Added README, code and plots

README.md

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+## 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. 

code/ForwardShooting.R

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+# Forward shooting
+options(digits=7) 
+
+## Evolution
+x1_array_forward_shooting <- c()
+x3_array_forward_shooting <- c()
+a1_array_forward_shooting <- c()
+a3_array_forward_shooting <- c()
+s1_array_forward_shooting <- c()
+s3_array_forward_shooting <- c()
+x1_t = x1_init
+x3_t = x3_init
+#stepsize
+comienzo = Sys.time()
+max = max(times_forward_shooting)
+
+for(t in times_forward_shooting){
+  if((100*t/max) %in% seq(from=0, to=100, by=1)){
+    cat(paste(floor(100*t/max), "%", sep=""))
+    cat("\n")
+  }
+  a1_t = a1(t)
+  a3_t = a3(t)
+  s1_t = s1(t)
+  s3_t = s3(t)
+  x1_t = x1_t*(1+r1_stepsize) + dx1(t)*stepsize
+  x3_t = x3_t*(1+r3_stepsize) + dx3(t)*stepsize
+  
+  a1_array_forward_shooting <- c(a1_array_forward_shooting, a1_t)
+  a3_array_forward_shooting <- c(a3_array_forward_shooting, a3_t)
+  s1_array_forward_shooting <- c(s1_array_forward_shooting, s1_t)
+  s3_array_forward_shooting <- c(s3_array_forward_shooting, s3_t)
+  x1_array_forward_shooting <- c(x1_array_forward_shooting, x1_t)
+  x3_array_forward_shooting <- c(x3_array_forward_shooting, x3_t)
+  
+}
+fin = Sys.time()
+fin-comienzo
+
+## Checking conditions
+options(digits=22) 
+
+l = length(times_forward_shooting)
+x1_array_forward_shooting[l]
+x1_growth = (x1_array_forward_shooting[l]-x1_array_forward_shooting[l-1])/x1_array_forward_shooting[l-1]/(1*stepsize) 
+x1_growth
+sum(x1_array_forward_shooting<0)
+
+x3_array_forward_shooting[l]
+x3_growth = (x3_array_forward_shooting[l]-x3_array_forward_shooting[l-1])/x3_array_forward_shooting[l-1]/(1*stepsize) 
+x3_growth
+sum(x3_array_forward_shooting<0)
+
+
+a1_growth = (a1_array_forward_shooting[l]-a1_array_forward_shooting[l-1])/a1_array_forward_shooting[l-1]/stepsize
+a1_growth
+
+a3_growth = (a3_array_forward_shooting[l]-a3_array_forward_shooting[l-1])/a3_array_forward_shooting[l-1]/stepsize
+a3_growth
+
+a1_array_forward_shooting[l]/x1_array_forward_shooting[l]
+plot((a1_array_forward_shooting/x1_array_forward_shooting)[(l-100):l])
+

