English

Complete the following activity to find MPC, MPS, APC and APS, if the expenditure Ec of a person with income I is given as: Ec = (0.0003)I2 + (0.075)I2 when I = 1000 - Mathematics and Statistics

Advertisements
Advertisements

Question

Complete the following activity to find MPC, MPS, APC and APS, if the expenditure Ec of a person with income I is given as:

Ec = (0.0003)I2 + (0.075)I2

when I = 1000

Sum

Solution

Given, EC = (0.0003)I2 + (0.075)I2

We have APC = `E_C/I`

= (0.0003). I + 0.075

At I = 1000, 

APC = (0.0003) × 1000 + 0.075

= 0.3 + 0.075

∴ APC = 0.375

Now, MPC = `(d(E_C))/(dI)`

= 2 × (0.0003).1 + 0.075

= (0.0006) × I + 0.075

When I = 1000

MPC = 0.6 + 0.075

= 0.675

At I = 1000, MPS = 1 – MPC

= 1 – 0.675

= 0.325

At I = 1000,

APS = 1 – APC = 1 – 0375

= 0.625

shaalaa.com
Application of Derivatives to Economics
  Is there an error in this question or solution?
2021-2022 (March) Set 1

APPEARS IN

RELATED QUESTIONS

Find the marginal revenue if the average revenue is 45 and elasticity of demand is 5.


A manufacturing company produces x items at the total cost of Rs (180 + 4x). The demand function of this product is P = (240 − x). Find x for which profit is increasing.


Find the elasticity of demand, if the marginal revenue is 50 and price is Rs 75.


The demand function of a commodity at price P is given as, D = `40 - "5P"/8`. Check whether it is increasing or decreasing function.


The total cost function for production of x articles is given as C = 100 + 600x – 3x2 . Find the values of x for which total cost is decreasing.


If the demand function is D = `((p + 6)/(p − 3))`, find the elasticity of demand at p = 4.


Find the price for the demand function D = `((2"p" + 3)/(3"p" - 1))`, when elasticity of demand is `11/14`.


For the demand function D = 100 – `p^2/2`. Find the elasticity of demand at p = 10 and comment on the results.


A manufacturing company produces x items at a total cost of ₹ 40 + 2x. Their price is given as p = 120 – x. Find the value of x for which profit is increasing.


A manufacturing company produces x items at a total cost of ₹ 40 + 2x. Their price is given as p = 120 – x. Find the value of x for which also find an elasticity of demand for price 80.


If the marginal revenue is 28 and elasticity of demand is 3, then the price is ______.


If the elasticity of demand η = 1, then demand is ______.


If 0 < η < 1, then the demand is ______.


If the average revenue is 45 and elasticity of demand is 5, then marginal revenue is ______.


A manufacturing company produces x items at a total cost of ₹ 40 + 2x. Their price per item is given as p = 120 – x. Find the value of x for which revenue is increasing

Solution: Total cost C = 40 + 2x and Price p = 120 – x

Revenue R = `square`

Differentiating w.r.t. x,

∴ `("dR")/("d"x) = square`

Since Revenue is increasing,

∴ `("dR")/("d"x)` > 0

∴ Revenue is increasing for `square`


A manufacturing company produces x items at a total cost of ₹ 40 + 2x. Their price per item is given as p = 120 – x. Find the value of x for which profit is increasing

Solution: Total cost C = 40 + 2x and Price p = 120 − x

Profit π = R – C

∴ π = `square`

Differentiating w.r.t. x,

`("d"pi)/("d"x)` = `square`

Since Profit is increasing,

`("d"pi)/("d"x)` > 0

∴ Profit is increasing for `square`


A manufacturing company produces x items at a total cost of ₹ 40 + 2x. Their price per item is given as p = 120 – x. Find the value of x for which elasticity of demand for price ₹ 80.

Solution: Total cost C = 40 + 2x and Price p = 120 – x

p = 120 – x

∴ x = 120 – p

Differentiating w.r.t. p,

`("d"x)/("dp")` = `square`

∴ Elasticity of demand is given by η = `- "P"/x*("d"x)/("dp")`

∴ η = `square`

When p = 80, then elasticity of demand η = `square`


If f(x) = x3 – 3x2 + 3x – 100, x ∈ R then f"(x) is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×