Advertisements
Advertisements
प्रश्न
The consumption expenditure Ec of a person with the income x. is given by Ec = 0.0006x2 + 0.003x. Find MPC, MPS, APC and APS when the income x = 200.
The consumption expenditure Ec of a person with income x is given by Ec = 0.0006x2 + 0.003x. Find the average propensity to consume (APC), marginal propensity to consume (MPC) when his income is ₹ 200. Also find his marginal propensity to save (MPS).
उत्तर
The expenditure Ec of a person with income x is given by
Ec = 0.0006x2 + 0.003x
So, marginal propensity to consume (MPC) = `("dE"_"c")/("dx")`
= `"d"/("dx")(0.0006x^2 + 0.003x)`
= 0.0006 × 2x + 0.003
= 0.0012x + 0.003
When x = 200,
MPC = (0.0012 × 200) + 0.003
= 0.24 + 0.003 = 0.243
MPS = 1 − MPC
= 1 − 0.243
= 0.757
Now APC =`"E"_"c"/"x"`
= `(0.0006x^2 + 0.003x)/x`
= 0.0006x + 0.003
When x = 200
APC = 0.0006 × 200 + 0.003
= 0.12 + 0.003 = 0.123
APS = 1 − APC
= 1 − 0.123
= 0.877
संबंधित प्रश्न
Find the intervals in which the function f(x) = 3x4 − 4x3 − 12x2 + 5 is
(a) strictly increasing
(b) strictly decreasing
The amount of pollution content added in air in a city due to x-diesel vehicles is given by P(x) = 0.005x3 + 0.02x2 + 30x. Find the marginal increase in pollution content when 3 diesel vehicles are added and write which value is indicated in the above question.
Test whether the function is increasing or decreasing.
f(x) = `"x" -1/"x"`, x ∈ R, x ≠ 0,
The function f (x) = x3 – 3x2 + 3x – 100, x∈ R is _______.
(A) increasing
(B) decreasing
(C) increasing and decreasing
(D) neither increasing nor decreasing
Find the intervals in which the function f given by f(x) = 2x2 − 3x is
- strictly increasing
- strictly decreasing
Find the intervals in which the following functions are strictly increasing or decreasing:
10 − 6x − 2x2
Find the values of x for `y = [x(x - 2)]^2` is an increasing function.
Show that f(x) = \[\frac{1}{1 + x^2}\] is neither increasing nor decreasing on R ?
Without using the derivative, show that the function f (x) = | x | is.
(a) strictly increasing in (0, ∞)
(b) strictly decreasing in (−∞, 0) .
Find the interval in which the following function are increasing or decreasing f(x) = x3 − 6x2 − 36x + 2 ?
Find the interval in which the following function are increasing or decreasing f(x) = 2x3 + 9x2 + 12x + 20 ?
Find the interval in which the following function are increasing or decreasing f(x) = −2x3 − 9x2 − 12x + 1 ?
Find the interval in which the following function are increasing or decreasing \[f\left( x \right) = \frac{x^4}{4} + \frac{2}{3} x^3 - \frac{5}{2} x^2 - 6x + 7\] ?
Find the interval in which the following function are increasing or decreasing f(x) = x4 − 4x3 + 4x2 + 15 ?
Find the interval in which the following function are increasing or decreasing \[f\left( x \right) = \frac{3}{2} x^4 - 4 x^3 - 45 x^2 + 51\] ?
Show that f(x) = loga x, 0 < a < 1 is a decreasing function for all x > 0 ?
Show that the function f(x) = cot \[-\] l(sinx + cosx) is decreasing on \[\left( 0, \frac{\pi}{4} \right)\] and increasing on \[\left( 0, \frac{\pi}{4} \right)\] ?
Prove that the function f(x) = x3 − 6x2 + 12x − 18 is increasing on R ?
State when a function f(x) is said to be increasing on an interval [a, b]. Test whether the function f(x) = x2 − 6x + 3 is increasing on the interval [4, 6] ?