code/Plotting.R

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+# Plotting
+## install.packages("tidyverse") <- Not totally necessary.
+## install.packages("ggplot2")
+## install.packages("ggsci")
+library(ggplot2)
+library(ggsci)
+
+## General variables
+saveplots=TRUE
+times = times_forward_shooting 
+  ## Also for reverse shooting plots; time in reverse shooting is inverted
+shootingtype="reverse"#"forward"#
+shootingtype="forward"#"reverse"#
+# directory = "/home/nuno/Documents/core/SRF/BackShooting/RCode/plots/temp"
+
+workingdir = "/home/<user>/Documents/<path>" # Write your own
+# directory = paste(workingdir, shootingtype, "shooting", "/", last, "years", sep="")
+# directory
+setwd(workingdir)
+# setwd(directory)
+
+if(shootingtype=="forward"){
+  x1_array_plotting <- x1_array_forward_shooting
+  x3_array_plotting <- x3_array_forward_shooting
+  a1_array_plotting <- a1_array_forward_shooting
+  a3_array_plotting <- a3_array_forward_shooting
+  s1_array_plotting <- s1_array_forward_shooting
+  s3_array_plotting <- s3_array_forward_shooting
+} else if(shootingtype=="reverse"){
+  x1_array_plotting <- x1_array_reverse_shooting
+  x3_array_plotting <- x3_array_reverse_shooting
+  a1_array_plotting <- a1_array_reverse_shooting
+  a3_array_plotting <- a3_array_reverse_shooting
+  s1_array_plotting <- s1_array_reverse_shooting
+  s3_array_plotting <- s3_array_reverse_shooting
+}
+
+height = 5
+width = floor(height*(1+sqrt(5))/2)
+imagenumbercounter = 1
+saveplot = function(imagename){
+  if(saveplots){
+    ggsave(paste(imagenumbercounter,"_", imagename, "_",shootingtype, "shooting",".png", sep =""), units="in", width=width, height=height)  
+    imagenumbercounter <<- imagenumbercounter+1
+    ## https://stackoverflow.com/questions/1236620/global-variables-in-r
+  }
+}
+options(digits=1) ## Just for display
+
+## x1 and x3
+
+xs <- list()
+xs$values <- c(x1_array_plotting, x3_array_plotting)
+xs$var <- c(rep("x1", length(x1_array_plotting)), rep("x3", length(x3_array_plotting)))
+xs$times = rep(times,2)
+xs <- as.data.frame(xs)
+title_text = "Evolution of state variables"
+(ggplot(data = xs, aes(x = times, y= values, color = var)) +
+  geom_line(size = 0.5)
+  + labs(
+    title=title_text,
+    x="Year since start", 
+    y="Capital and labor" 
+  )
+  +theme(
+    legend.title = element_blank(),
+    plot.title = element_text(hjust = 0.5),
+    legend.position="bottom",
+    legend.box="vertical"
+  )
+  + scale_color_lancet(
+    breaks=c("x1", "x3"),
+    labels=c("Capital", "Labor")
+    
+  )
+  + scale_y_continuous(breaks = seq(min(x1_array_plotting), max(x1_array_plotting), length.out=5)) ## Necessary for displaying very large numbers
+)
+saveplot("StateVariablesX1X3")
+
+## x1 and x3: log plot
+title_text = "Evolution of state variables"
+(ggplot(data = xs, aes(x = times, y= values, color = var)) +
+    geom_line(size = 0.5)
+  +labs(
+    title=title_text,
+    subtitle="(logarithmic scale)",
+    x="Year since start", 
+    y="Capital and labor" 
+  )
+  +theme(
+    legend.title = element_blank(),
+    plot.title = element_text(hjust = 0.5),
+    plot.subtitle = element_text(hjust = 0.5),
+    legend.position="bottom",
+    legend.box="vertical"
+  )
+  + scale_color_lancet(
+    breaks=c("x1", "x3"),
+    labels=c("Capital", "Labor")
+    
+  )
+  + scale_y_continuous(trans = 'log2')
+)
+saveplot("StateVariablesX1X3logplot")
+
+
+## Only x3
+equis3 <- list()
+equis3$values <- c(x3_array_plotting)
+equis3$times = times
+equis3 <- as.data.frame(equis3)
+
+title_text = "Evolution of movement size"
+(ggplot(data = equis3, aes(x = times, y= values)) 
+  +geom_line(size = 0.5)
+  +labs(
+    title=title_text,
+    x="Year since start", 
+    y="Labor" 
+  )
+  +theme(
+    legend.title = element_blank(),
+    plot.title = element_text(hjust = 0.5),
+    legend.position="bottom",
+    legend.box="vertical"
+  )
+)
+saveplot("StateVariableX3")
+
+
+## s1, s3, s4
+sigmas <- list()
+s4_array_plotting=1-s1_array_plotting-s3_array_plotting
+sigmas$values <- c(s1_array_plotting, s3_array_plotting,s4_array_plotting)
+sigmas$fraction <- c(rep("s1", length(s1_array_plotting)), rep("s3", length(s3_array_plotting)),rep("s4", length(s3_array_plotting)))
+sigmas$times = rep(times,3)
+sigmas <- as.data.frame(sigmas)
+
+title_text = "Evolution of labor fractions"
+(ggplot(data = sigmas, aes(x = times, y= values, color = fraction)) +
+    geom_line(size = 0.5)
+  +labs(
+    title=title_text,
+    x="Year since start", 
+    y="Fraction of total labor" 
+  )
+  +theme(
+    legend.title = element_blank(),
+    plot.title = element_text(hjust = 0.5),
+    legend.position="bottom",
+    legend.direction="vertical"
+  )
+  + scale_color_lancet(
+    breaks=c("s1", "s3", "s4"),
+    labels=c("Direct work", "Movement building", "Money-making")
+    
+  )
+)
+saveplot("MovementFractions")
+
+## s1 and s3
+sigmas <- list()
+sigmas$values <- c(s1_array_plotting, s3_array_plotting)
+sigmas$fraction <- c(rep("s1", length(s1_array_plotting)), rep("s3", length(s3_array_plotting)))
+sigmas$times = rep(times,2)
+sigmas <- as.data.frame(sigmas)
+
+title_text = "Evolution of labor fractions"
+subtitle_text = "(only direct work and movement building)"
+(ggplot(data = sigmas, aes(x = times, y= values, color = fraction)) +
+    geom_line(size = 0.5)
+  +labs(
+    title=title_text,
+    subtitle=subtitle_text, 
+    x="Year since start", 
+    y="Fraction of total labor" 
+  )
+  +theme(
+    legend.title = element_blank(),
+    plot.subtitle = element_text(hjust = 0.5), 
+    plot.title = element_text(hjust = 0.5),
+    legend.position="bottom",
+    legend.direction="vertical"
+  )
+  + scale_color_lancet(
+    breaks=c("s1", "s3"),
+    labels=c("Direct work", "Movement building")
+    
+  )
+)
+saveplot("MovementFractionsS1S3")
+
+## Just direct work.
+sigma1 <- list()
+sigma1$values <- c(s1_array_plotting)
+sigma1$times = times
+sigma1 <- as.data.frame(sigma1)
+
+title_text = "Evolution of direct work \nas a fraction of total labor"
+(ggplot(data = sigma1, aes(x = times, y= values)) 
+  +geom_line(size = 0.5)
+  +labs(
+    title=title_text,
+    x="Year since start", 
+    y="Fraction of total labor" 
+  )
+  +theme(
+    legend.title = element_blank(),
+    plot.title = element_text(hjust = 0.5),
+    legend.position="bottom",
+    legend.box="vertical"
+  )
+)
+saveplot("MovementFractionsS1")
+
+
+## Just movement building
+sigma3 <- list()
+sigma3$values <- c(s3_array_plotting)
+sigma3$times = times
+sigma3 <- as.data.frame(sigma3)
+
+title_text = "Evolution of movement building\nas a fraction of total labor"
