Week 1: Sub-Topic: Steady States
Trying to explain the concept of steady state economics to a group of people with little to no formal math or economics training is a little difficult. I thought I could do a variation on a Robinson Crusoe economy but then realized I would have to talk ab out proportional growth rates, etc.
Here's what I have so far:
I need to refine it, come up with some numbers and figures for illustrations. It's amazing that there aren't any applets or applications etc dealing with steady state in non chemistry settings.
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Just in case, I'll work through a simple problem below illustrating an application of steady states
Here's an attempt to explain what happens using a variation of the Robinson Crusoe problem:
You have a castaway (Robinson Crusie, or RC) who is stranded on an island (we'll call this time t0). He has only one stock of a food good (we'll use fish, great source of protein) and we'll just accept that he is a person that can survive on just fish, although he will need a certain amount to eat to survive. There is no one he can trade with and the stock of fish has a specific growth rate (i.e. a set reproductive rate for each fish, etc.) that is given, with F(tx) representing the absolute number of fish at any point in time (for example: 10 fish, 350 fish, etc.)
Now you can see we're making a lot of assumptions regarding the kind of economy he has but it's important so that there are only 2 factors to consider: the number of fish and how many he'd like to eat, or his consumption level.
Let's say we know what the growth rate of the stock of fish is, and that will be the change in fish from knowing the number of fish existing at every point in time. This can be calculating by finding the derivative of the stock of fish.
Don't know what a derivative is? Here's some more info
https://www.khanacademy.org/math/calculus
Here is a site for calculating simple derivatives: http://www.numberempire.com/derivativecalculator.php, and the Wolfram Widget which will actually give you the graphs (useful for those that are more visual) http://www.wolframalpha.com/widgets/view.jsp?id=c44e503833b64e9f27197a484f4257c0
So let's list what we should know in order to solve it as a math problem:
1) The number of fish we start with, F(t0)
2) The number of fish there is at every point in time (assuming that RC is not eating any, so this equation will model what it would like if he wasn't there), F(tx) where x= the time period
3) How much he eats, so C= amount per time
Using #2 we can also find the growth rate of the stock of fish at the point in time
Now the stock of fish at any point in time, since he is actually there and eating, is F(tx)- C, and the change of that system would be represented as the derivative of [F(tx)-C]. In this case, a steady state condition would be that the amount he eats at a point in time is the same amount as the stock of fish will produce at that time. Basically, we can say that there is no change or that the system is in equilibrium (for example, http://en.wikipedia.org/wiki/Economic_equilibrium.
So actual values:
Let's set t0 of fish, or F(t0)= 2
We'll also say his consumption level is C0=16.
Let's also say that the growth rate is G(F(tx))