7.2.4 Suppose the demand function for beer is given by q= 3p-1/4 %3D where p denotes price and q quantity supplied. Find the elasticity of demand. [The same method gives the elasticity of demand for any demand function of the form q = ap°, where a and b are positive real numbers. The result of part (ii) of the final part of Problem 6-4 is true in this more general case.]
7.2.4 Suppose the demand function for beer is given by q= 3p-1/4 %3D where p denotes price and q quantity supplied. Find the elasticity of demand. [The same method gives the elasticity of demand for any demand function of the form q = ap°, where a and b are positive real numbers. The result of part (ii) of the final part of Problem 6-4 is true in this more general case.]
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![7.3 MONOTONIC FUNCTIONS
125
7.2.4 Suppose the demand function for beer is given by
q= 3p-1/4
where p denotes price and q quantity supplied. Find the elasticity of demand.
[The same method gives the elasticity of demand for any demand function of the
form q =
ap-", where a and b are positive real numbers. The result of part (ii) of
the final part of Problem 6-4 is true in this more general case.]
7.2.5 Suppose that a firm's output Q is related to labour input L by the production
function
Q = L2/5.
Suppose further that L is given by the linear function
L = 4+3t.
Find dQ/dt.
7.2.6 Using the composite function rule, show that
d.
1 dv
d.x
v2 dx
Using this result and the product rule, derive the quotient rule.
.2.7 In Example 2 of Section 7.1, we used the quotient rule to show that
x2
dy
a(2- a)
if
then
y =
(22² – x + 1)² "
x2 - x + 1
d.x
Obtain the same result by writing y = u-, where u = 1- x-1 +x-2, and usi
the composite function rule.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9378ef80-7767-4c68-bae6-da61c50171e5%2F45d7195e-abff-479b-95c8-8c25c6006f49%2Fsb8cj2uh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:7.3 MONOTONIC FUNCTIONS
125
7.2.4 Suppose the demand function for beer is given by
q= 3p-1/4
where p denotes price and q quantity supplied. Find the elasticity of demand.
[The same method gives the elasticity of demand for any demand function of the
form q =
ap-", where a and b are positive real numbers. The result of part (ii) of
the final part of Problem 6-4 is true in this more general case.]
7.2.5 Suppose that a firm's output Q is related to labour input L by the production
function
Q = L2/5.
Suppose further that L is given by the linear function
L = 4+3t.
Find dQ/dt.
7.2.6 Using the composite function rule, show that
d.
1 dv
d.x
v2 dx
Using this result and the product rule, derive the quotient rule.
.2.7 In Example 2 of Section 7.1, we used the quotient rule to show that
x2
dy
a(2- a)
if
then
y =
(22² – x + 1)² "
x2 - x + 1
d.x
Obtain the same result by writing y = u-, where u = 1- x-1 +x-2, and usi
the composite function rule.
Expert Solution
Step 1
The demand function given is a constant elasticity demand function. A constant elasticity demand function is of the form . It is also known as a log-linear demand curve.
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