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The elasticity of demand with respect to price for a commodity is given by (4-x)x, where p is the price when demand is x. Find the demand function when the price is 4 and the demand is 2

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प्रश्न

The elasticity of demand with respect to price for a commodity is given by `((4 - x))/x`, where p is the price when demand is x. Find the demand function when the price is 4 and the demand is 2. Also, find the revenue function

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उत्तर

The elasticity at the demand

ηd = `((4 - x))/x`

`- "p"/x ("d"x)/"dp" = ((4 - x)/x)`

`"p"/x ("d"x)/"dp" = ((x - 4)/x)`

`1/x[x/(x -4)] "d"x = 1/"p"  "dp"`

Integrating on both sides

`int 1/((x - 4)) = int 1/"p"  "dp"`

log |x – 4| = log |p| + log k

log |x – 4| = log |pk|

⇒ (x – 4) = pk ........(1)

When p = 4 and x = 2

(2 – 4) = 4k

⇒ – 2 = 4k

k = `(-1)/2`

Equation (1)

⇒ (x – 4) = `"p"((-1)/2)`

– 2(x – 4) = p

⇒ p = 8 – 2x

Revenue function R = px = (8 – 2x)x

R = 8x – 2x2 

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Application of Integration in Economics and Commerce
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 3: Integral Calculus – 2 - Exercise 3.2 [पृष्ठ ७२]

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सामाचीर कलवी Business Mathematics and Statistics [English] Class 12 TN Board
अध्याय 3 Integral Calculus – 2
Exercise 3.2 | Q 3 | पृष्ठ ७२

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