+(ggplot(data = sigma3, aes(x = times, y= values)) 
+  +geom_line(size = 0.5)
+  +labs(
+    title=title_text,
+    x="Year since start", 
+    y="Fraction of labor" 
+  )
+  +theme(
+    legend.title = element_blank(),
+    plot.title = element_text(hjust = 0.5),
+    legend.position="bottom",
+    legend.box="vertical"
+  )
+)
+saveplot("MovementFractionsS3")
+
+## Just direct work - logplot
+sigma1 <- list()
+sigma1$values <- c(s1_array_plotting)
+sigma1$times = times
+sigma1 <- as.data.frame(sigma1)
+
+title_text = "Evolution of direct work \nas a fraction of labor"
+(ggplot(data = sigma1, aes(x = times, y= values)) 
+  +geom_line(size = 0.5)
+  +labs(
+    title=title_text,
+    subtitle="(logarithmic scale)", 
+    x="Year since start", 
+    y="Fraction of labor" 
+  )
+  +theme(
+    legend.title = element_blank(),
+    plot.subtitle = element_text(hjust = 0.5), 
+    plot.title = element_text(hjust = 0.5),
+    legend.position="bottom",
+    legend.box="vertical"
+  )
+  + scale_y_continuous(trans = 'log2')
+)
+saveplot("MovementFractionsS1logplot")
+
+## Just movement building
+sigma3 <- list()
+sigma3$values <- c(s3_array_plotting)
+sigma3$times = times
+sigma3 <- as.data.frame(sigma3)
+
+title_text = "Evolution of movement building\nas a fraction of labor"
+(ggplot(data = sigma3, aes(x = times, y= values)) 
+  +geom_line(size = 0.5)
+  +labs(
+    title=title_text,
+    subtitle="(logarithmic scale)", 
+    x="Year since start", 
+    y="Fraction of total labor" 
+  )
+  +theme(
+    legend.title = element_blank(),
+    plot.subtitle = element_text(hjust = 0.5), 
+    plot.title = element_text(hjust = 0.5),
+    legend.position="bottom",
+    legend.box="vertical"
+  )
+  + scale_y_continuous(trans = 'log2')
+)
+saveplot("MovementFractionsS3logplot")
+
+## sigma_1*x3 and sigma3*x3, sigma_4*x3, 
+sigmaxs <- list()
+sigmaxs$values <- c(s1_array_plotting*x3_array_plotting, s3_array_plotting*x3_array_plotting, s4_array_plotting*x3_array_plotting)
+sigmaxs$fraction <- c(rep("s1x3", length(s1_array_plotting)), rep("s3x3", length(s3_array_plotting)), rep("s4x3", length(s3_array_plotting)))
+sigmaxs$times = rep(times,3)
+sigmaxs <- as.data.frame(sigmaxs)
+
+title_text = "Evolution of labor\n in absolute terms"
+(ggplot(data = sigmaxs, aes(x = times, y= values, color = fraction)) +
+    geom_line(size = 0.5)
+  +labs(
+    title=title_text,
+    x="Year since start", 
+    y="Absolute number\nof movement participants" 
+  )
+  +theme(
+    legend.title = element_blank(),
+    plot.title = element_text(hjust = 0.5),
+    legend.position="bottom",
+    legend.direction="vertical"
+  )
+  + scale_color_lancet(
+    breaks=c("s1x3", "s3x3", "s4x3"),
+    labels=c("Direct work", "Movement building", "Money-making")
+    
+  )
+)
+saveplot("MovementParticipantNumbersS1S3S4")
+
+## sigma_1*x3 and sigma3*x3
+sigmaxs <- list()
+sigmaxs$values <- c(s1_array_plotting*x3_array_plotting, s3_array_plotting*x3_array_plotting)
+sigmaxs$fraction <- c(rep("s1x3", length(s1_array_plotting)), rep("s3x3", length(s3_array_plotting)))
+sigmaxs$times = rep(times,2)
+sigmaxs <- as.data.frame(sigmaxs)
+
+title_text = "Evolution of movement participants\nin absolute terms"
+(ggplot(data = sigmaxs, aes(x = times, y= values, color = fraction)) +
+    geom_line(size = 0.5)
+  +labs(
+    title=title_text,
+    subtitle="(only direct workers and movement builders)", 
+    x="Year since start", 
+    y="Absolute number\nof movement participants" 
+  )
+  +theme(
+    legend.title = element_blank(),
+    plot.title = element_text(hjust = 0.5),
+    legend.position="bottom",
+    legend.direction="vertical"
+  )
+  + scale_color_lancet(
+    breaks=c("s1x3", "s3x3"),
+    labels=c("Direct work", "Movement building")
+    
+  )
+)
+saveplot("MovementParticipantNumbersS1S3")
+
+## sigma_1*x3 and sigma3*x3 logplot
+sigmaxs <- list()
+sigmaxs$values <- c(s1_array_plotting*x3_array_plotting, s3_array_plotting*x3_array_plotting)
+sigmaxs$fraction <- c(rep("s1x3", length(s1_array_plotting)), rep("s3x3", length(s3_array_plotting)))
+sigmaxs$times = rep(times,2)
+sigmaxs <- as.data.frame(sigmaxs)
+
+title_text = "Evolution of movement participants\nin absolute terms \n(logarithmic scale)"
+(ggplot(data = sigmaxs, aes(x = times, y= values, color = fraction)) +
+    geom_line(size = 0.5)
+  +labs(
+    title=title_text,
+    subtitle="(only direct workers and movement builders)", 
+    x="Year since start", 
+    y="Absolute number\nof movement participants" 
+  )
+  +theme(
+    legend.title = element_blank(),
+    plot.title = element_text(hjust = 0.5),
+    legend.position="bottom",
+    legend.direction="vertical"
+  )
+  + scale_color_lancet(
+    breaks=c("s1x3", "s3x3"),
+    labels=c("Direct work", "Movement building")
+    
+  )
+  + scale_y_continuous(trans = 'log2')
+)
+saveplot("MovementParticipantNumbersS1S3logplot")
+
+## alpha1 and alpha3
+alphas <- list()
+alphas$values <- c(a1_array_plotting, a3_array_plotting)
+alphas$fraction <- c(rep("a1", length(s1_array_plotting)), rep("a2", length(s3_array_plotting)))
+alphas$times = rep(times,2)
+alphas <- as.data.frame(alphas)
+
+title_text = "Evolution of spending"
+(ggplot(data = alphas, aes(x = times, y= values, color = fraction)) +
+    geom_line(size = 0.5)
+  +labs(
+    title=title_text,
+    x="Year since start", 
+    y="Spending" 
+  )
+  +theme(
+    legend.title = element_blank(),
+    plot.title = element_text(hjust = 0.5),
+    legend.position="bottom",
+    legend.direction="vertical"
+  )
+  + scale_color_lancet(
+    breaks=c("a1", "a2"),
+    labels=c("Direct spending","Spending on movement building")
+    
+  )
+)
+saveplot("SpendingA1A3")
+
+## alpha1 and alpha3: log plot
+
+alphas <- list()
+alphas$values <- c(a1_array_plotting, a3_array_plotting)
+alphas$fraction <- c(rep("a1", length(s1_array_plotting)), rep("a2", length(s3_array_plotting)))
+alphas$times = rep(times,2)
+alphas <- as.data.frame(alphas)
+
+title_text = "Evolution of spending"
+(ggplot(data = alphas, aes(x = times, y= values, color = fraction)) +
+    geom_line(size = 0.5)
+  +labs(
+    title=title_text,
+    subtitle="(logarithmic scale)",
+    x="Year since start", 
+    y="Spending" 
+  )
+  +theme(
+    legend.title = element_blank(),
+    plot.title = element_text(hjust = 0.5),
+    plot.subtitle = element_text(hjust = 0.5),
+    legend.position="bottom",
+    legend.direction="vertical"
+  )
+  + scale_color_lancet(
+    breaks=c("a1", "a2"),
+    labels=c("Direct spending","Spending on movement building")
+  )
+  + scale_y_continuous(trans = 'log2')
+)
+saveplot("SpendingA1A3logplot")
+

