Advertisements
Advertisements
प्रश्न
If the supply function for a product is p = 3x + 5x2. Find the producer’s surplus when x = 4
Advertisements
उत्तर
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
संबंधित प्रश्न
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
Determine the cost of producing 200 air conditioners if the marginal cost (is per unit) is C'(x) = `x^2/200 + 4`
The marginal revenue (in thousands of Rupees) functions for a particular commodity is `5 + 3"e"^(- 003x)` where x denotes the number of units sold. Determine the total revenue from the sale of 100 units. (Given e–3 = 0.05 approximately)
The marginal cost of production of a firm is given by C'(x) = 5 + 0.13x, the marginal revenue is given by R'(x) = 18 and the fixed cost is ₹ 120. Find the profit 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
Calculate the producer’s surplus at x = 5 for the supply function p = 7 + x
Find the consumer’s surplus and producer’s surplus for the demand function pd = 25 – 3x and supply function ps = 5 + 2x
A company has determined that marginal cost function for x product of a particular commodity is given by MC = `125 + 10x - x^2/9`. Where C is the cost of producing x units of the commodity. If the fixed cost is ₹ 250 what is the cost of producing 15 units
For the marginal revenue function MR = 6 – 3x2 – x3, Find the revenue function and demand function
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]
