# Revenue Curves Relationship between Total Marginal and Average

25/07/2021

Cost and revenue are just like two different faces of the same coin. The costs and revenues of a firm determine its nature and the levels of profit. Cost refers to the expenses incurred by a producer for the production of a commodity. Revenue denotes the amount of income, which a firm receives by the sale of its output. The revenue concepts commonly used in economic are total revenue, average revenue and marginal revenue.

Total Revenue

Total revenue refers to the total sale proceeds of a firm by selling its total output at a given price.

Total revenue is the amount of money that a firm receives for the offer of goods and services in the market. A firm’s total revenue can be calculated as the quantity of goods sold multiplied by the price. The total revenue includes the product of the quantity sold and the price.

Total revenue=Total Quantity Sold × Unit Price

Mathematically,

TR = PQ

TR = Total Revenue

P = Price

Q = Quantity sold.

Average Revenue

Average revenue is the revenue per unit of the commodity sold. It is obtained by dividing the total revenue by the number of units sold.

Average revenue is used as price in a perfectly competitive market. This can be found by the ratio of the firm’s total revenue and the number of goods sold.

AR = Total Revenue/ Total Output Sold

Mathematically

AR = TR/Q;

Where,

AR = Average revenue

TR = Total revenue

Q = Quantity sold.

Marginal Revenue

Marginal revenue is the addition to total revenue by selling one more unit of the commodity.

Marginal revenue refers to the extra money received by selling one more additional unit of the commodity. It is an addition to the total revenue of a firm as new additional units are sold. By selling an additional unit, a firm earns additional revenue that adds to the total revenue and this addition to revenue is called marginal revenue.

Algebraically it is the total revenue earned by selling ‘n’ units of the commodity instead of n-1. Thus,

MRn = TRn – TRn-1; where MRn = Marginal revenue of the nth unit

TRn = Total revenue of n units

TRn-1 = Total revenue of n-1 units

N = Any given number of units sold.

#### Relationship:

Both AR and MR are Calculated from TR:

The average cost and marginal costs are calculated from total cost. In the same fashion, average revenue and marginal revenue can also be calculated from total revenue.

When AR and MR are Parallel to X-axis:

If average revenue and marginal revenue are parallel to horizontal axis then it means both AR and MR are equal to each other i.e. AR = MR.

When both AR and MR are Straight Lines:

Under imperfect competition, when AR falls, MR also falls and it is always below AR line because there are large numbers of buyers and sellers, products are not homogeneous and the firms can enter or exit the market.

If AR Curve is Rising Upward from Left to Right:

In case AR curve is rising upward from left to right, then MR curve will also move upward. It means MR will be greater than AR.

When AR and MR are Convex:

AR and MR curves are convex to the origin. It means as more and more units of a commodity are sold, average revenue falls at lower speed. MR curve also moves in the same direction. The convexity shows that MR falls but at a faster speed.

When AR and MR are Concave:

If AR is concave to the origin, MR will also be concave to the origin. It means average revenue is falling at a higher rate for each additional unit of a commodity sold. Similar would be the case for MR curve.

Revenue and Elasticity:

The elasticity of demand, average revenue and marginal revenue has a close relationship. If a firm knows any two of the three elements viz; average revenue and marginal revenue then it can easily find out the third element i.e. elasticity of demand.

The formula for the calculation is:

E = A / A-M

Where,

E = elasticity of demand

A = average revenue

M = marginal revenue