code/ReverseShooting.R

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+# Reverse shooting
+options(digits=22)
+
+## Evolution
+x1_array_reverse_shooting <- c()
+x3_array_reverse_shooting <- c()
+a1_array_reverse_shooting <- c()
+a3_array_reverse_shooting <- c()
+s1_array_reverse_shooting <- c()
+s3_array_reverse_shooting <- c()
+l = length(a1_array_forward_shooting)
+x1_t = x1_array_forward_shooting[l] 
+x3_t = x3_array_forward_shooting[l]
+
+comienzo = Sys.time()
+max = max(times_reverse_shooting)
+t=times_reverse_shooting[1]
+for(t in times_reverse_shooting){
+  if((100*t/max) %in% seq(from=0, to=100, by=3)){
+    print(paste(floor(100*t/max), "%", sep=""))
+    #print("\n")
+  }
+  
+  t_previous = t-stepsize
+  a1_t = a1(t_previous)
+  a3_t = a3(t_previous)
+  s1_t = s1(t_previous)
+  s3_t = s3(t_previous)
+  guessmin =  0
+  guessmax = x3_t
+  x3_target = x3_t
+
+  x3_t = dx3_reverse_shooting(t, guessmin, guessmax, x3_target, t_previous) 
+  # x3_t = x3_t - dx3(t-stepsize)*stepsize #
+  x1_t = (x1_t - dx1(t-stepsize)*stepsize)/(1+r1_stepsize)
+  
+  ## But then I can calulate s1, s3 again, and do another iteration.
+  # for(i in c(1:10)){
+  #   # using the new x3_t
+  #   s3_t = s3(t_previous)
+  #   x3_t = dx3_reverse_shooting(t, guessmin, guessmax, x3_target) 
+  #   x3_t
+  # }
+  # s1_t = s1(t_previous) 
+  # x1_t = (x1_t - dx1(t-stepsize)*stepsize)/(1+r_stepsize)
+  
+  a1_array_reverse_shooting <- c(a1_t, a1_array_reverse_shooting)
+  a3_array_reverse_shooting <- c(a3_t, a3_array_reverse_shooting)
+  s1_array_reverse_shooting <- c(s1_t, s1_array_reverse_shooting)
+  s3_array_reverse_shooting <- c(s3_t, s3_array_reverse_shooting)
+  x1_array_reverse_shooting <- c(x1_t, x1_array_reverse_shooting)
+  x3_array_reverse_shooting <- c(x3_t, x3_array_reverse_shooting)
+  
+}
+fin = Sys.time()
+fin-comienzo
+options(digits=7)
+x1_array_reverse_shooting[1] ## 10^11
+x3_array_reverse_shooting[1]
+
+
+# View(x1_array_reverse_shooting)
+

