Advertisements
Advertisements
Question
Find the revenue function and the demand function if the marginal revenue for x units is MR = 10 + 3x – x2
Advertisements
Solution
The marginal revenue function
MR = 10 + 3x – x2
The Revenue function
R = `int ("MR") "d"x`
= `int (10 + 3x - x^2) "d"x`
R = `[10x + 3(x^2/2) - (x^3/3)] + "k"`
When x = 0
R = 0
⇒ k = 0
∴ R = `10x + (3x^2)/2 - x^3/3`
⇒ px = `10x + (3x^2)/2 - x^3/3`
⇒ p = `(10x + (3x^2)/2 - x^3/3)/x`
∴∴ The demand function p = `10 + (3x^2)/2 - x^2/3`
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
A company receives a shipment of 500 scooters every 30 days. From experience, it is known that the inventory on hand is related to the number of days x. Since the shipment, I(x) = 500 – 0.03x2, the daily holding cost per scooter is ₹ 0.3. Determine the total cost for maintaining inventory for 30 days
Given the marginal revenue function `4/(2x + 3)^2 - 1` show that the average revenue function is P = `4/(6x + 9) - 1`
The demand function for a commodity is p = e–x .Find the consumer’s surplus when p = 0.5
Choose the correct alternative:
The marginal revenue and marginal cost functions of a company are MR = 30 – 6x and MC = – 24 + 3x where x is the product, then the profit function is
Choose the correct alternative:
The demand function for the marginal function MR = 100 – 9x2 is
Choose the correct alternative:
When x0 = 2 and P0 = 12 the producer’s surplus for the supply function Ps = 2x2 + 4 is
The marginal revenue function for a firm given by MR = `2/(x + 3) - (2x)/(x + 3)^2 + 5`. Show that the demand function is P = `(2x)/(x + 3)^2 + 5`
For the marginal revenue function MR = 6 – 3x2 – x3, Find the revenue function and demand function
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
