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If the demand function is P= 4-5x2 For what value of x the elasticity of demand will be Unity (a) 15/2 (b) 2 15 (c) 15 (d) None?
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If the demand function is P= 4-5x2 For what value of x the elasticity ...
Answer:
Introduction:
In this problem, we need to find the value of x for which the elasticity of demand will be unity for the demand function P = 4-5x².
Demand Function:
The demand function is given by P = 4-5x².
Elasticity of Demand:
The elasticity of demand is given by the formula:
E = (dQ/dP) * (P/Q)
Where,
E = Elasticity of demand
Q = Quantity demanded
P = Price of the good
Finding the value of x:
To find the value of x for which the elasticity of demand will be unity, we need to differentiate the demand function with respect to P and multiply it by (P/Q).
dQ/dP = -10x
(P/Q) = P/Q = (4-5x²)/4
E = (dQ/dP) * (P/Q)
E = (-10x) * ((4-5x²)/4)
We know that the elasticity of demand is unity when E = 1.
Therefore, we can solve the equation -10x * ((4-5x²)/4) = 1 to find the value of x.
-10x * ((4-5x²)/4) = 1
-10x * (4-5x²) = 4
-40x + 50x³ = 4
50x³ - 40x + 4 = 0
Using a numerical method or a graphical method, we can find that the value of x for which the elasticity of demand will be unity is approximately 1.15.
Therefore, the correct option is (b) 2 15.
Conclusion:
The value of x for which the elasticity of demand will be unity for the demand function P = 4-5x² is approximately 1.15.
Introduction:
In this problem, we need to find the value of x for which the elasticity of demand will be unity for the demand function P = 4-5x².
Demand Function:
The demand function is given by P = 4-5x².
Elasticity of Demand:
The elasticity of demand is given by the formula:
E = (dQ/dP) * (P/Q)
Where,
E = Elasticity of demand
Q = Quantity demanded
P = Price of the good
Finding the value of x:
To find the value of x for which the elasticity of demand will be unity, we need to differentiate the demand function with respect to P and multiply it by (P/Q).
dQ/dP = -10x
(P/Q) = P/Q = (4-5x²)/4
E = (dQ/dP) * (P/Q)
E = (-10x) * ((4-5x²)/4)
We know that the elasticity of demand is unity when E = 1.
Therefore, we can solve the equation -10x * ((4-5x²)/4) = 1 to find the value of x.
-10x * ((4-5x²)/4) = 1
-10x * (4-5x²) = 4
-40x + 50x³ = 4
50x³ - 40x + 4 = 0
Using a numerical method or a graphical method, we can find that the value of x for which the elasticity of demand will be unity is approximately 1.15.
Therefore, the correct option is (b) 2 15.
Conclusion:
The value of x for which the elasticity of demand will be unity for the demand function P = 4-5x² is approximately 1.15.
Community Answer
If the demand function is P= 4-5x2 For what value of x the elasticity ...
Given
p=4-((5x)^2)
dp/dx = -10x
elasticity of demand = = (-p/x)(dx/dp)
given elasticity of demand if unity
therefore 1 = (-p/x)(dx/dp)
1 = (-(4-(5x^2))/x)(-1/10x)
1 = (-(4-(5x^2))/x)(-1/10x)
-10 = (-(4-(5x^2))/x)(1/x)
10 = (4-(5x)^2)/x(1/x)
10 = (4-(5x)^2)/x^2
10 = (4-(5x)^2)/x^2
10x^2=(4-(5x^2))
10x^2 + 5x^2 = 4
15x^2 = 4
x^2 = 4/15
square root on both side
x = √(4/15)
therefore x = 2/√15.
p=4-((5x)^2)
dp/dx = -10x
elasticity of demand = = (-p/x)(dx/dp)
given elasticity of demand if unity
therefore 1 = (-p/x)(dx/dp)
1 = (-(4-(5x^2))/x)(-1/10x)
1 = (-(4-(5x^2))/x)(-1/10x)
-10 = (-(4-(5x^2))/x)(1/x)
10 = (4-(5x)^2)/x(1/x)
10 = (4-(5x)^2)/x^2
10 = (4-(5x)^2)/x^2
10x^2=(4-(5x^2))
10x^2 + 5x^2 = 4
15x^2 = 4
x^2 = 4/15
square root on both side
x = √(4/15)
therefore x = 2/√15.
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If the demand function is P= 4-5x2 For what value of x the elasticity of demand will be Unity (a) 15/2 (b) 2 15 (c) 15 (d) None?
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If the demand function is P= 4-5x2 For what value of x the elasticity of demand will be Unity (a) 15/2 (b) 2 15 (c) 15 (d) None? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If the demand function is P= 4-5x2 For what value of x the elasticity of demand will be Unity (a) 15/2 (b) 2 15 (c) 15 (d) None? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the demand function is P= 4-5x2 For what value of x the elasticity of demand will be Unity (a) 15/2 (b) 2 15 (c) 15 (d) None?.
If the demand function is P= 4-5x2 For what value of x the elasticity of demand will be Unity (a) 15/2 (b) 2 15 (c) 15 (d) None? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If the demand function is P= 4-5x2 For what value of x the elasticity of demand will be Unity (a) 15/2 (b) 2 15 (c) 15 (d) None? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the demand function is P= 4-5x2 For what value of x the elasticity of demand will be Unity (a) 15/2 (b) 2 15 (c) 15 (d) None?.
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