code/TransitionDynamics.R

@@ -0,0 +1,55 @@
+# Transition dynamics
+# install.packages("pracma")
+library(pracma)
+
+## For forward shooting
+a1 <- function(t){
+  term_a1 = λ_1 * 
+    ((1- λ_1)/( λ_1 * w_3 * exp(γ_1 * t)))^((1-λ_1) * (1-η)) /
+    (k1_forward_shooting * exp((ρ-r_1) * t))
+  result_a1 = term_a1^(1/η)
+  return(result_a1)
+}
+
+a3 <- function(t){
+  first_term_a3 = w_3 * exp(γ_1 * t) * δ_3 * λ_3 *
+    β_3 * exp(γ_3 * t) / (r_1 - γ_1 - r_3)
+  second_term_a3 = (1-λ_3)/(λ_3 * w_3 * exp(γ_1 * t))
+  subresult_a3 = first_term_a3 * (second_term_a3^(δ_3*(1-λ_3)))
+  result_a3 = subresult_a3^(1/(1-δ_3))
+  return(result_a3)
+}
+
+s1 <- function(t){
+  result_s1 = ((1-λ_1)/ λ_1) * (a1_t / (x3_t * w_3 * exp(γ_1 * t)))
+  return(result_s1)
+}
+
+s3 <- function(t){
+  result_s3 = ((1-λ_3)/ λ_3) * (a3_t / (x3_t * w_3 * exp(γ_1 * t)))
+  return(result_s3)
+}
+
+dx1 <- function(t){
+  result_x1 = - a1_t - a3_t + x3_t * w_3 * exp(γ_1 * t) * (1-s1_t - s3_t)
+  return(result_x1)
+}
+dx3 <- function(t){
+  result_x3 = β_3 * exp(γ_3 * t) * (a3(t)^λ_3 * (s3_t*x3_t)^(1-λ_3))^δ_3
+  return(result_x3)
+}
+
+dx3_reverse_shooting <- function(t, guessmin, guessmax, x3_target, t_previous){
+  ## Inverting dx3 turns out to be a little bit involved. 
+  check_hypothesis <- function(x3_hypothesis){
+    dx3_hypothesis = β_3 * exp(γ_3 * t_previous) * (a3(t_previous)^λ_3 * (s3_t*x3_hypothesis)^(1-λ_3))^δ_3
+    difference = x3_target - (x3_hypothesis + dx3_hypothesis*stepsize)
+    return(difference)
+  }
+  x3_best_guess <- bisect(check_hypothesis, guessmin, guessmax)$root
+  #uniroot(check_hypothesis, lower=guessmin, upper=guessmax, tol = 10^(-22))[[1]]
+   # x3_best_guess <- uniroot(check_hypothesis, lower=(x3_target-2), upper=(x3_target), tol = 10^(-22), extendInt = "down")[[1]]
+  ## x3_best_guess <- uniroot(check_hypothesis, c(0, x3_target), tol = 10^(-22), a = 0, extendInt = "upX")[[1]]
+  return(x3_best_guess)
+}
+

code/Variables.R

@@ -0,0 +1,36 @@
+# Variables
+η = 0.9 ## 1.1
+ρ = 0.005
+r_1 = 0.06
+r_3 = -0.02
+γ_1 = 0.03
+γ_3 = 0.01
+w_3 = 5000 ## Mean on the EA Survey 2018: ~7000
+β_3 = 1 ## 1 ## 0.5 Corresponds to roughly 5 people convincing 10 other people per year on a 50k year budget
+  ## Dramatic if beta = 0.5, w_3 = 1000
+λ_1 = 0.5
+λ_3 = 0.5
+δ_3 = 0.44
+
+## k1_forward_shooting
+k1_forward_shooting = 3*10^(-7) 
+  ## 1*10^(-7) fails. 2*10^(-7) fails
+  ## Artfully guessed.
+k1_reverse_shooting = k1_forward_shooting
+
+
+stepsize = 0.1
+  ## stepsize = 0.1 => seconds (7s). 
+  ## stepsize = 0.01 => minutes (3 mins).
+r1_stepsize = ((1+r_1)^stepsize)-1
+r3_stepsize = ((1+r_3)^stepsize)-1
+
+first = 0
+last = 1000
+times_forward_shooting = seq(from=first, to=last, by=stepsize)
+times_reverse_shooting = seq(from=last, to=first, by=-stepsize)
+
+### Initial conditions. Correspond to "year 0". 
+x1_init = 10^10
+x3_init = 10^5
+

