b)
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
=
uni2206
Q
D
/
uni2206
P * P / Q = –2*20 / 60 = –2 / 3
ε
S
=
uni2206
Q
S
/
uni2206
P * P / Q = 4*20 / 60 = 4 / 3
c)
Find the price and quantity where
price elasticity
of demand is unitary.
ε
D
=
uni2206
Q
D
/
uni2206
P * P / Q
D
=>
–1 = –2* P / Q
D
=>
2P = Q
D
& 2P+Q
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 T-shirts according to average income.
T-shirt 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 T-shirts 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%
% Change in price = (5.5 – 4.5) / ((4.5 + 5.5) / 2)*100% = 20%
Price elasticity of demand =
,
D P
ε
= % Change in quantity demanded / % Change in price = – 2
b)
Calculate the income elasticity of demand (using the midpoint method) when average income increases
from $20,000 to $30,000, when the price of a T-shirt is $4.50.
% Change in quantity demanded = (3,600 – 2,400) / ((3,600 + 2,400) / 2)*100% = 40%
% Change in income = (30,000 – 20,000) / ((30,000 + 20,000) / 2)*100% = 40%
Income elasticity of demand =
,
D Y
ε
= % Change in quantity demanded / % Change in income = 1