Advertisements
Advertisements
प्रश्न
Find the revenue function and the demand function if the marginal revenue for x units is MR = 10 + 3x – x2
Advertisements
उत्तर
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
संबंधित प्रश्न
The cost of an overhaul of an engine is ₹ 10,000 The operating cost per hour is at the rate of 2x – 240 where the engine has run x km. Find out the total cost if the engine runs for 300 hours after overhaul
The marginal cost function of a product is given by `"dc"/("d"x)` = 100 – 10x + 0.1x2 where x is the output. Obtain the total and the average cost function of the firm under the assumption, that its fixed cost is ₹ 500
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 = 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 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 the marginal revenue function of a firm is MR = `"e"^((-x)/10)`, then revenue is
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:
When x0 = 5 and p0 = 3 the consumer’s surplus for the demand function pd = 28 – x2 is
Choose the correct alternative:
For a demand function p, if `int "dp"/"p" = "k" int ("d"x)/x` then k is equal to