plots/10000years/.Rhistory

@@ -0,0 +1,512 @@
+k1_reverse_shooting = k1_forward_shooting
+## Artfully guessed, such that s1 < 1
+stepsize = 0.1
+## stepsize = 0.1 => seconds (7s).
+## stepsize = 0.01 => minutes (3 mins).
+r_stepsize = ((1+r_1)^stepsize)-1
+first = 0
+last = 10000
+times_forward_shooting = seq(from=first, to=last, by=stepsize)
+times_reverse_shooting = seq(from=last, to=first, by=-stepsize)
+### Initial conditions. Correspond to "year 0".
+x1_init = 10^10 ## 1 billion? 15 billion? 100 billion? Too much?
+x3_init = 10^5
+# Forward shooting
+options(digits=7)
+## Evolution
+x1_array_forward_shooting <- c()
+x3_array_forward_shooting <- c()
+a1_array_forward_shooting <- c()
+a3_array_forward_shooting <- c()
+s1_array_forward_shooting <- c()
+s3_array_forward_shooting <- c()
+x1_t = x1_init
+x3_t = x3_init
+#stepsize
+comienzo = Sys.time()
+max = max(times_forward_shooting)
+for(t in times_forward_shooting){
+if((100*t/max) %in% seq(from=0, to=100, by=1)){
+cat(paste(floor(100*t/max), "%", sep=""))
+cat("\n")
+}
+a1_t = a1(t)
+a3_t = a3(t)
+s1_t = s1(t)
+s3_t = s3(t)
+x1_t = x1_t*(1+r_stepsize) + dx1(t)*stepsize
+x3_t = x3_t + dx3(t)*stepsize
+a1_array_forward_shooting <- c(a1_array_forward_shooting, a1_t)
+a3_array_forward_shooting <- c(a3_array_forward_shooting, a3_t)
+s1_array_forward_shooting <- c(s1_array_forward_shooting, s1_t)
+s3_array_forward_shooting <- c(s3_array_forward_shooting, s3_t)
+x1_array_forward_shooting <- c(x1_array_forward_shooting, x1_t)
+x3_array_forward_shooting <- c(x3_array_forward_shooting, x3_t)
+}
+fin = Sys.time()
+fin-comienzo
+## Checking condition
+options(digits=22)
+l = length(times_forward_shooting)
+x1_array_forward_shooting[l]
+x1_growth = (x1_array_forward_shooting[l]-x1_array_forward_shooting[l-1])/x1_array_forward_shooting[l-1]/(1*stepsize)
+x1_growth
+sum(x1_array_forward_shooting<0)
+x3_array_forward_shooting[l]
+x3_growth = (x3_array_forward_shooting[l]-x3_array_forward_shooting[l-1])/x3_array_forward_shooting[l-1]/(1*stepsize)
+x3_growth
+sum(x3_array_forward_shooting<0)
+a1_growth = (a1_array_forward_shooting[l]-a1_array_forward_shooting[l-1])/a1_array_forward_shooting[l-1]/stepsize
+a1_growth
+a3_growth = (a3_array_forward_shooting[l]-a3_array_forward_shooting[l-1])/a3_array_forward_shooting[l-1]/stepsize
+a3_growth
+a1_array_forward_shooting[l]/x1_array_forward_shooting[l]
+plot((a1_array_forward_shooting/x1_array_forward_shooting)[(l-100):l])
+# Plotting
+## install.packages("tidyverse") <- Not totally necessary.
+## install.packages("ggplot2")
+## install.packages("ggsci")
+library(ggplot2)
+library(ggsci)
+## General variables
+saveplots=TRUE
+times = times_forward_shooting
+## Also for reverse shooting plots; time in reverse shooting is inverted
+shootingtype="reverse"#"forward"#
+shootingtype="forward"#"reverse"#
+# directory = "/home/nuno/Documents/core/SRF/BackShooting/RCode/plots/temp"
+directory = paste("/home/nuno/Documents/core/SRF/BackShooting/RCode/plots/satisfactory3/", shootingtype, "shooting", "/", last, "years", sep="")
+directory
+setwd(directory)
+if(shootingtype=="forward"){
+x1_array_plotting <- x1_array_forward_shooting
+x3_array_plotting <- x3_array_forward_shooting
+a1_array_plotting <- a1_array_forward_shooting
+a3_array_plotting <- a3_array_forward_shooting
+s1_array_plotting <- s1_array_forward_shooting
+s3_array_plotting <- s3_array_forward_shooting
+} else if(shootingtype=="reverse"){
+x1_array_plotting <- x1_array_reverse_shooting
+x3_array_plotting <- x3_array_reverse_shooting
+a1_array_plotting <- a1_array_reverse_shooting
+a3_array_plotting <- a3_array_reverse_shooting
+s1_array_plotting <- s1_array_reverse_shooting
+s3_array_plotting <- s3_array_reverse_shooting
+}
+height = 5
+width = floor(height*(1+sqrt(5))/2)
+imagenumbercounter = 1
+saveplot = function(imagename){
+if(saveplots){
+ggsave(paste(imagenumbercounter,"_", imagename, "_",shootingtype, "shooting",".png", sep =""), units="in", width=width, height=height)
+imagenumbercounter <<- imagenumbercounter+1
+## https://stackoverflow.com/questions/1236620/global-variables-in-r
+}
+}
+options(digits=1) ## Just for display
+## x1 and x3
+xs <- list()
+xs$values <- c(x1_array_plotting, x3_array_plotting)
+xs$var <- c(rep("x1", length(x1_array_plotting)), rep("x3", length(x3_array_plotting)))
+xs$times = rep(times,2)
+xs <- as.data.frame(xs)
+title_text = "Evolution of state variables"
+(ggplot(data = xs, aes(x = times, y= values, color = var)) +
+geom_line(size = 0.5)
++ labs(
+title=title_text,
+#subtitle="n =303",
+x="Year since start",
+y="Capital and labor"
+#caption="@EA Mental Health Survey"
+)
++theme(
+legend.title = element_blank(),
+#plot.subtitle = element_text(hjust = 0.5),
+plot.title = element_text(hjust = 0.5),
+#axis.text.y = element_blank(),
+legend.position="bottom",
+legend.box="vertical"
+)
++ scale_color_lancet(
+breaks=c("x1", "x3"),
+labels=c("Capital", "Labor")
+)
++ scale_y_continuous(breaks = seq(min(x1_array_plotting), max(x1_array_plotting), length.out=5))
+)
+saveplot("StateVariablesX1X3")
+## x1 and x3: log plot
+title_text = "Evolution of state variables"
+(ggplot(data = xs, aes(x = times, y= values, color = var)) +
+geom_line(size = 0.5)
++labs(
+title=title_text,
+subtitle="(logarithmic scale)",
+#subtitle="n =303",
+x="Year since start",
+y="Capital and labor"
+#caption="@EA Mental Health Survey"
+)
++theme(
+legend.title = element_blank(),
+#plot.subtitle = element_text(hjust = 0.5),
+plot.title = element_text(hjust = 0.5),
+plot.subtitle = element_text(hjust = 0.5),
+#axis.text.y = element_blank(),
+legend.position="bottom",
+legend.box="vertical"
+)
++ scale_color_lancet(
+breaks=c("x1", "x3"),
+labels=c("Capital", "Labor")
+)
++ scale_y_continuous(trans = 'log2')
+)
+saveplot("StateVariablesX1X3logplot")
+## Only x3
+equis3 <- list()
+equis3$values <- c(x3_array_plotting)
+equis3$times = times
+equis3 <- as.data.frame(equis3)
+title_text = "Evolution of movement size"
+(ggplot(data = equis3, aes(x = times, y= values))
++geom_line(size = 0.5)
++labs(
+title=title_text,
+#subtitle="n =303",
+x="Year since start",
+y="Labor"
+#caption="@EA Mental Health Survey"
+)
++theme(
+legend.title = element_blank(),
+#plot.subtitle = element_text(hjust = 0.5),
+plot.title = element_text(hjust = 0.5),
+#axis.text.y = element_blank(),
+legend.position="bottom",
+legend.box="vertical"
+)
+##+ scale_color_lancet()
+)
+saveplot("StateVariableX3")
+## s1, s3, s4
+sigmas <- list()
+s4_array_plotting=1-s1_array_plotting-s3_array_plotting
+sigmas$values <- c(s1_array_plotting, s3_array_plotting,s4_array_plotting)
+sigmas$fraction <- c(rep("s1", length(s1_array_plotting)), rep("s3", length(s3_array_plotting)),rep("s4", length(s3_array_plotting)))
+sigmas$times = rep(times,3)
+sigmas <- as.data.frame(sigmas)
+title_text = "Evolution of labor fractions"
+(ggplot(data = sigmas, aes(x = times, y= values, color = fraction)) +
+geom_line(size = 0.5)
++labs(
+title=title_text,
+#subtitle="n =303",
+x="Year since start",
+y="Fraction of total labor"
+#caption="@EA Mental Health Survey"
+)
++theme(
+legend.title = element_blank(),
+#plot.subtitle = element_text(hjust = 0.5),
+plot.title = element_text(hjust = 0.5),
+#axis.text.y = element_blank(),
+legend.position="bottom",
+legend.direction="vertical"
+)
++ scale_color_lancet(
+breaks=c("s1", "s3", "s4"),
+labels=c("Direct work", "Movement building", "Money-making")
+)
+)
+saveplot("MovementFractions")
+## s1 and s3
+sigmas <- list()
+sigmas$values <- c(s1_array_plotting, s3_array_plotting)
+sigmas$fraction <- c(rep("s1", length(s1_array_plotting)), rep("s3", length(s3_array_plotting)))
+sigmas$times = rep(times,2)
+sigmas <- as.data.frame(sigmas)
+title_text = "Evolution of labor fractions"
+subtitle_text = "(only direct work and movement building)"
+(ggplot(data = sigmas, aes(x = times, y= values, color = fraction)) +
+geom_line(size = 0.5)
++labs(
+title=title_text,
+subtitle=subtitle_text,
+x="Year since start",
+y="Fraction of total labor"
+#caption="@EA Mental Health Survey"
+)
++theme(
+legend.title = element_blank(),
+plot.subtitle = element_text(hjust = 0.5),
+plot.title = element_text(hjust = 0.5),
+#axis.text.y = element_blank(),
