In this video we’ll calculate and compare total, average and marginal revenue.
We’ll examine the different measurements of revenue and highlight the key differences
between them.
Total revenue equals the total amount of revenue earned by a firm.
It is calculated by multiplying price times quantity sold.
If a firm sells 100 units for $5 each, then their total revenue is equal to $500.
Average revenue is equal to the amount of revenue a firm receives for each unit sold.
Since it is equal to revenue divided by quantity sold you could also say its the price of the
product.
Marginal revenue is equal to the additional revenue earned from the sale of an additional
unit.
You calculate it by dividing the change in total revenue by the change in quantity.
We need to understand this at a basic level for now, but will be building on this as we
progress.
Now we’ll look at a table of some simple figures to demonstrate how we calculate the
different revenues.
The first column here is for price, which is the same as average revenue.
As the price falls we see the quantity sold increases.
Total revenue is a simple multiplication of the price and quantity.
This gives us $0 at a price of $20 and total revenue of $40 when the price is $8.
If you have a careful eye you’ve noticed that total revenue first increased, then decreased
at quantity 5.
This is helpful when calculating marginal revenue.
We look a the change in total revenue and divide by the change in quantity.
In this example the change in quantity is always equal to 1 and the change in total
revenue is different.
We can’t calculate marginal revenue at quantity 0, but we see that total revenue rises to
$18 when we sell our first unit.
As we sell progressively more our marginal revenue continues to fall and at quantity
5, becomes negative.
Our firm maximises their revenue by selling at a price of $12 and should not lower their
price any further.
Let’s plot average revenue and marginal revenue together so you can see how their
behaviour is related.
Now let’s plot the data.
I’ve shrunken the table in the right hand corner for reference.
I’ll draw this like I would draw any demand curve.
For each price, I’ll check the associated quantity and place a mark.
If we connect each point we arrive at our demand curve, which is also our average revenue
curve.
This is the case because we assume that the firm consistently sells at the same price
in order to sell a certain amount of a product.
We do the same thing for marginal revenue and plot the points corresponding to the related
quantity.
The main thing different we do here is plot the points in between the quantities.
This is our normal approach for marginal values.
Now we connect all the dots and build our marginal revenue curve.
The unusual thing here is that the marginal revenue curve cuts the X-axis and is negative.
The importance of this will be more relevant as we proceed through this part of the course.
Plotting them together reveals two lines that grow in distance the higher the level of output.
When looking at demand and marginal revenue together, this diagram is most commonly what
you’re going to encounter.
The marginal revenue curve is twice as steep as the average revenue curve.
If you’re interested in knowing exactly why, I’ll put a link in the video description
box for a comprehensive explanation.
For now, just get comfortable with this graph as we’ll be coming back to it quite frequently
as we dig deeper into market structures and their corresponding diagrams.
In this diagram we see the total revenue curve for a firm facing a downward sloping demand
curve.
As we saw in our table earlier, total revenue increases towards a maximum then starts to
decrease.
To think about it another way, total revenue increases as marginal revenue is positive
and peaks where marginal revenue is zero.
Beyond this point, the sale of additional units takes away from that maximum and slowly
reduces total revenue.
I also want to illustrate one other thing here.
There’s a deeper relationship between these two diagrams that you should be able to understand
after studying the AS videos and getting more comfortable with average and marginal revenue.
The demand curve itself is elastic, unitary elastic and inelastic.
The initial portion, highlighted in yellow, is the elastic portion of the demand curve.
This results in an increase in total revenue as the price falls.
Rising total revenue will continue to the point at which PED is equal to 1.
Here, total revenue is maximised.
Beyond this point, the PED is inelastic, which means any further lowering of price decreases
total revenue.
If you’re struggling with this concept, leave a question below and we can work on
an explanation together.
I’ll pin the best explanation to the top of the comments.
By now you should be more comfortable with total, marginal and average revenue and understand
how they are different.
We’ve graphed all three and have even seen the relationship between PED and total revenue.
As always, if there’s anything you didn’t understand or need further explanation on,
leave a comment below and I’ll do my best to respond.
That’s us done for now and I will see you in the next one!