Definitions of total, average, and marginal revenue

Revenue represents the income a firm earns from selling its products or services. It is influenced by the price at which items are sold and the quantity moved in a given period. Different types of revenue provide insights into a firm's financial performance and pricing strategies.

Total revenue

Total revenue is the overall income generated from sales over a specific timeframe. It is also known as turnover.

$\text{Total revenue (TR)}=Q\times P$

Where:

• Q = Quantity sold
• P = Price per unit

Average revenue

Average revenue measures the income per unit sold and directly corresponds to the price.

$\text{Average revenue (AR)}=\frac{\text{TR}}{Q}$

Where:

• TR = Total revenue
• Q = Quantity sold

Marginal revenue

Marginal revenue is the additional income from selling one more unit. It can remain steady if prices are fixed or vary if prices adjust to boost sales.

$\text{Marginal revenue (MR)}={\text{TR}}_n-{\text{TR}}_{n-1}$

Where:

• TR_n = Total revenue at the new sales level
• TR_n-1 = Total revenue at one unit less

Worked example - Calculating total, average, and marginal revenue

A firm sells 200 units at £12 each, generating £2,400 in total revenue. If it then sells 201 units at the same price, total revenue rises to £2,412. Calculate the average revenue for the initial sales and the marginal revenue for the additional unit.

Step 1: Identify the values

• Quantity sold initially (Q) = 200 units
• Price per unit (P) = £12
• Total revenue initially (TR) = £2,400
• New total revenue (TR_n) = £2,412
• Previous total revenue (TR_n-1) = £2,400

Step 2: Calculate average revenue

$\text{Average revenue (AR)}=\frac{\pounds \mathrm{2,400}}{200}=\pounds 12$

Step 3: Calculate marginal revenue

$\text{Marginal revenue (MR)}=\pounds \mathrm{2,412}-\pounds \mathrm{2,400}=\pounds 12$

The relationship between revenue and demand curves

A firm's demand curve illustrates the quantity of a product it can sell at various prices, directly linking to its revenue. Since price equals average revenue, the demand curve also represents the average revenue curve. Total revenue is calculated as quantity multiplied by price, so shifts along the demand curve affect overall income.

Key features of demand curves and revenue

• Demand curves show potential sales volumes at different price points.
• The shape of the curve determines whether a firm can influence prices or must accept market rates.
• Revenue calculations depend on the curve's elasticity, with total revenue peaking at specific points.

Revenue for price takers

Price takers operate in markets where they cannot influence prices, such as perfectly competitive environments. They must accept the prevailing market price.

Characteristics of revenue for price takers

• Perfectly elastic demand curve - The curve is horizontal, meaning any price increase leads to zero sales.
• Constant price - Revenue per unit remains the same regardless of output.
• Equal average and marginal revenue - Each additional unit sold adds the same amount to total revenue.
• Proportional total revenue growth - As sales increase, total revenue rises in direct proportion.

In this scenario, average revenue equals marginal revenue, and both match the fixed market price.

Revenue for price makers

Price makers have some control over pricing, often in monopolistic or oligopolistic markets. They face a downward-sloping demand curve, requiring price reductions to sell more.

Characteristics of revenue for price makers

• Downward-sloping demand curve - Higher output demands lower prices to attract buyers.
• Varying marginal revenue - It decreases as sales grow because price cuts affect all units.
• Marginal revenue curve - This is steeper than the average revenue curve, typically twice as steep for a linear demand curve.
• Negative marginal revenue - Occurs when further sales reduce total revenue.

Maximising total revenue

Firms aim to maximise total revenue by operating at the optimal point on their demand curve, guided by price elasticity of demand (PED).

Role of price elasticity of demand in revenue maximisation

Price elasticity of demand varies along a linear downward-sloping demand curve: elastic to the left of the midpoint (PED < -1), unit elastic at the midpoint (PED = -1), and inelastic to the right (PED > -1).

How PED affects total revenue:

• Total revenue increases when moving towards the midpoint from the elastic side, as price reductions yield proportionate sales gains.
• Total revenue decreases when moving beyond the midpoint into the inelastic area, as sales gains are disproportionate to price cuts.
• Maximum total revenue occurs at the midpoint, where PED = -1 and marginal revenue equals zero.

Additional points on revenue maximisation:

• The demand curve doubles as the average revenue curve.
• Marginal revenue reaches zero at the total revenue peak.
• Beyond this peak, marginal revenue turns negative as extra sales diminish overall income.