+legend.position="bottom",
+legend.direction="vertical"
+)
++ scale_color_lancet(
+breaks=c("s1", "s3"),
+labels=c("Direct work", "Movement building")
+)
+)
+saveplot("MovementFractionsS1S3")
+## Just direct work.
+sigma1 <- list()
+sigma1$values <- c(s1_array_plotting)
+sigma1$times = times
+sigma1 <- as.data.frame(sigma1)
+title_text = "Evolution of direct work \nas a fraction of total labor"
+(ggplot(data = sigma1, aes(x = times, y= values))
++geom_line(size = 0.5)
++labs(
+title=title_text,
+#subtitle="n =303",
+x="Year since start",
+y="Fraction of total labor"
+#caption="@EA Mental Health Survey"
+)
++theme(
+legend.title = element_blank(),
+#plot.subtitle = element_text(hjust = 0.5),
+plot.title = element_text(hjust = 0.5),
+#axis.text.y = element_blank(),
+legend.position="bottom",
+legend.box="vertical"
+)
+##+ scale_color_lancet()
+)
+saveplot("MovementFractionsS1")
+## Just movement building
+sigma3 <- list()
+sigma3$values <- c(s3_array_plotting)
+sigma3$times = times
+sigma3 <- as.data.frame(sigma3)
+title_text = "Evolution of movement building\nas a fraction of total labor"
+(ggplot(data = sigma3, aes(x = times, y= values))
++geom_line(size = 0.5)
++labs(
+title=title_text,
+#subtitle="n =303",
+x="Year since start",
+y="Fraction of labor"
+#caption="@EA Mental Health Survey"
+)
++theme(
+legend.title = element_blank(),
+#plot.subtitle = element_text(hjust = 0.5),
+plot.title = element_text(hjust = 0.5),
+#axis.text.y = element_blank(),
+legend.position="bottom",
+legend.box="vertical"
+)
+##+ scale_color_lancet()
+)
+saveplot("MovementFractionsS3")
+## Just direct work - logplot
+sigma1 <- list()
+sigma1$values <- c(s1_array_plotting)
+sigma1$times = times
+sigma1 <- as.data.frame(sigma1)
+title_text = "Evolution of direct work \nas a fraction of labor"
+(ggplot(data = sigma1, aes(x = times, y= values))
++geom_line(size = 0.5)
++labs(
+title=title_text,
+subtitle="(logarithmic scale)",
+x="Year since start",
+y="Fraction of labor"
+#caption="@EA Mental Health Survey"
+)
++theme(
+legend.title = element_blank(),
+plot.subtitle = element_text(hjust = 0.5),
+plot.title = element_text(hjust = 0.5),
+#axis.text.y = element_blank(),
+legend.position="bottom",
+legend.box="vertical"
+)
+##+ scale_color_lancet()
++ scale_y_continuous(trans = 'log2')
+)
+saveplot("MovementFractionsS1logplot")
+## Just movement building
+sigma3 <- list()
+sigma3$values <- c(s3_array_plotting)
+sigma3$times = times
+sigma3 <- as.data.frame(sigma3)
+title_text = "Evolution of movement building\nas a fraction of labor"
+(ggplot(data = sigma3, aes(x = times, y= values))
++geom_line(size = 0.5)
++labs(
+title=title_text,
+subtitle="(logarithmic scale)",
+x="Year since start",
+y="Fraction of total labor"
+#caption="@EA Mental Health Survey"
+)
++theme(
+legend.title = element_blank(),
+plot.subtitle = element_text(hjust = 0.5),
+plot.title = element_text(hjust = 0.5),
+#axis.text.y = element_blank(),
+legend.position="bottom",
+legend.box="vertical"
+)
+##+ scale_color_lancet()
++ scale_y_continuous(trans = 'log2')
+)
+saveplot("MovementFractionsS3logplot")
+## sigma_1*x3 and sigma3*x3, sigma_4*x3,
+sigmaxs <- list()
+sigmaxs$values <- c(s1_array_plotting*x3_array_plotting, s3_array_plotting*x3_array_plotting, s4_array_plotting*x3_array_plotting)
+sigmaxs$fraction <- c(rep("s1x3", length(s1_array_plotting)), rep("s3x3", length(s3_array_plotting)), rep("s4x3", length(s3_array_plotting)))
+sigmaxs$times = rep(times,3)
+sigmaxs <- as.data.frame(sigmaxs)
+title_text = "Evolution of labor\n in absolute terms"
+(ggplot(data = sigmaxs, aes(x = times, y= values, color = fraction)) +
+geom_line(size = 0.5)
++labs(
+title=title_text,
+#subtitle="n =303",
+x="Year since start",
+y="Absolute number\nof movement participants"
+#caption="@EA Mental Health Survey"
+)
++theme(
+legend.title = element_blank(),
+#plot.subtitle = element_text(hjust = 0.5),
+plot.title = element_text(hjust = 0.5),
+#axis.text.y = element_blank(),
+legend.position="bottom",
+legend.direction="vertical"
+)
++ scale_color_lancet(
+breaks=c("s1x3", "s3x3", "s4x3"),
+labels=c("Direct work", "Movement building", "Money-making")
+)
+)
+saveplot("MovementParticipantNumbersS1S3S4")
+## sigma_1*x3 and sigma3*x3
+sigmaxs <- list()
+sigmaxs$values <- c(s1_array_plotting*x3_array_plotting, s3_array_plotting*x3_array_plotting)
+sigmaxs$fraction <- c(rep("s1x3", length(s1_array_plotting)), rep("s3x3", length(s3_array_plotting)))
+sigmaxs$times = rep(times,2)
+sigmaxs <- as.data.frame(sigmaxs)
+title_text = "Evolution of movement participants\nin absolute terms"
+(ggplot(data = sigmaxs, aes(x = times, y= values, color = fraction)) +
+geom_line(size = 0.5)
++labs(
+title=title_text,
+subtitle="(only direct workers and movement builders)",
+x="Year since start",
+y="Absolute number\nof movement participants"
+#caption="@EA Mental Health Survey"
+)
++theme(
+legend.title = element_blank(),
+#plot.subtitle = element_text(hjust = 0.5),
+plot.title = element_text(hjust = 0.5),
+#axis.text.y = element_blank(),
+legend.position="bottom",
+legend.direction="vertical"
+)
++ scale_color_lancet(
+breaks=c("s1x3", "s3x3"),
+labels=c("Direct work", "Movement building")
+)
+)
+saveplot("MovementParticipantNumbersS1S3")
+## sigma_1*x3 and sigma3*x3 logplot
+sigmaxs <- list()
+sigmaxs$values <- c(s1_array_plotting*x3_array_plotting, s3_array_plotting*x3_array_plotting)
+sigmaxs$fraction <- c(rep("s1x3", length(s1_array_plotting)), rep("s3x3", length(s3_array_plotting)))
+sigmaxs$times = rep(times,2)
+sigmaxs <- as.data.frame(sigmaxs)
+title_text = "Evolution of movement participants\nin absolute terms \n(logarithmic scale)"
+(ggplot(data = sigmaxs, aes(x = times, y= values, color = fraction)) +
+geom_line(size = 0.5)
++labs(
+title=title_text,
+subtitle="(only direct workers and movement builders)",
+x="Year since start",
+y="Absolute number\nof movement participants"
+#caption="@EA Mental Health Survey"
+)
++theme(
+legend.title = element_blank(),
+#plot.subtitle = element_text(hjust = 0.5),
+plot.title = element_text(hjust = 0.5),
+#axis.text.y = element_blank(),
+legend.position="bottom",
+legend.direction="vertical"
+)
++ scale_color_lancet(
+breaks=c("s1x3", "s3x3"),
+labels=c("Direct work", "Movement building")
+)
++ scale_y_continuous(trans = 'log2')
+)
+saveplot("MovementParticipantNumbersS1S3logplot")
+## alpha1 and alpha3
+alphas <- list()
+alphas$values <- c(a1_array_plotting, a3_array_plotting)
+alphas$fraction <- c(rep("a1", length(s1_array_plotting)), rep("a2", length(s3_array_plotting)))
+alphas$times = rep(times,2)
+alphas <- as.data.frame(alphas)
+title_text = "Evolution of spending"
+(ggplot(data = alphas, aes(x = times, y= values, color = fraction)) +
+geom_line(size = 0.5)
++labs(
+title=title_text,
+#subtitle="n =303",
+x="Year since start",
+y="Spending"
+#caption="@EA Mental Health Survey"
+)
++theme(
+legend.title = element_blank(),
+#plot.subtitle = element_text(hjust = 0.5),
+plot.title = element_text(hjust = 0.5),
+#axis.text.y = element_blank(),
+legend.position="bottom",
+legend.direction="vertical"
+)
++ scale_color_lancet(
+breaks=c("a1", "a2"),
+labels=c("Direct spending","Spending on movement building")
+)
+)
+saveplot("SpendingA1A3")
+## alpha1 and alpha3: log plot
+alphas <- list()
+alphas$values <- c(a1_array_plotting, a3_array_plotting)
+alphas$fraction <- c(rep("a1", length(s1_array_plotting)), rep("a2", length(s3_array_plotting)))
+alphas$times = rep(times,2)
+alphas <- as.data.frame(alphas)
+title_text = "Evolution of spending"
+(ggplot(data = alphas, aes(x = times, y= values, color = fraction)) +
+geom_line(size = 0.5)
++labs(
+title=title_text,
+subtitle="(logarithmic scale)",
+x="Year since start",
+y="Spending"
+#caption="@EA Mental Health Survey"
+)
++theme(
+legend.title = element_blank(),
+#plot.subtitle = element_text(hjust = 0.5),
+plot.title = element_text(hjust = 0.5),
+plot.subtitle = element_text(hjust = 0.5),
+#axis.text.y = element_blank(),
+legend.position="bottom",
+legend.direction="vertical"
+)
++ scale_color_lancet(
+breaks=c("a1", "a2"),
+labels=c("Direct spending","Spending on movement building")
+)
++ scale_y_continuous(trans = 'log2')
+)
+saveplot("SpendingA1A3logplot")

