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महाराष्ट्र राज्य शिक्षण मंडळएचएससी वाणिज्य (इंग्रजी माध्यम) इयत्ता १२ वी

If 0 < η < 1, then the demand is ______. - Mathematics and Statistics

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प्रश्न

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

पर्याय

  • constant

  • inelastic

  • unitary elastic

  • elastic

MCQ
रिकाम्या जागा भरा

उत्तर

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

shaalaa.com
Application of Derivatives to Economics
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 1.4: Applications of Derivatives - Q.1

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 demand function of a commodity at price P is given as, D = `40 - "5P"/8`. Check whether it is increasing or decreasing function.


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


Find the price, if the marginal revenue is 28 and elasticity of demand is 3.


If the demand function is D = `((p + 6)/(p − 3))`, find the elasticity of demand at p = 4.


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.


For the demand function D = 100 – `"p"^2/2`. Find the elasticity of demand at p = 6 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 profit 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.


Find MPC, MPS, APC and APS, if the expenditure Ec of a person with income I is given as Ec = (0.0003) I2 + (0.075) I ; When I = 1000.


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 the elasticity of demand η = 1, then demand 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


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`


Complete the following activity to find MPC, MPS, APC and APS, if the expenditure Ec of a person with income I is given as:

Ec = (0.0003)I2 + (0.075)I2

when I = 1000


If elasticity of demand η = 0 then demand is ______.


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


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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