30.72 35.66
89 35.61 34.48
75 36.19 34.09
92 30.78 35.15
97 32.75 37.34
