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Marginal And Incremental Analysis

 Marginal and Incremental Analysis

Total, Average and Marginal Association

     The association between total, average and marginal perception is highly constructive in marginal investigation of optimal decision making. This association among total, average and marginal numbers holds in case of all perceptions such as revenue, cost of production, profit, utility.

Illustration 11

The Total Revenue Function is TR = 75Q – 10Q^2, where Q is the value of output. Calculate the total revenue, marginal revenue and average revenue by substituting the values of output from 0 – 6.

Solution

Output
Q

Revenue Function
75Q – 15Q^2

Total Revenue
TR

Marginal Revenue MR
TRn – TRn-1

Average Revenue AR
TR / Q

0

75(0) – 10(0)^2

0

0

0

1

75(1) – 10(1)^2

65

65

65

2

75(2) – 10(2)^2

110

45

55

3

75(3) – 10(3)^2

135

25

45

4

75(4) – 10(4)^2

140

5

35

5

75(5) – 10(5)^2

125

-15

25

6

75(6) – 10(6)^2

90

-35

15

Explanation

  1. When we substitute the value of Q from 0-6 we procure the total revenue, marginal revenue, average revenue at various levels of productivity.
  1. It is observed at zero level of productivity there is no sales and hence there is no total revenue, average and marginal revenue.
  1. As the productivity is enlarged and by substituting the higher values of productivity Q are the total revenue function hikes eventually which is represented in the TR column.
  1. A significant fact to be observed is that when one unit of quantity is manufactured and sold, the total revenue is equal to $65.
  1. This is somewhat apparent from the meaning of total revenue, average and marginal revenue.
  1. However the productivity beyond 5 units when manufactured commences to decline the total revenue and so the marginal and average revenue which becomes negative.

Association Among AR and MR Curves

The inclination of linear MR curve is two fold of AR curve and this is illustrated mathematically below.

Illustration 12

The average or the demand function curve be P = m – nQ, where P is the price and Q is the Volume or Quantity denoting the Y axis and n is the incline of the average or the demand curve.

Now ascertain the marginal revenue curve by differentiating the total revenue function. Also construct the curve of this analysis.

Solution

TR = P * Q

which is equal to (m – nQ) * Q

=          mQ – nQ^2

Now, differentiating the above total revenue function with regards to Quantity Q, we procure,

dTR     =          dPQ
dQ                   dQ

            =          m – 2nQ                      ………Equation (1)

As MR = dTR
                dQ

                        MR      =          m – 2nQ                      ………Equation (2)

                                   

Evaluating the Equations (1) and (2), we observe that intercept of the marginal revenue curve on the Y axis is equal to the average revenue and the incline co-efficient of the marginal revenue function is twice the incline co-efficient n of the average revenue function.

This entails that marginal revenue curve will intersect half way length among Y axis and the average revenue curve.

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