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# Revenue Analysis

The amount of money that a producer receives in exchange for the sale of goods is known as revenue.

Revenue Analysis

The amount of money that a producer receives in exchange for the sale of goods is known as revenue. In short, revenue means sales revenue. It is the amount received by a firm from the sale of a given quantity of a commodity at the prevailing price in the market. For example, if a firm sells 10 books at the price of Rs.100 each, the total revenue will be  Rs. 1000.

## 1. Revenue Concepts

The three basic revenue concepts are: Total Revenue, Average Revenue and Marginal Revenue.

### a. Total Revenue:

Total revenue is the amount of income received by the firm from the sale of its products. It is obtained by multiplying the price of the commodity by the number of units sold.  TR=P × Q

where,

TR denotes Total Revenue,

P denotes Price and

Q denotes Quantity sold.

For example, a cell-phone company sold 100 cell-phones at the price of  Rs. 500 each.

TR is  Rs. 50,000. (TR= 500 × 100 = 50,000).

When price is constant, the behaviour of TR is shown in table 4.8 and diagram 4.10, assuming P=5. When P = 5; TR = PQ

When price is declining with increase in quantity sold. (Eg. Imperfect Competition on the goods market) the behaviour of TR is shown in table 4.9 and diagram 4.11. TR can be obtained from Demand fuction: If Q = 11–P,

When P = 1, Q = 10  TR = PQ = 1 × 10 = 10

When P = 3, Q = 8, TR = 24

When P = 0, Q = 1, TR = 10

### b. Average Revenue

Average revenue is the revenue per unit of the commodity sold. It is calculated by dividing the Total Revenue(TR) by the number of units sold (Q)

AR = TR /Q; if TR = PQ, AR = PQ/Q = P

AR denotes Average Revenue, TR denotes Total Revenue and Q denotes Quantity of unit sold.

For example, if the Total Revenue from the sale of 5 units is Rs 30, the Average Revenue is Rs.6. (AR= 30/5 =6) It is to be noted that AR is equal to Price.

AR=TR/Q = PQ/Q=P

### c. Marginal Revenue

Marginal revenue (MR) is the addition to the total revenue by the sale of an additional unit of a commodity. MR can be found out by dividing change in total revenue by the change in quantity sold out. MR = ∆TR / ∆Q where MR denotes Marginal Revenue, ∆TR denotes change in Total Revenue and ∆Q denotes change in total quantity.

The other method of estimating MR is:

MR=TRn –TRn-1 (or) TRn+1 – TRn

where, MR denotes Marginal Revenue, TRn denotes total revenue of nth item, TRn-1 denotes Total Revenue of n -1th item and TRn+1 denotes Total Revenue of n+1th item.

If TR = PQ MR = dTR/dQ = P, which is equal to AR.

## 2. Relationship between AR and MR Curves

If a firm is able to sell additional units at the same price then AR and MR will be constant and equal. If the firm is able to sell additional units only by reducing the price, then both AR and MR will fall and be different .

### Constant AR and MR (at Fixed Price)

When price remains constant or fixed, the MR will be also constant and will coincide with AR. Under perfect competition as the price is uniform and fixed, AR is equal to MR and their shape will be a straight line horizontal to X axis. The AR and MR Schedule under constant price is given in Table 4.10 and in the diagram 4.12  ### Declining AR and MR (at Declining Price)

When a firm sells large quantities at lower prices both AR and MR will fall but the fall in MR will be more steeper than the fall in the AR.

It is to be noted that MR will be lower than AR. Both AR and MR will be sloping downwards straight from left to right. The MR curve divides the distance between AR Curve and Y axis into two equal parts. The decline in AR need not be a straight line or linear. If the prices are declining with the increase in quantity sold, the AR can be non-linear, taking a shape of concave or convex to the origin.  ## 3. Relationship among TR, AR and MR Curves:

When marginal revenue is positive, total revenue rises, when MR is zero the total revenue becomes maximum. When marginal revenue becomes negative total revenue starts falling. When AR and MR both are falling, then MR falls at a faster rate than AR.

## 4. TR, AR, MR and Elasticity of Demand

The relationship among AR, MR and elasticity of demand (e) is stated as follows.

MR = AR ( e-1/e)

The relationship between the AR curve and MR curve depends upon the elasticity of AR curve (AR = DD = Price).

a. When price elasticity of demand is greater than one, MR is positive and TR is increasing.

b. When price elasticity of demand is less than one, MR is negative and TR is decreasing.

c. When price elasticity of demand is equal to one, MR is equal to zero and TR is maximum and constant.

It is to be noted that, a the output range of 1 to 5 units, the price elasticity of demand is greater than one according to total outlay method. Hence, TR is increasing and MR is positive.  At the output range of 5 to 6 units, the price elasticity of demand is equal to one.

Hence, TR is maximum and MR equals to zero.

At the output range of 6 units to 10 units, the price elasticity of demand is less than unity. Hence, TR is decreasing and MR is negative.

Tags : Economics , 11th Economics : Chapter 4 : Cost and Revenue Analysis
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11th Economics : Chapter 4 : Cost and Revenue Analysis : Revenue Analysis | Economics