LaborCapitalAndTheOptimalGrowthOfSocialMovements/CobbDouglas/README.md

## README

## About 
This is some R code for the paper [Labor, Capital, and the Optimal Growth ofSocial Movements](https-//nunosempere.github.io/ea/MovementBuildingForUtilityMaximizers.pdf)

## Structure of the code.

1. `Variables.R`- Contains variables
2. `Transition dynamics.R`- If we know our system at time t, generate an approximation of our system at time t+stepsize. 
3. `Forward Shooting.R`- Carries out the forward shooting. 
4. `ReverseShooting.R`- Nonfunctional. Ignore. 
5. `Plotting.R`- Generates graphs of the results

## How to run

Open files 1.,2.,3., and 5. in an IDE for R, like RStudio. Run them in order. For `Plotting.R`, add or create the directory in which you want the graphs to be generated, making sure it has suitable permissions. 

## Gotchas
Using a very small stepsize runs into floating point errors. Consider a stylized example-

```r
options(digits=22)

dx <- 10^43
numsteps <- 10^7
stepsize <- 10^(-3) 

## Example 1
x <- pi*1e+60
print(x)
for(i in c(1-numsteps)){
  x <- x+dx*stepsize
}
x == pi*1e+60
print(x)

## Example 2
x <- pi*1e+60 + numsteps*stepsize*dx
x == pi*1e+60
print(x)

```

The two examples should give the same results, but don't. 

### Why reverse shooting doesn't work

Consider this example-

```r
## Stylized forward shooting

x <- 0
for(i in c(1-200)){
  x <- x + 7^i
}

## Stylized reverse shooting

y <- x
for(i in c(200-1)){
  y <- y - 7^i
}
print(y)
# [1] -3.762262199769919175323e+152
```

Here, `y` should at the end be 0, but floating point errors ensure that it isn't. Given that our variables grow exponentially, we work with very large numbers and reverse shooting encounters similar errors.