# Revenue

## Revenue Diagrams and Price Elasticity of Demand

For most goods, the demand curve slopes downwards, as consumers will buy more as price falls. This is shown in the following demand schedule:

 Price (£s per unit) Quantity Demanded (Per Week) Total Revenue (£s Per Week) 50 100 5000 40 200 8000 30 300 9000 20 400 8000 10 500 5000

This data is shown in Fig 1 below: The top half of the diagram shows the demand curve (which is also the AR curve) and the MR curve.

The bottom half of the diagram shows the corresponding TR at each price and output.

Total revenue initially rises as price falls from £50 down to £30. This is because demand is price elastic (greater than -1) over this price range. The % change in quantity is greater than the % change in price.

NB: When demand is price elastic, MR is positive and TR rises with increased output.

As price falls, demand becomes less elastic, and at all prices below £30 total revenue falls with price. This is because demand is now price inelastic (less than -1). The % change in quantity is now smaller than the % change in price. (See also the notes on 1.2.3 for more on elasticity)

NB: When demand is price inelastic, MR is negative and TR falls with increased output.

It follows from this that a firm will experience a fall in its profits if it produces at an output where MR is negative.

In perfect markets (see notes on 3.4.2) there is just a single price (AR) at which a firm can sell its goods, regardless of output. In this circumstance, AR and MR are equal, and TR increases in direct proportion to output. This is shown in Fig 2 below: If the market price is £20, a firm in a perfect market can sell as much as it can produce at that price, but will sell nothing at any higher price. An increase in output of one unit raises TR by £20, so price, AR and MR are all the same.

The bottom half of the diagram shows that TR is a straight line. If the market price was higher, TR would have a steeper slope.

Explain in a paragraph the circumstances under which a firm may be reluctant to lower its price in order to sell more goods.
Your answer should include: Inelastic / Negative / Marginal Revenue / Total Revenue / Fall

## Revenue

Revenue is another word for the income a firm receives from the ale of its products.

Total Revenue (TR) = Price per unit (P) X Output (Q), i.e. TR = P__x__Q

For instance if a firm produces 500 widgets per week and sells them at £2.00 each:

TR = £2 x 500 = £1000 per week.

Average Revenue (AR) = Total Revenue ÷ Output, i.e. AR = TR÷Q

Using the above example, if TR is £1000, and output is 500, then AR = £2.00. Average Revenue is just another term for price per unit.

Marginal Revenue (MR) = Change in Total Revenue when output increases by one unit. i.e. MR = ΔTR ÷ ΔQ

In many circumstances, a firm will have to lower price to sell a higher quantity. Suppose a firm can sell 500 units per week at £2.00, but to sell 550 units it needs to lower price to £1.90. We can work out the MR as follows:

At a price of £2.00 TR = 500 X £2.00 = £1000

At a price of £1.90 TR = 550 X £1.90 = £1045

Therefore ΔTR = £1045 - £1000 = £45.

ΔQ = 550 -500 = 50

MR = £45÷ 50 = £0.90

Notice that MR is less than AR (price). This is because the demand curve in most circumstances is downward sloping.