Advertisements
Advertisements
प्रश्न
The elasticity of demand with respect to price for a commodity is given by `((4 - x))/x`, where p is the price when demand is x. Find the demand function when the price is 4 and the demand is 2. Also, find the revenue function
उत्तर
The elasticity at the demand
ηd = `((4 - x))/x`
`- "p"/x ("d"x)/"dp" = ((4 - x)/x)`
`"p"/x ("d"x)/"dp" = ((x - 4)/x)`
`1/x[x/(x -4)] "d"x = 1/"p" "dp"`
Integrating on both sides
`int 1/((x - 4)) = int 1/"p" "dp"`
log |x – 4| = log |p| + log k
log |x – 4| = log |pk|
⇒ (x – 4) = pk ........(1)
When p = 4 and x = 2
(2 – 4) = 4k
⇒ – 2 = 4k
k = `(-1)/2`
Equation (1)
⇒ (x – 4) = `"p"((-1)/2)`
– 2(x – 4) = p
⇒ p = 8 – 2x
Revenue function R = px = (8 – 2x)x
R = 8x – 2x2
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 revenue function for a commodity is MR = 9 – 4x2. Find the demand function.
The marginal cost function of a commodity is given by MC = `14000/sqrt(7x + 4)` and the fixed cost is ₹ 18,000. Find the total cost and average cost
Calculate consumer’s surplus if the demand function p = 122 – 5x – 2x2, and x = 6
Choose the correct alternative:
If the marginal revenue function of a firm is MR = `"e"^((-x)/10)`, then revenue is
Choose the correct alternative:
The given demand and supply function are given by D(x) = 20 – 5x and S(x) = 4x + 8 if they are under perfect competition then the equilibrium demand is
Choose the correct alternative:
The producer’s surplus when the supply function for a commodity is P = 3 + x and x0 = 3 is
A company has determined that marginal cost function for x product of a particular commodity is given by MC = `125 + 10x - x^2/9`. Where C is the cost of producing x units of the commodity. If the fixed cost is ₹ 250 what is the cost of producing 15 units
For the marginal revenue function MR = 6 – 3x2 – x3, Find the revenue function and demand function
The marginal cost of production of a firm is given by C'(x) = `20 + x/20` the marginal revenue is given by R’(x) = 30 and the fixed cost is ₹ 100. Find the profit function
