The expenditure Ec of a person with income I is given by Ec = (0.000035) I^2 + (0.045) I. Find marginal propensity to consume (MPC) and marginal propensity to save (MPS) when I = 5000. Also find A (average) PC and A (average) PS. - Mathematics and Statistics

Advertisements
Advertisements

The expenditure Ec of a person with income I is given by Ec = (0.000035) I2 + (0.045) I. Find marginal propensity to consume (MPC) and marginal propensity to save (MPS) when I = 5000. Also find A (average) PC and A (average)

PS.

Advertisements

Solution

`E_c=(0.000035)I^2+(0.045)I`

`MP_c=(dE_c)/(dI)`

`=d/(dI)[(0.000035)I^2+(0.045)I]`

`=(0.000035)(2I)+(0.045)`

`=(0.00007)I+0.045`

`(MPC)_(I=5000)=(0.00007)(5000)+0.045`

`=0.395`

We know

`MPS=1-MPC`

`(MPS)_(I=5000)=1-(MPC)_(I=5000)`

`=1-0.395`

`=0.605`

`Now " "APC=E_c/I=((0.000035)^2+(0.045)I)/I`

`=(0.000035)I+(0.045)`

`(APC)_(I=5000)=(0.000035)(5000)+(0.045)`

`=0.175+0.045`

`=0.22`

We have

`(APS)=1-APC`

`(APS)_(I=5000)=1-(APC)_(I=5000)`

`=1-0.22`

`=0.78`

 

  Is there an error in this question or solution?
2014-2015 (March)

APPEARS IN

RELATED QUESTIONS

A firm wants to maximize its profit. The total cost function is C = 370Q + 550 and revenue is R = 730Q-3Q2. Find the output for which profit is maximum and also find the profit amount at this output.


The total cost function of a firm is `C = x^2 + 75x + 1600` for output x. Find the output (x) for which average
cost is minimum. Is `C_A = C_M` at this output?


Evaluate : `int_1^2 1/((x+1)(x+3)) dx` 


In a firm the cost function for output x is given as C = `"x"^3/3 - 20"x"^2 + 70 "x"`.  Find the 3 output for which marginal cost  (Cm) is minimum.


Solve the following assignment problem to minimize the cost: 

Persons Jobs
I II III
A 7 3 5
B 2 7 4
C 6 5 3
D 3 4 7

Examine the function f(x) = `x + 25/x ` for maxima and minima 


A manufacturer can sell x items at a price of ₹ (280 - x) each .The cost of producing items is ₹ (x2 + 40x + 35) Find the number of items to be sold so that the manufacturer can make maximum profit.


Cost of assembling x wallclocks is `( x^3/3 - 40x^2)` and labour charges are 500x. Find the number of wall clocks to be manufactured for which average cost and marginal cost attain their respective minimum.


Find the value of x for which the function `f(x) = x^3 - 3x^2 - 9x + 25` is increasing.


The average cost function associated with producing and marketing x units of an item is given by AC = 2x – 11 + `50/x`. Find the range of values of the output x, for which AC is increasing.


A television manufacturer finds that the total cost for the production and marketing of x number of television sets is C(x) = 300x2 + 4200x + 13500. If each product is sold for ₹ 8,400. show that the profit of the company is increasing.


A monopolist has a demand curve x = 106 – 2p and average cost curve AC = 5 + `x/50`, where p is the price per unit output and x is the number of units of output. If the total revenue is R = px, determine the most profitable output and the maximum profit.


A tour operator charges ₹ 136 per passenger with a discount of 40 paise for each passenger in excess of 100. The operator requires at least 100 passengers to operate the tour. Determine the number of passengers that will maximize the amount of money the tour operator receives.


Find the local minimum and local maximum of y = 2x3 – 3x2 – 36x + 10.


The total revenue function for a commodity is R `= 15x + x^2/3 - 1/36 x^4`. Show that at the highest point average revenue is equal to the marginal revenue.


The total cost function y for x units is given by y = `4x((x+2)/(x+1)) + 6`. Prove that marginal cost [MC] decreases as x increases.


For the cost function C = 2000 + 1800x - 75x2 + x3 find when the total cost (C) is increasing and when it is decreasing.


The maximum value of f(x) = sin x is:


If f(x, y) is a homogeneous function of degree n, then `x (del "f")/(del x) + "y" (del "f")/(del y)` is equal to:


Share
Notifications



      Forgot password?
Use app×