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प्रश्न
The demand function of a commodity at price P is given as, D = `40 - "5P"/8`. Check whether it is increasing or decreasing function.
उत्तर
Given, the demand function is
D = `40 - "5P"/8`
∴ `"dD"/"dP" = 0 - 5/8(1) = (-5)/8 < 0`
∴ The given function is a decreasing function.
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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 total cost of manufacturing x articles C = 47x + 300x2 – x4 . Find x, for which average cost is decreasing
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`.
If the demand function is D = 50 – 3p – p2. Find the elasticity of demand at p = 5 comment on the result
If the demand function is D = 50 – 3p – p2. Find the elasticity of demand at p = 2 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 profit is increasing.
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.
If the average revenue is 45 and elasticity of demand is 5, then marginal revenue is ______.
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 revenue is increasing
Solution: Total cost C = 40 + 2x and Price p = 120 – x
Revenue R = `square`
Differentiating w.r.t. x,
∴ `("dR")/("d"x) = square`
Since Revenue is increasing,
∴ `("dR")/("d"x)` > 0
∴ Revenue 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`
