# REVENUE CONCEPTS AND RETURNS TO SCALE Definition

Revenue is amount of money which individual, firm or government realizes (obtains) in a given period, Individuals and firms obtain revenue either from production and sale of goods or rendering of services. While government obtains revenue from various sources e.g. taxes, royalties, fees, etc.

Types of revenue

We wish to discuss three types of revenue: total, average and marginal revenue.

1) Total Revenue (TR)

It is the total amount of money which a producer or a seller receives in a period. Total revenue (TR) equals quantity (Q) sold multiplied by unit price (P).

TR = Q × P

Example 1

Find total revenue if total quantity sold is 50 units and unit price is N5.

That is,  TR = 50 x 5 = N250.

Diagram

We show below total revenue graph both under perfect competition when the price is fixed and under imperfect competition when the price varies (it is not fixed). 2) Average Revenue (AR)

• AR is revenue per unit sold.
• It is total revenue divided by total quantity (Q) sold. Example 2

Find average revenue if total revenue is N60 and total units sold is 10 units. We shows below average revenue and marginal revenue graphs both under perfect competition and imperfect competition

Why is MR, AR and price are the same under perfect competition, and the curve is parallel to the Y axis (base)? It is because the price is fixed; it does not vary (change) with quantity sold. Thus (therefore) each additional unit sold adds exactly equal amount to total revenue as the previous ones.

Why are AR and MR curves in figure 5 are downwards sloping? It is because the price falls as more quantity are sold. That is, the price is reduced in order to sell more units. Why is MR curve lies below AR curve? It is because as the price is reduced, each additional unit sold adds less amount to total revenue than the previous ones.

3) Marginal Revenue (MR)

• It is the addition to total revenue due to sale of one extra unit.
• It is a change in total revenue due to a change in quantity sold. Example 3

The sale of 10 units brings in N1000. The total revenue rises to N1120 due to the sale of one extra unit. Find the marginal revenue (MR). Marginal Revenue Product (MRP)

• It is an additional revenue obtained from using an extra unit of a factor input to produce and sell an additional unit.
• Briefly, it is an additional revenue realizes from using (and selling) one more unit of a factor.

It is obtained by multiplying the marginal physical product (MPP) of the factor with the marginal revenue of the product.

MRP = MPP × MR.

Note: MRP and MR are not the same thing (not synonyms). Marginal revenue is additional revenue realized from sale of one more unit.

Returns to scale (RS)

Definition

1. It is the relationship between proportionate change in inputs to a proportionate change in output.
2. A change in factor inputs brings about a proportionate change in output. Briefly, RS shows relationship between inputs and output.

1. Constant returns to scale: There are constant returns to scale,if inputs double, (increase by 10%), output also double (increases by 10%).
2. Increasing returns to scale: There are increasing returns to scale, if inputs double (increase by 10%), output is more than double (increases by 20%).
3. Decreasing returns to scale: There are decreasing returns to scale, if inputs double (increase by 10%), output is less than double (increases by only 5%).

This discussion is summarized in table 2 below:- 