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प्रश्न
For the demand function D = 100 – `p^2/2`. Find the elasticity of demand at p = 10 and comment on the results.
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उत्तर
Given, demand function is D = 100 – `p^2/2`
∴ `(dD)/(dp) = 0 - (2p)/2 = - p`
`eta = (-p)/D . (dD)/(dp)`
∴ `eta = (-p)/(100 - p^2/2).(-p)`
= `p^2/((200 - p^2)/2)`
∴ `eta = (2p)^2/(200 - p^2)`
When p = 10,
`eta = (2(10)^2)/(200 - (10)^2) = 200/100` = 2
∴ Elasticity of demand at p = 10 is 2
Here, η > 0
∴ The demand is elastic.
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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 ______.
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`
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 ______.
