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Find the Elasticity of Demand, If the Marginal Revenue is 50 and Price is Rs 75.

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प्रश्न

Find the elasticity of demand, if the marginal revenue is 50 and price is Rs 75.

योग
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उत्तर

Given, marginal revenue `("R"_"m") = 50` and price (P) = ₹ 75

using, Rm = p`(1 - 1/η)`

∴ 50 = 75 `(1 - 1/η)`

∴ `50/75 = 1 - 1/η`

∴ `2/3 = 1 - 1/η`

∴ `1/η = 1/3` 

∴ η = 3

∴ elasticity of demand = 3

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अध्याय 4: Applications of Derivatives - Exercise 4.4 [पृष्ठ ११२]

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बालभारती Mathematics and Statistics 1 (Commerce) [English] Standard 12 Maharashtra State Board
अध्याय 4 Applications of Derivatives
Exercise 4.4 | Q 7.3 | पृष्ठ ११२

संबंधित प्रश्न

Find the marginal revenue if the average revenue is 45 and elasticity of demand is 5.


A manufacturing company produces x items at the total cost of Rs (180 + 4x). The demand function of this product is P = (240 − x). Find x for which profit is increasing.


The manufacturing company produces x items at the total cost of ₹ 180 + 4x. The demand function for this product is P = (240 – x). Find x for which revenue is increasing


The total cost of manufacturing x articles C = 47x + 300x2 – x4 . Find x, for which average cost is decreasing


If the demand function is D = 50 – 3p – p2. Find the elasticity of demand at p = 5 comment on the result.


For the demand function D = 100 – `p^2/2`. Find the elasticity of demand at p = 10 and comment on the results.


A manufacturing company produces x items at a total cost of ₹ 40 + 2x. Their price is given as p = 120 – x. Find the value of x for which revenue is increasing.


A manufacturing company produces x items at a total cost of ₹ 40 + 2x. Their price is given as p = 120 – x. Find the value of x for which also find an elasticity of demand for price 80.


Fill in the blank:

A road of 108 m length is bent to form a rectangle. If the area of the rectangle is maximum, then its dimensions are _______.


If the marginal revenue is 28 and elasticity of demand is 3, then the price is ______.


If 0 < η < 1, then the demand is ______.


If the average revenue is 45 and elasticity of demand is 5, then marginal revenue is ______.


State whether the following statement is True or False:  

If the marginal revenue is 50 and the price is ₹ 75, then elasticity of demand is 4


The manufacturing company produces x items at the total cost of ₹ 180 + 4x. The demand function for this product is P = (240 − 𝑥). Find x for which profit is increasing


A manufacturing company produces x items at a total cost of ₹ 40 + 2x. Their price per item is given as p = 120 – x. Find the value of x for which profit is increasing

Solution: Total cost C = 40 + 2x and Price p = 120 − x

Profit π = R – C

∴ π = `square`

Differentiating w.r.t. x,

`("d"pi)/("d"x)` = `square`

Since Profit is increasing,

`("d"pi)/("d"x)` > 0

∴ Profit is increasing for `square`


A manufacturing company produces x items at a total cost of ₹ 40 + 2x. Their price per item is given as p = 120 – x. Find the value of x for which elasticity of demand for price ₹ 80.

Solution: Total cost C = 40 + 2x and Price p = 120 – x

p = 120 – x

∴ x = 120 – p

Differentiating w.r.t. p,

`("d"x)/("dp")` = `square`

∴ Elasticity of demand is given by η = `- "P"/x*("d"x)/("dp")`

∴ η = `square`

When p = 80, then elasticity of demand η = `square`


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Ec = (0.0003)I2 + (0.075)I2

when I = 1000


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In a factory, for production of Q articles, standing charges are ₹500, labour charges are ₹700 and processing charges are 50Q. The price of an article is 1700 - 3Q. Complete the following activity to find the values of Q for which the profit is increasing.

Solution: Let C be the cost of production of Q articles.

Then C = standing charges + labour charges + processing charges

∴ C = `square` 

Revenue R = P·Q = (1700 - 3Q)Q = 1700Q- 3Q2

Profit `pi = R - C = square`

 Differentiating w.r.t. Q, we get

`(dpi)/(dQ) = square`

If profit is increasing , then `(dpi)/(dQ) >0`

∴ `Q < square` 

Hence, profit is increasing for `Q < square` 


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