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 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 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
If MR = 20 – 5x + 3x2, Find total revenue function
If the supply function for a product is p = 3x + 5x2. Find the producer’s surplus when x = 4
The demand and supply functions under perfect competition are pd = 1600 – x2 and ps = 2x2 + 400 respectively. Find the producer’s surplus
Choose the correct alternative:
The profit of a function p(x) is maximum when
Choose the correct alternative:
For a demand function p, if `int "dp"/"p" = "k" int ("d"x)/x` then k is equal to
A manufacture’s marginal revenue function is given by MR = 275 – x – 0.3x2. Find the increase in the manufactures total revenue if the production is increased from 10 to 20 units
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
A company requires f(x) number of hours to produce 500 units. It is represented by f(x) = 1800x–0.4. Find out the number of hours required to produce additional 400 units. [(900)0.6 = 59.22, (500)0.6 = 41.63]
