Advertisements
Advertisements
Question
If the supply function for a product is p = 3x + 5x2. Find the producer’s surplus when x = 4
Solution
The supply function p = 3x + 5x²
When x = 4
⇒ p = 3(4) + 5(4)²
p = 12 + 5(16)
= 12 + 80
p = 92
∴ x0 = 4 and p0 = 92
Producer’s Surplus
P.S = `x_0"p"_0 - int_0^(x_0) "g"(x) "d"x`
= `(4)(92) - int_0^4 (3x + 5x^2) "d"x`
= `368 - [(3x^2)/2 + (5x^3)/3]_0^4`
= `368 - {(3/2 (4)^2 + 5/3 (4)^3) - [0]}`
= `368 - {3/2 (16) + 5/3 (64)}`
= `368 - [24 + 320/3]`
= `368 - 24 - 320/3`
= `344 - 320/3`
= `(1032 - 320)/3`
= `712/3`
= `237.3`
∴PS = 237.3 units
APPEARS IN
RELATED QUESTIONS
If the marginal revenue function for a commodity is MR = 9 – 4x2. Find the demand function.
A firm’s marginal revenue function is MR = `20"e"^((-x)/10) (1 - x/10)`. Find the corresponding demand function
If the marginal revenue function is R'(x) = 1500 – 4x – 3x2. Find the revenue function and average revenue function
If MR = 20 – 5x + 3x2, Find total revenue function
Calculate the producer’s surplus at x = 5 for the supply function p = 7 + x
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
Choose the correct alternative:
If the marginal revenue of a firm is constant, then the demand function is
Choose the correct alternative:
For a demand function p, if `int "dp"/"p" = "k" int ("d"x)/x` then k is equal to
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
