Advertisements
Advertisements
Question
Find the consumer’s surplus and producer’s surplus for the demand function pd = 25 – 3x and supply function ps = 5 + 2x
Advertisements
Solution
Given pd = 25 – 3x and ps = 5 + 2x
At market equilibrium, pd = pss
⇒ 25 – 3x = 5 + 2x
⇒ 5x = 20
⇒ x = 4
When x0 = 4
p0 = 25 – 12 = 13
C.S = `int_0^4 (25 - 3x) "d"x - 13(4)`
= `(25x - (3x^2)/2)_0^4 - 52`
= `100 - 3/2 (16) - 52`
= 24
So the consumer’s surplus is 24 units.
P.S = `13(4) - int_0^4 (2x + 5) "d"x`
= `52 - (x^2 + 5x)_0^4`
= `52 - 16 - 20`
= 16
So the producer’s surplus is 16 units.
APPEARS IN
RELATED QUESTIONS
Elasticity of a function `("E"y)/("E"x)` is given by `("E"y)/("E"x) = (-7x)/((1 - 2x)(2 + 3x))`. Find the function when x = 2, y = `3/8`
A company receives a shipment of 500 scooters every 30 days. From experience, it is known that the inventory on hand is related to the number of days x. Since the shipment, I(x) = 500 – 0.03x2, the daily holding cost per scooter is ₹ 0.3. Determine the total cost for maintaining inventory for 30 days
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 for a commodity is MR = 9 – 4x2. Find the demand function.
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
Calculate the producer’s surplus at x = 5 for the supply function p = 7 + x
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 the demand function p(x), the elasticity of demand with respect to price is unity then
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
