Advertisements
Advertisements
Question
If the demand function is D = 50 – 3p – p2. Find the elasticity of demand at p = 2 comment on the result
Solution
Given, demand function is D = 50 – 3p – p2
∴ `"dD"/"dp" = 0 - 3 - 2"p"`
= `- 3 - 2"p"`
Elasticity of demand is given by
`eta =- ("p")/"D" * "dD"/"dp"`
∴ `eta = (-"p")/(50 - 3"p" - "p"^2) * (- 3 - 2"p")`
∴ `eta = (p(3 + 2p))/(50 - 3p - p^2)`
(i) When p = 5
`eta = (5(3 + 2xx 5))/(50 - 3(5) - (5)^2) = (5xx13)/(50 - 15 - 25)`
= `65/10 = 6.5`
Since η > 1 the demand is elastic
(ii) When p = 2 then,
`eta = (2(3 + 2 xx 2))/(50 - 3(2) - (2)^2) = (2xx7)/(50 -6 - 4)`
= `14/40 = 7/20`
Since, < η < 1, the demand is inelastic.
APPEARS IN
RELATED QUESTIONS
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.
Find the elasticity of demand, if the marginal revenue is 50 and price is Rs 75.
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.
Find the price for the demand function D = `((2"p" + 3)/(3"p" - 1))`, when elasticity of demand is `11/14`.
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 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 elasticity of demand η = 1, then demand 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
If f(x) = x3 – 3x2 + 3x – 100, x ∈ R then f"(x) 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`
