METU
Department of Economics
Econ 101: Introduction to Economics I
All sections (010203)
Fall 2010
PROBLEM SET 4 (With Answers)
PART A PROBLEMS
1.
The table below gives the demand schedules for good A when the price of good B (P
B
) is 8 YTL and 12 YTL.
Complete the last column of the table by computing the cross elasticity of demand between goods A and B for each
of the three prices of A. Are A and B complements or substitutes?
P
B
= 8 YTL
P
B
= 12 YTL
P
A
Q
A
Q’
A
Elasticity (
ε
)
8
2000
4000
1.67
7
4000
6000
1.00
6
6000
8000
0.71
ε
1
= % Change in quantity of “A” demanded
= (4,000 – 2,000) / ((4,000 + 2,000) / 2)
= 5 / 3
% Change in price B
(12 – 8) / ((12 + 8) / 2)
ε
2
= % Change in quantity of “A” demanded
= (6,000 – 4,000) / ((6,000 + 4,000) / 2)
= 1
% Change in price B
(12 – 8) / ((12 + 8) / 2)
ε
3
= % Change in quantity of “A” demanded
= (8,000 – 6,000) / ((8,000 + 6,000) / 2)
= 5 / 7
% Change in price B
(12 – 8) / ((12 + 8) / 2)
Since the cross elasticities are positive, we know that A and B are substitutes.
2.
a)
Calculate price elasticity of demand for the functions when P=8 and when P=6.
i) P = 40 – 0.5Q or Q = 80 – 2P so
u
Q /
u
P = – 2
When P = 8, Q = 64, thus
ε
= – 0.25 where
ε
= (
u
Q/
u
P)*P/Q
When P = 6, Q = 68, thus
ε
= – 0.176
ii)
Q = – 4+0.75P
→
u
Q/
u
P = 0.75
When P = 8, Q = 2 thus
ε
= 3
When P = 6, Q = 0.5 thus
ε
= 9
iii)
4Q + 4P = 64 thus Q = 16 – P so
u
Q/
u
P = 1
When P = 8, Q = 8 thus
ε
= 1
When P = 6, Q = 10 thus
ε
= 0.6
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Documentb)
Calculate the arc elasticity of demand between P = 6 and P = 8 for (ii)
Q = – 4 + 0.75P
When P = 8, Q = 2 & When P = 6, Q = 0.5
Arc elasticity of demand = % Change in quantity demanded
= (2 – 0.5) / ((2 + 0.5) / 2)
= 4.2
% Change in price
(8 – 6)/ ((8 + 6)/2)
3.
a)
Find the equilibrium price and quantity.
100 – 2P = – 20+4P
P* = 20
Q* = 60
b)
Find the
point elasticity
of demand and supply at the equilibrium.
ε
D
=
u
Q
D
/
u
P * P / Q = –2*20 / 60 = –2 / 3
ε
S
=
u
Q
S
/
u
P * P / Q = 4*20 / 60 = 4 / 3
c)
Find the price and quantity where
price elasticity
of demand is unitary.
ε
D
=
u
Q
D
/
u
P * P / Q
D
=>
–1 = –2* P / Q
D
=>
2P = Q
D
D
= 100
Thus, 4P = 100
=>
P = 25 & Q = 50
d)
Find the
maximum expenditures
by consumers (TR) given their demand.
Max Expenditure by Consumers = 25 * 50 = 1,250
4.
The following table shows the price and yearly quantity of Tshirts according to average income.
Tshirt price
Quantity demanded
(average
income is $20,000)
Quantity demanded
(average
income is $30,000)
$4.50
2,400
3,600
$5.50
1,600
2,800
$6.50
800
2,400
$7.50
400
1,800
a)
Calculate the price elasticity of demand (using the midpoint method) when the price of Tshirts rises
from $4.50 to $5.50, when average income is $20,000.
% Change in quantity demanded = (1,600 – 2,400) / ((1,600 + 2,400) / 2)*100% = – 40%
This is the end of the preview. Sign up
to
access the rest of the document.
 Spring '11
 gulipektunc
 Economics, Microeconomics

Click to edit the document details