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The demand function is given by p = (10-2x) (20-2x) where x= demand and P= Price . find elasticity of demand w.r.t. price when x=4?
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The demand function is given by p = (10-2x) (20-2x) where x= demand an...
To find the elasticity of demand with respect to price, we need to calculate the derivative of the demand function with respect to price and then multiply it by the ratio of price to demand.
1. Calculating the derivative of the demand function:
The demand function is given by:
p = (10-2x)(20-2x)
To find the derivative of the demand function with respect to price, we need to differentiate it with respect to x, and then multiply it by the derivative of x with respect to p.
Differentiating the demand function with respect to x:
dp/dx = (10-2x)(-2) + (20-2x)(-2)
= -20 + 4x - 40 + 4x
= -60 + 8x
Now, differentiating x with respect to p:
dx/dp = 1/dp/dx
= 1/(-60 + 8x)
2. Calculating the elasticity of demand:
The elasticity of demand is given by the formula:
E = (dp/dx) * (x/p)
Substituting the values we calculated:
E = (-60 + 8x) * (x/p)
3. Finding the elasticity of demand when x = 4:
To find the elasticity of demand when x = 4, we substitute x = 4 in the formula for E:
E = (-60 + 8(4)) * (4/p)
= (-60 + 32) * (4/p)
= -28 * (4/p)
= -112/p
Therefore, the elasticity of demand with respect to price when x = 4 is -112/p.
Explanation:
The elasticity of demand measures the responsiveness of demand to changes in price. A negative elasticity indicates that demand is inversely related to price, meaning that as price increases, demand decreases.
In this case, the elasticity of demand is given by -112/p. This means that for every 1% increase in price, demand will decrease by 112%. The magnitude of the elasticity value indicates the sensitivity of demand to price changes. A larger absolute value indicates a greater sensitivity.
It is important to note that the elasticity of demand is not constant along the demand curve. It varies at different price levels. The elasticity can be different at different points on the curve depending on the slope and curvature of the demand function.
The elasticity of demand helps firms and policymakers understand the impact of price changes on demand and adjust their pricing strategies accordingly. It also helps in determining the optimal pricing and revenue-maximizing strategies for a firm.
1. Calculating the derivative of the demand function:
The demand function is given by:
p = (10-2x)(20-2x)
To find the derivative of the demand function with respect to price, we need to differentiate it with respect to x, and then multiply it by the derivative of x with respect to p.
Differentiating the demand function with respect to x:
dp/dx = (10-2x)(-2) + (20-2x)(-2)
= -20 + 4x - 40 + 4x
= -60 + 8x
Now, differentiating x with respect to p:
dx/dp = 1/dp/dx
= 1/(-60 + 8x)
2. Calculating the elasticity of demand:
The elasticity of demand is given by the formula:
E = (dp/dx) * (x/p)
Substituting the values we calculated:
E = (-60 + 8x) * (x/p)
3. Finding the elasticity of demand when x = 4:
To find the elasticity of demand when x = 4, we substitute x = 4 in the formula for E:
E = (-60 + 8(4)) * (4/p)
= (-60 + 32) * (4/p)
= -28 * (4/p)
= -112/p
Therefore, the elasticity of demand with respect to price when x = 4 is -112/p.
Explanation:
The elasticity of demand measures the responsiveness of demand to changes in price. A negative elasticity indicates that demand is inversely related to price, meaning that as price increases, demand decreases.
In this case, the elasticity of demand is given by -112/p. This means that for every 1% increase in price, demand will decrease by 112%. The magnitude of the elasticity value indicates the sensitivity of demand to price changes. A larger absolute value indicates a greater sensitivity.
It is important to note that the elasticity of demand is not constant along the demand curve. It varies at different price levels. The elasticity can be different at different points on the curve depending on the slope and curvature of the demand function.
The elasticity of demand helps firms and policymakers understand the impact of price changes on demand and adjust their pricing strategies accordingly. It also helps in determining the optimal pricing and revenue-maximizing strategies for a firm.
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The demand function is given by p = (10-2x) (20-2x) where x= demand and P= Price . find elasticity of demand w.r.t. price when x=4?
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The demand function is given by p = (10-2x) (20-2x) where x= demand and P= Price . find elasticity of demand w.r.t. price when x=4? for B Com 2024 is part of B Com preparation. The Question and answers have been prepared according to the B Com exam syllabus. Information about The demand function is given by p = (10-2x) (20-2x) where x= demand and P= Price . find elasticity of demand w.r.t. price when x=4? covers all topics & solutions for B Com 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The demand function is given by p = (10-2x) (20-2x) where x= demand and P= Price . find elasticity of demand w.r.t. price when x=4?.
The demand function is given by p = (10-2x) (20-2x) where x= demand and P= Price . find elasticity of demand w.r.t. price when x=4? for B Com 2024 is part of B Com preparation. The Question and answers have been prepared according to the B Com exam syllabus. Information about The demand function is given by p = (10-2x) (20-2x) where x= demand and P= Price . find elasticity of demand w.r.t. price when x=4? covers all topics & solutions for B Com 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The demand function is given by p = (10-2x) (20-2x) where x= demand and P= Price . find elasticity of demand w.r.t. price when x=4?.
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