ECON 101 Tutorial: Week 2
Shane Murphy
s.murphy5@lancaster.ac.uk
Office Hours: Monday 3:00-4:00 – LUMS C86
Outline
•
•
•
•
•
Substitute Lecturer Next Week
Roll Call
Class Rep
Problems
Discussion
Class Rep
Exercise
Consider the following demand function: QA=1008PA+0.5PB+2Y, where QA is the quantity demanded of
good A, PA is the price of good A, PB is the price of good B
and Y is the income.
a) If PA =7, PB=12 and Y=4.5 calculate the price elasticity
of demand of good A. Is the demand elastic or
inelastic?
First, let us solve for QA
QA= 100 - 8PA + 0.5PB + 2Y
= 100 – 8 (7) + 0.5 (12) + 2 (4.5)
= 100 – 56 + 6 + 9 = 59
Exercise
Consider the following demand function: QA=1008PA+0.5PB+2Y, where QA is the quantity demanded of
good A, PA is the price of good A, PB is the price of
good B and Y is the income.
a) If PA =7, PB=12 and Y=4.5 calculate the price
elasticity of demand of good A. Is the demand elastic
or inelastic?
Exercise
a) If PA =7, PB=12, Y=4.5 and QA= 59, and QA=1008PA+0.5PB+2Y calculate the price elasticity of
demand of good A. Is the demand elastic or
inelastic?
Ped = dQA/dPA * PA/QA
dQA/dPA = -8
ped = dQA/dPA * PA/QA = -8 * 7/59 = -56/59
By convention, we write ped = 56/59 (positive)
Elasticity of Demand is Inelastic (ped<1)
Exercise
b) If PA =7, PB=12, Y=4.5 and QA= 59, and QA=1008PA+0.5PB+2Y calculate the calculate the income
elasticity. What kind of good is A? (Normal/Inferior?
If normal then necessity or luxury?)
ied = dQA/dY * Y/QA
dQA/dY = 2
ied = dQA/dY * Y/QA = 2 * 4.5/59 = 9/59
This is a normal good (ied>0)
This is a necessity (0<ied<1)
Exercise
c) If PA =7, PB=12, Y=4.5 and QA= 59, and QA=1008PA+0.5PB+2Y calculate the cross price elasticity.
What kind of goods are A and B? (Complements
or substitutes?)
cped = dQA/dPB * PB/QA
dQA/dPB = 0.5
cped = dQA/dPB * PB/QA = 0.5 * 12/59 = 6/59
These goods are substitutes (cped > 0)
Exercise 5
Suppose that your demand
Schedule for DVDs is as follows:
Price Quantity
Demanded
(Y = 10,000)
Quantity
Demanded
(Y = 12,000)
8
40
50
10
32
45
12
24
30
14
16
20
16
8
12
a) Use the midpoint method to calculate your price elasticity
of demand as the price of DVDs increases from 8 to 10 for
income of 10,000 and income of 12,000.
Income of 10,000:
ped = [(QA – QB)/([QA + QB]/2)/[(PA – PB)/([PA + PB]/2)
= [(40 – 32)/([40 + 32]/2)/[(8 – 10)/([8 + 10]/2)
= (8/36)/(-2/9)
= -4/4 = -1
Exercise 5
Suppose that your demand
Schedule for DVDs is as follows:
Price Quantity
Demanded
(Y = 10,000)
Quantity
Demanded
(Y = 12,000)
8
40
50
10
32
45
12
24
30
14
16
20
16
8
12
a) Use the midpoint method to calculate your price elasticity
of demand as the price of DVDs increases from 8 to 10 for
income of 10,000 and income of 12,000.
Income of 12,000:
ped = [(QA – QB)/([QA + QB]/2)/[(PA – PB)/([PA + PB]/2)
= [(50 – 45)/([50 + 45]/2)/[(8 – 10)/([8 + 10]/2)
= (5/47.5)/(-2/9)
= -45/95 = -0.47
Exercise 5
Suppose that your demand
Schedule for DVDs is as follows:
Price Quantity
Demanded
(Y = 10,000)
Quantity
Demanded
(Y = 12,000)
8
40
50
10
32
45
12
24
30
14
16
20
16
8
12
b) Use the midpoint method to calculate your income elasticity of
demand as your income increases from 10,000 to 12,000 for
price of 12 and price of 16.
Price of 12:
ied = [(QA – QB)/([QA + QB]/2)/[(YA – YB)/([YA + YB]/2)
= [(24 – 30)/([24 + 30]/2)/
[(10,000 – 12,000)/([10 ,000+ 12,000]/2)
= (-6/27)/(-2/11)
= 66/54 = 1.22
Exercise 5
Suppose that your demand
Schedule for DVDs is as follows:
Price Quantity
Demanded
(Y = 10,000)
Quantity
Demanded
(Y = 12,000)
8
40
50
10
32
45
12
24
30
14
16
20
16
8
12
b) Use the midpoint method to calculate your income elasticity of
demand as your income increases from 10,000 to 12,000 for
price of 12 and price of 16.
Price of 16:
ied = [(QA – QB)/([QA + QB]/2)/[(YA – YB)/([YA + YB]/2)
= [(8 – 12)/([8 + 12]/2)/
[(10,000 – 12,000)/([10 ,000+ 12,000]/2)
= (-4/10)/(-2/11)
= 44/20 = 2.2
Exercise 7
Consider public policy aimed at smoking
a) Studies indicate the ped for cigarettes is about 0.4. If a packed of
cigarettes is currently priced at 6 and the government wants to reduce
smoking by 20%, by how much should it increase the price?
b) If the government permanently increases the price of cigarettes, will the
policy have a larger effect on smoking one year from now or five years
from now?
c) Studies also find that teenagers have a higher price elasticity of demand
for cigarettes than do adults. Why might this be true?
a)
ped = % change in Q/% change in P
0.4 = -0.2/% change in P
% change in P = -0.2/0.4 = -1/2
price should increase by 50 percent (4 using the midpoint method)
b)
Goods tend to be more elastic over longer time horizons, so the policy
will have a smaller effect in the short run than the long run
Exercise 7
Consider public policy aimed at smoking
a) Studies indicate the ped for cigarettes is about 0.4. If a packed of cigarettes is
currently priced at 6 and the government wants to reduce smoking by 20%, by
how much should it increase the price?
b) If the government permanently increases the price of cigarettes, will the policy
have a larger effect on smoking one year from now or five years from now?
c) Studies also find that teenagers have a higher price elasticity of demand for
cigarettes than do adults. Why might this be true?
c)
ped might be a function of income
as income increases, elasticity falls
ped might be a function of age
as people get older, they are less flexible, and have more inelastic
demand functions
ped might be a function of the experiences of the consumer
Older smokers might be more addicted and less elastic to price
changes
Older smokers might have a taste for fewer substitutes for smoking