Advertisements
Advertisements
प्रश्न
The price elasticity of demand for a commodity is `"p"/x^3`. Find the demand function if the quantity of demand is 3 when the price is ₹ 2.
Advertisements
उत्तर
Price elasticity of demand
`eta_"d" = "p"/x^3`
`(-"p")/x ("d"x)/"dp" = "p"/x^3`
`(-x^3)/x "d"x = "p"/"p" "dp"`
`- x^2 "d"x = "dp"`
Integrating on both sides
`- int x^2 "d"x = int "dp"`
`(-x^3)/3 = "p"+ "k"` ........(1)
When x = 3 and p = 2
`(-(3)^3)/3 = 2 + "k"`
`(- 27)/3 = 2 + "k"`
⇒ – 9 = 2 + k
∴ k = – 11
Equation (1)
⇒ `(-x^3)/3 = "p" - 11`
∴ p = `11 - x^3/3`
APPEARS IN
संबंधित प्रश्न
The marginal cost function is MC = `300 x^(2/5)` and fixed cost is zero. Find out the total cost and average cost functions
If the marginal cost function of x units of output is `"a"/sqrt("a"x + "b")` and if the cost of output is zero. Find the total cost as a function of x
Calculate consumer’s surplus if the demand function p = 122 – 5x – 2x2, and x = 6
If the supply function for a product is p = 3x + 5x2. Find the producer’s surplus when x = 4
The demand function for a commodity is p =`36/(x + 4)`. Find the consumer’s surplus when the prevailing market price is ₹ 6
The demand equation for a products is x = `sqrt(100 - "p")` and the supply equation is x = `"P"/2 - 10`. Determine the consumer’s surplus and producer’s surplus, under market equilibrium
Choose the correct alternative:
If MR and MC denotes the marginal revenue and marginal cost functions, then the profit functions is
Choose the correct alternative:
The profit of a function p(x) is maximum when
Choose the correct alternative:
The marginal cost function is MC = `100sqrt(x)`. find AC given that TC = 0 when the output is zero is
For the marginal revenue function MR = 6 – 3x2 – x3, Find the revenue function and demand function
