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
An account fetches interest at the rate of 5% per annum compounded continuously. An individual deposits ₹ 1,000 each year in his account. How much will be in the account after 5 years. (e0.25 = 1.284)
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 revenue function is R'(x) = 1500 – 4x – 3x2. Find the revenue function and average revenue function
If MR = 14 – 6x + 9x2, Find the demand function
The demand function p = 85 – 5x and supply function p = 3x – 35. Calculate the equilibrium price and quantity demanded. Also, calculate consumer’s surplus
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:
If MR and MC denote the marginal revenue and marginal cost and MR – MC = 36x – 3x2 – 81, then the maximum profit at x is equal to
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`
