Introduction
This part of the course looks at the theoretical structure of businesses (now to be known as firms) including assumptions of their revenues and costs.
In the first section we will think seriously about the kinds of costs a firm faces and the assumptions behind these costs.
We will also look at revenue (the money a firm takes in for its trading activities), which will give us an idea of the firm’s profit (the money that is left over).
The things we learn here are the basic building blocks of what we will then do in all the 1.6 units- theory of the firm.
Even though it is all very theoretical, you will master these concepts if you break it down and ensure you understand it through practice.
Marginal, Average, and Total
Say that you’re looking at all the costs that a business needs to pay. When analysing the costs, you could think of them in the following three ways:
Total: Add all the (costs) together.
Average: Add all the (costs) and divide by the number of units sold.
Marginal: The additional (costs) that I get from producing one extra unit.
Note that we could substitute (costs) for other variables (e.g. revenue, output, utility) when discussing these concepts.
There is a relationship here:
- To work out the Marginal, work out the difference between the Total of the previous unit value and the Total this unit value.
- To work out the Total, add on the Marginal to the Total of the previous unit value.
You can practise below:
|
Output |
Total |
Average |
Marginal |
|
0 |
0 |
- |
- |
|
1 |
5 |
5 |
5 |
|
2 |
14 |
7 |
7 |
|
3 |
27 |
9 |
13 |
|
4 |
32 |
8 |
5 |
|
5 |
35 |
7 |
3 |
|
6 |
36 |
6 |
1 |
<click for answers>
Notice how there is no Marginal or Average value for output 0 (you can’t have an average for 0 goods; there is no output before 0 from which to derive a marginal figure).
Now check out the graph for these figures. What relationships can we find?
<click for answers>
- Marginal and Average are both equal to Total at output 1.
And more importantly:
- When Marginal is above Average, Average Rises
- When Marginal is below Average, Average Falls
- Given what’s above, it makes sense that Marginal will equal Average at the point where Average is at its maximum.
These last three points are a fundamental part of theory of the firm. We always draw Marginal intersecting Average where Average is either maximised or minimised.
Relationship Between Marginal and Average
Take the example chart of a person flipping a coin. This person is pretty streaky with their flipping: several wins (marginal rate = 1) in a row, then several losses (marginal rate = 0), followed by several wins. What happens to the average and marginal figures?
At first the average and marginal are the same, and as long as the person keeps winning they remain at 1. But look what happens when the person starts the first losing streak. Marginal jumps to 0 immediately, and average follows more slowly. As long as the person keeps losing, average keeps falling.
Then look what happens when they start winning again. Marginal jumps to 1 immediately, and average starts to rise. Notice how marginal crosses average at a minimum point for average. As long as the streak continues and marginal = 1, average will continue to climb.
Later streaks of winning ad losing follow the same pattern. But as the number of rounds increases, the average rises and falls ever more slowly. It’s as though the average is weighed down by all the rounds that have come before, and by the time it gets to higher rounds it’s ‘heavy’ with its own history. Yet the marginal has no such worries; it is free to flip as quickly as it pleases, as it is only concerned with the value of the next round.
Given that average is the average of this round and all previous rounds, and the marginal is the value of this next round only, this makes perfect sense.
Batting Averages and Batting Marginals
Another way of illustrating this is through baseball. Baseball uses a statistic called a batting average. This measure is a percentage of the number of times a player is at bat (i.e. has a go) where they get a hit (i.e. advance to a base). This figure is calculated per game, per season, and over a batter’s career. Some games a batter will try a few times and never get to base and the batting average (for the game) would be 0. Some games a player will get a hit every time they are at bat and their batting average (for the game) would be 1. A professional player with a batting average above 0.300 for the season is considered very good.
The chart shows Nolan Arenado of the Colorado Rockies’ batting performance for the 2019 season. The blue line is the batting average per game; let’s say this is the marginal. The orange line is the batting average for the season; let’s say this is the average.
The chart shows what we would expect to see: orange average follows the blue marginal, and in the early games the average can travel quite freely. At about 50 games Nolan has a streak of great games, which brings his season average up to nearly 0.350 for that part in the season. As the season goes on the average levels out; the good games still bring up the season average, but not as much as they did in the early part of the season. Nolan finishes the season with a great streak of games, but by this point the average is pretty set so it only changes slightly.
It’s as we said before: marginal is free and average is heavy, and average always follows the marginal.
1.5.1 PowerPoint