# 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 |
Revenue Function |
Total Revenue |
Marginal Revenue MR |
Average Revenue AR |

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__

- When we substitute the value of Q from 0-6 we procure the total revenue, marginal revenue, average revenue at various levels of productivity.

- It is observed at zero level of productivity there is no sales and hence there is no total revenue, average and marginal revenue.

- 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.

- A significant fact to be observed is that when one unit of quantity is manufactured and sold, the total revenue is equal to $65.

- This is somewhat apparent from the meaning of total revenue, average and marginal revenue.

- 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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**Other topics under Managerial Economics: Nature, Scope and Optimization Techniques:**

- Basic Model of the Firm and Role of Profits
- Demand and Demand Function
- Derivative of Function of a Function (Chain Rule)
- Macro Economics Policy
- Managerial Assessment Making Procedure
- Maximisation by Marginal Examination
- Optimisation Concepts and Techniques
- Restrained Maximisation
- Restrained Maximisation: Substitution Method