3.7 - Revenue
Types of revenue and their calculations
Revenue represents the income a firm earns from selling its products or services. It varies based on the selling price and the number of units sold, and is influenced by the demand conditions the firm faces.
Total revenue
Total revenue (TR) measures the overall income a firm receives from sales over a specific period. It is also known as turnover.
Where:
- Quantity sold = Number of units sold
- Price = Selling price per unit (£)
Average revenue
Average revenue (AR) indicates the income per unit sold and directly corresponds to the price at which the product is sold.
Where:
- Total revenue = Overall income from sales (£)
- Quantity sold = Number of units sold
Marginal revenue
Marginal revenue (MR) shows the additional income gained from selling one more unit of output. It reflects changes in total revenue when output increases by a single unit.
Where:
- TRn = Total revenue at the new sales level (£)
- TRn-1 = Total revenue at one unit less (£)
When prices remain constant across sales levels, marginal revenue stays the same. However, if prices must be lowered to boost sales, marginal revenue varies with the quantity sold.
Worked example - Calculating types of revenue
A firm sells widgets. At 500 units sold, total revenue is £7,500. When sales increase to 501 units, total revenue rises to £7,515. Calculate the average revenue at 501 units and the marginal revenue for the 501st unit.
Step 1: Identify the values
- Quantity sold at new level = 501 units
- Total revenue at new level (TRn) = £7,515
- Total revenue at previous level (TRn-1) = £7,500
Step 2: Calculate average revenue
Step 3: Calculate marginal revenue
The relationship between revenue and demand curves
Demand curves illustrate the quantity of a product that consumers are willing to buy at different prices, directly linking to a firm's revenue. Since price equals average revenue, the demand curve also represents the average revenue curve.
How demand curves influence revenue:
- Quantity and price linkage - The curve shows the maximum quantity sellable at each price, or the highest price achievable for a given quantity.
- Total revenue calculation - Total revenue at any point is the product of quantity sold and the corresponding price on the curve.
- Revenue behaviour - Depending on the curve's shape, revenue may rise or fall with changes in output; for instance, constant prices lead to steady marginal revenue, while falling prices alter it.
Firms' revenue patterns depend on whether they are price takers or price makers.
Revenue for price takers with perfectly elastic demand
Price takers operate in markets where they cannot influence the prevailing price and must accept it as set by overall supply and demand.
Characteristics of perfectly elastic demand:
- Horizontal demand curve - The curve is flat, meaning unlimited quantities can be sold at the market price, but raising the price results in zero sales.
- No incentive to lower price - Firms can sell all output at the market price, so reducing it would unnecessarily cut revenue.
- Equality of AR and MR - Since price remains constant, each additional unit sold adds the same amount to total revenue, so average revenue equals marginal revenue.
- Proportional total revenue growth - As sales increase, total revenue rises in direct proportion, with no diminishing returns from price changes.
Revenue for price makers with downward sloping demand
Price makers have some control over their selling price due to product differentiation or market power, facing a demand curve that requires price reductions to increase sales.
Features of downward sloping demand curves:
- Negative slope - To sell more units, the firm must lower the price.
- MR steeper than AR - The marginal revenue curve slopes downward twice as steeply as the average revenue (demand) curve.
- Changing marginal revenue - As quantity increases, marginal revenue decreases and can become negative if further sales reduce total revenue.
Maximising total revenue on demand curves
For firms with downward sloping demand curves, total revenue reaches its peak at a specific point related to price elasticity of demand (PED).
Conditions for maximum total revenue:
- PED at midpoint - Total revenue is maximised where PED equals -1, typically at the curve's midpoint for straight-line demand curves.
- Elastic demand effects - To the left of the midpoint (PED < -1), lowering prices increases total revenue due to a more than proportional rise in quantity.
- Inelastic demand effects - To the right of the midpoint (PED > -1 but less than 0 in absolute terms), lowering prices decreases total revenue as quantity rises less than proportionally.
- Role of marginal revenue - Maximum total revenue occurs where marginal revenue equals zero; beyond this, additional sales make marginal revenue negative, reducing overall revenue.