हिंदी
तमिलनाडु बोर्ड ऑफ सेकेंडरी एज्युकेशनएचएससी वाणिज्य कक्षा १२

Find the consumer’s surplus and producer’s surplus for the demand function pd = 25 – 3x and supply function ps = 5 + 2x - Business Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

Find the consumer’s surplus and producer’s surplus for the demand function pd = 25 – 3x and supply function ps = 5 + 2x

योग
Advertisements

उत्तर

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.

shaalaa.com
Application of Integration in Economics and Commerce
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 3: Integral Calculus – 2 - Exercise 3.3 [पृष्ठ ७५]

APPEARS IN

सामाचीर कलवी Business Mathematics and Statistics [English] Class 12 TN Board
अध्याय 3 Integral Calculus – 2
Exercise 3.3 | Q 11 | पृष्ठ ७५

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 revenue function for a commodity is MR = 9 – 4x2. Find the demand function.


Under perfect competition for a commodity the demand and supply laws are Pd = `8/(x + 1) - 2` and Ps = `(x + 3)/2` respectively. Find the consumer’s and producer’s surplus


Choose the correct alternative:

The demand and supply functions are given by D(x) = 16 – x2 and S(x) = 2x2 + 4 are under perfect competition, then the equilibrium price x is


Choose the correct alternative:

When x0 = 5 and p0 = 3 the consumer’s surplus for the demand function pd = 28 – x2 is


Choose the correct alternative:

The producer’s surplus when the supply function for a commodity is P = 3 + x and x0 = 3 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


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


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]


The price elasticity of demand for a commodity is `"p"/x^3`. Find the demand function if the quantity of demand is 3 when the price is ₹ 2.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×