Find the intervals in which f(x) = log (1 + x) −\[\frac{x}{1 + x}\] is increasing or decreasing ?
Prove that the following function is increasing on R f \[f\left( x \right) = 4 x^3 - 18 x^2 + 27x - 27\] ?
Prove that the function f given by f(x) = x3 − 3x2 + 4x is strictly increasing on R ?
Find the value(s) of a for which f(x) = x3 − ax is an increasing function on R ?
Let f defined on [0, 1] be twice differentiable such that | f (x) | ≤ 1 for all x ∈ [0, 1]. If f(0) = f(1), then show that | f'(x) | < 1 for all x ∈ [ 0, 1] ?
Find 'a' for which f(x) = a (x + sin x) + a is increasing on R ?
Find the values of 'a' for which the function f(x) = sin x − ax + 4 is increasing function on R ?
Write the interval in which f(x) = sin x + cos x, x ∈ [0, π/2] is increasing ?
The function f(x) = 2 log (x − 2) − x2 + 4x + 1 increases on the interval
The function f(x) = x2 e−x is monotonic increasing when
Function f(x) = 2x3 − 9x2 + 12x + 29 is monotonically decreasing when
If the function f(x) = kx3 − 9x2 + 9x + 3 is monotonically increasing in every interval, then
Every invertible function is
Function f(x) = ax is increasing on R, if
If the function f(x) = x3 − 9kx2 + 27x + 30 is increasing on R, then
Show that f(x) = cos x is a decreasing function on (0, π), increasing in (−π, 0) and neither increasing nor decreasing in (−π, π).
Show that f(x) = cos x is a decreasing function on (0, π), increasing in (−π, 0) and neither increasing nor decreasing in (−π, π).
If the demand function is D = 50 - 3p - p2, find the elasticity of demand at (a) p = 5 (b) p = 2 , Interpret your result.
Prove that the function f : N → N, defined by f(x) = x2 + x + 1 is one-one but not onto. Find the inverse of f: N → S, where S is range of f.
Test whether the following functions are increasing or decreasing : f(x) = x3 – 6x2 + 12x – 16, x ∈ R.
Find the values of x for which f(x) = `x/(x^2 + 1)` is (a) strictly increasing (b) decreasing.
Prove that y = `(4sinθ)/(2 + cosθ) - θ` is an increasing function if `θ ∈[0, pi/2]`
Solve the following : Find the intervals on which the function y = xx, (x > 0) is increasing and decreasing.
State whether the following statement is True or False:
The function f(x) = `"x"*"e"^("x" (1 - "x"))` is increasing on `((-1)/2, 1)`.
Show that function f(x) =`3/"x" + 10`, x ≠ 0 is decreasing.
Find the values of x, for which the function f(x) = x3 + 12x2 + 36𝑥 + 6 is monotonically decreasing
The function f(x) = `x - 1/x`, x ∈ R, x ≠ 0 is increasing
Find the values of x such that f(x) = 2x3 – 15x2 + 36x + 1 is increasing function
A man of height 1.9 m walks directly away from a lamp of height 4.75m on a level road at 6m/s. The rate at which the length of his shadow is increasing is
In which interval is the given function, f(x) = 2x3 - 21x2 + 72x + 19 monotonically decreasing?
The values of k for which the function f(x) = kx3 – 6x2 + 12x + 11 may be increasing on R are ______.
Determine for which values of x, the function y = `x^4 – (4x^3)/3` is increasing and for which values, it is decreasing.
Let x0 be a point in the domain of definition of a real valued function `f` and there exists an open interval I = (x0 – h, ro + h) containing x0. Then which of the following statement is/ are true for the above statement.
Show that function f(x) = tan x is increasing in `(0, π/2)`.
The function f(x) = `|x - 1|/x^2` is monotonically decreasing on ______.
If f(x) = x + cosx – a then ______.
The function f(x) = sin4x + cos4x is an increasing function if ______.
