3. Change

Why? The world is not static. Here's what it's like now - what's it going to look like tomorrow?

• Planning.
• Forecasting.
• Most what if questions are about change.
• How does a system (cost, production, services) respond to change?

Change can be thought of in 2 ways; absolute change and relative change.

Notation for an absolute change: change in x, $\Delta x$, change in y, $\Delta y$.

If x goes from 25 to 29, the the absolute change is 29 - 25 = 4.

Notation for a relative change: say x goes from 25 to 26?

The absolute change is (26 - 25) = 1.

The the relative change is (26 - 25)/25 = 0.04, ie $\frac{\Delta x}{x}$.

Examples:

Learning function. Average cost vs. cumulative output.

Marginal -- cost/revenue.

Example - ways of describing change.

x = Volume	y = cost
10	50
11	53

Change x by 1 unit, y changes by 3 units.

Change x by 1 unit, y changes by 6%

Change x by 10%, y changes by 6%.

Change x by 10%, y changes by 3.

All valid ways of describing the change, but 1 and 3 are the most common.

Change can be of three qualitative types (you should be able to draw a graph illustrating each one).

Positive.

0.

Negative.