Advertisements
Advertisements
Question
A firm’s marginal revenue function is MR = `20"e"^((-x)/10) (1 - x/10)`. Find the corresponding demand function
Solution
M.R = `20"e"^((-x)/10) (1 - x/10)`
M.R = `20"e"^((-1)/10^((x))) [1 + ((-1)/10) x]`
R = `int "MR" "d"x`
R = `int 20["e"^((-1)/10^((x))) (x)] "d"x`
R = `20x ["e"^((-1)/10^((x)))] + "c"`
When x = 0
R = 0
⇒ k = 0
∴ R = `(20x "e"^(- 1/10x))/x`
Demand function p = `"R"/x = (20x "e"^(- 1/10x))/x`
∴ p = `20 "e"^((-x)/10)`
APPEARS IN
RELATED QUESTIONS
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
If the marginal revenue function is R'(x) = 1500 – 4x – 3x2. Find the revenue function and average revenue function
If the marginal cost (MC) of production of the company is directly proportional to the number of units (x) produced, then find the total cost function, when the fixed cost is ₹ 5,000 and the cost of producing 50 units is ₹ 5,625
Calculate consumer’s surplus if the demand function p = 50 – 2x and x = 20
Calculate the producer’s surplus at x = 5 for the supply function p = 7 + x
Find the consumer’s surplus and producer’s surplus for the demand function pd = 25 – 3x and supply function ps = 5 + 2x
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:
When x0 = 2 and P0 = 12 the producer’s surplus for the supply function Ps = 2x2 + 4 is
Choose the correct alternative:
For a demand function p, if `int "dp"/"p" = "k" int ("d"x)/x` then k is equal to
The demand equation for a product is Pd = 20 – 5x and the supply equation is Ps = 4x + 8. Determine the consumers surplus and producer’s surplus under market equilibrium