plots/1000years/.Rhistory

@@ -0,0 +1,512 @@
+sum(x1_array_forward_shooting<0)
+x3_array_forward_shooting[l]
+x3_growth = (x3_array_forward_shooting[l]-x3_array_forward_shooting[l-1])/x3_array_forward_shooting[l-1]/(1*stepsize)
+x3_growth
+sum(x3_array_forward_shooting<0)
+a1_growth = (a1_array_forward_shooting[l]-a1_array_forward_shooting[l-1])/a1_array_forward_shooting[l-1]/stepsize
+a1_growth
+a3_growth = (a3_array_forward_shooting[l]-a3_array_forward_shooting[l-1])/a3_array_forward_shooting[l-1]/stepsize
+a3_growth
+a1_array_forward_shooting[l]/x1_array_forward_shooting[l]
+plot((a1_array_forward_shooting/x1_array_forward_shooting)[(l-100):l])
+# Forward shooting
+options(digits=7)
+## Evolution
+x1_array_forward_shooting <- c()
+x3_array_forward_shooting <- c()
+a1_array_forward_shooting <- c()
+a3_array_forward_shooting <- c()
+s1_array_forward_shooting <- c()
+s3_array_forward_shooting <- c()
+x1_t = x1_init
+x3_t = x3_init
+#stepsize
+comienzo = Sys.time()
+max = max(times_forward_shooting)
+for(t in times_forward_shooting){
+if((100*t/max) %in% seq(from=0, to=100, by=1)){
+cat(paste(floor(100*t/max), "%", sep=""))
+cat("\n")
+}
+a1_t = a1(t)
+a3_t = a3(t)
+s1_t = s1(t)
+s3_t = s3(t)
+x1_t = x1_t*(1+r1_stepsize) + dx1(t)*stepsize
+x3_t = x3_t*(1+r3_stepsize) + dx3(t)*stepsize
+a1_array_forward_shooting <- c(a1_array_forward_shooting, a1_t)
+a3_array_forward_shooting <- c(a3_array_forward_shooting, a3_t)
+s1_array_forward_shooting <- c(s1_array_forward_shooting, s1_t)
+s3_array_forward_shooting <- c(s3_array_forward_shooting, s3_t)
+x1_array_forward_shooting <- c(x1_array_forward_shooting, x1_t)
+x3_array_forward_shooting <- c(x3_array_forward_shooting, x3_t)
+}
+# Variables
+η = 0.9 ## 1.1
+ρ = 0.005
+r_1 = 0.06
+r_3 = -0.05
+γ_1 = 0.03
+γ_3 = 0.01
+w_3 = 5000 ## Mean on the EA Survey 2018: ~7000
+β_3 = 1 ## 1 ## 0.5 Corresponds to roughly 5 people convincing 10 other people per year on a 50k year budget
+## Dramatic if beta = 0.5, w_3 = 1000
+λ_1 = 0.5
+λ_3 = 0.5
+δ_3 = 0.44
+## k1_forward_shooting
+k1_forward_shooting = 3*10^(-7) ## 1*10^(-7) fails. 2*10^(-7) fails
+k1_reverse_shooting = k1_forward_shooting
+## Artfully guessed, such that s1 < 1
+stepsize = 0.1
+## stepsize = 0.1 => seconds (7s).
+## stepsize = 0.01 => minutes (3 mins).
+r1_stepsize = ((1+r_1)^stepsize)-1
+r3_stepsize = ((1+r_3)^stepsize)-1
+first = 0
+last = 1000
+times_forward_shooting = seq(from=first, to=last, by=stepsize)
+times_reverse_shooting = seq(from=last, to=first, by=-stepsize)
+### Initial conditions. Correspond to "year 0".
+x1_init = 10^10 ## 1 billion? 15 billion? 100 billion? Too much?
+x3_init = 10^5
+# Forward shooting
+options(digits=7)
+## Evolution
+x1_array_forward_shooting <- c()
+x3_array_forward_shooting <- c()
+a1_array_forward_shooting <- c()
+a3_array_forward_shooting <- c()
+s1_array_forward_shooting <- c()
+s3_array_forward_shooting <- c()
+x1_t = x1_init
+x3_t = x3_init
+#stepsize
+comienzo = Sys.time()
+max = max(times_forward_shooting)
+for(t in times_forward_shooting){
+if((100*t/max) %in% seq(from=0, to=100, by=1)){
+cat(paste(floor(100*t/max), "%", sep=""))
+cat("\n")
+}
+a1_t = a1(t)
+a3_t = a3(t)
+s1_t = s1(t)
+s3_t = s3(t)
+x1_t = x1_t*(1+r1_stepsize) + dx1(t)*stepsize
+x3_t = x3_t*(1+r3_stepsize) + dx3(t)*stepsize
+a1_array_forward_shooting <- c(a1_array_forward_shooting, a1_t)
+a3_array_forward_shooting <- c(a3_array_forward_shooting, a3_t)
+s1_array_forward_shooting <- c(s1_array_forward_shooting, s1_t)
+s3_array_forward_shooting <- c(s3_array_forward_shooting, s3_t)
+x1_array_forward_shooting <- c(x1_array_forward_shooting, x1_t)
+x3_array_forward_shooting <- c(x3_array_forward_shooting, x3_t)
+}
+fin = Sys.time()
+fin-comienzo
+## Checking condition
+options(digits=22)
+l = length(times_forward_shooting)
+x1_array_forward_shooting[l]
+x1_growth = (x1_array_forward_shooting[l]-x1_array_forward_shooting[l-1])/x1_array_forward_shooting[l-1]/(1*stepsize)
+x1_growth
+sum(x1_array_forward_shooting<0)
+x3_array_forward_shooting[l]
+x3_growth = (x3_array_forward_shooting[l]-x3_array_forward_shooting[l-1])/x3_array_forward_shooting[l-1]/(1*stepsize)
+x3_growth
+sum(x3_array_forward_shooting<0)
+a1_growth = (a1_array_forward_shooting[l]-a1_array_forward_shooting[l-1])/a1_array_forward_shooting[l-1]/stepsize
+a1_growth
+a3_growth = (a3_array_forward_shooting[l]-a3_array_forward_shooting[l-1])/a3_array_forward_shooting[l-1]/stepsize
+a3_growth
+a1_array_forward_shooting[l]/x1_array_forward_shooting[l]
+plot((a1_array_forward_shooting/x1_array_forward_shooting)[(l-100):l])
+# Plotting
+## install.packages("tidyverse") <- Not totally necessary.
+## install.packages("ggplot2")
+## install.packages("ggsci")
+library(ggplot2)
+library(ggsci)
+## General variables
+saveplots=TRUE
+times = times_forward_shooting
+## Also for reverse shooting plots; time in reverse shooting is inverted
+shootingtype="reverse"#"forward"#
+shootingtype="forward"#"reverse"#
+directory = paste("/home/nuno/Documents/core/SRF/BackShooting/RCode/plots/satisfactory3/", shootingtype, "shooting", "/", last, "years", sep="")
+directory
+setwd(directory)
+if(shootingtype=="forward"){
+x1_array_plotting <- x1_array_forward_shooting
+x3_array_plotting <- x3_array_forward_shooting
+a1_array_plotting <- a1_array_forward_shooting
+a3_array_plotting <- a3_array_forward_shooting
+s1_array_plotting <- s1_array_forward_shooting
+s3_array_plotting <- s3_array_forward_shooting
+} else if(shootingtype=="reverse"){
+x1_array_plotting <- x1_array_reverse_shooting
+x3_array_plotting <- x3_array_reverse_shooting
+a1_array_plotting <- a1_array_reverse_shooting
+a3_array_plotting <- a3_array_reverse_shooting
+s1_array_plotting <- s1_array_reverse_shooting
+s3_array_plotting <- s3_array_reverse_shooting
+}
+height = 5
+width = floor(height*(1+sqrt(5))/2)
+imagenumbercounter = 1
+saveplot = function(imagename){
+if(saveplots){
+ggsave(paste(imagenumbercounter,"_", imagename, "_",shootingtype, "shooting",".png", sep =""), units="in", width=width, height=height)
+imagenumbercounter <<- imagenumbercounter+1
+## https://stackoverflow.com/questions/1236620/global-variables-in-r
+}
+}
+options(digits=1) ## Just for display
+xs <- list()
+xs$values <- c(x1_array_plotting, x3_array_plotting)
+xs$var <- c(rep("x1", length(x1_array_plotting)), rep("x3", length(x3_array_plotting)))
+xs$times = rep(times,2)
+xs <- as.data.frame(xs)
+title_text = "Evolution of state variables"
+(ggplot(data = xs, aes(x = times, y= values, color = var)) +
+geom_line(size = 0.5)
++ labs(
+title=title_text,
+#subtitle="n =303",
+x="Year since start",
+y="Capital and labor"
+#caption="@EA Mental Health Survey"
+)
++theme(
+legend.title = element_blank(),
+#plot.subtitle = element_text(hjust = 0.5),
+plot.title = element_text(hjust = 0.5),
+#axis.text.y = element_blank(),
+legend.position="bottom",
+legend.box="vertical"
+)
++ scale_color_lancet(
+breaks=c("x1", "x3"),
+labels=c("Capital", "Labor")
+)
++ scale_y_continuous(breaks = seq(min(x1_array_plotting), max(x1_array_plotting), length.out=5))
+)
+## x1 and x3: log plot
+title_text = "Evolution of state variables"
+(ggplot(data = xs, aes(x = times, y= values, color = var)) +
+geom_line(size = 0.5)
++labs(
+title=title_text,
+subtitle="(logarithmic scale)",
+#subtitle="n =303",
+x="Year since start",
+y="Capital and labor"
+#caption="@EA Mental Health Survey"
+)
++theme(
+legend.title = element_blank(),
+#plot.subtitle = element_text(hjust = 0.5),
+plot.title = element_text(hjust = 0.5),
+plot.subtitle = element_text(hjust = 0.5),
+#axis.text.y = element_blank(),
+legend.position="bottom",
+legend.box="vertical"
+)
++ scale_color_lancet(
+breaks=c("x1", "x3"),
+labels=c("Capital", "Labor")
+)
++ scale_y_continuous(trans = 'log2')
+)
+saveplot("StateVariablesX1X3logplot")
+## Only x3
+equis3 <- list()
+equis3$values <- c(x3_array_plotting)
+equis3$times = times
+equis3 <- as.data.frame(equis3)
+title_text = "Evolution of movement size"
+(ggplot(data = equis3, aes(x = times, y= values))
++geom_line(size = 0.5)
++labs(
+title=title_text,
+#subtitle="n =303",
+x="Year since start",
+y="Labor"
+#caption="@EA Mental Health Survey"
+)
++theme(
+legend.title = element_blank(),
+#plot.subtitle = element_text(hjust = 0.5),
+plot.title = element_text(hjust = 0.5),
+#axis.text.y = element_blank(),
+legend.position="bottom",
+legend.box="vertical"
+)
+##+ scale_color_lancet()
+)
+saveplot("StateVariableX3")
+## s1, s3, s4
+sigmas <- list()
+s4_array_plotting=1-s1_array_plotting-s3_array_plotting
+sigmas$values <- c(s1_array_plotting, s3_array_plotting,s4_array_plotting)
+sigmas$fraction <- c(rep("s1", length(s1_array_plotting)), rep("s3", length(s3_array_plotting)),rep("s4", length(s3_array_plotting)))
+sigmas$times = rep(times,3)
+sigmas <- as.data.frame(sigmas)
+title_text = "Evolution of labor fractions"
+(ggplot(data = sigmas, aes(x = times, y= values, color = fraction)) +
+geom_line(size = 0.5)
++labs(
+title=title_text,
+#subtitle="n =303",
+x="Year since start",
+y="Fraction of total labor"
+#caption="@EA Mental Health Survey"
+)
++theme(
+legend.title = element_blank(),
+#plot.subtitle = element_text(hjust = 0.5),
+plot.title = element_text(hjust = 0.5),
+#axis.text.y = element_blank(),
+legend.position="bottom",
+legend.direction="vertical"
+)
++ scale_color_lancet(
+breaks=c("s1", "s3", "s4"),
+labels=c("Direct work", "Movement building", "Money-making")
+)
+)
+# Variables
+η = 0.9 ## 1.1
+ρ = 0.005
+r_1 = 0.06
+r_3 = -0.02
+γ_1 = 0.03
+γ_3 = 0.01
+w_3 = 5000 ## Mean on the EA Survey 2018: ~7000
+β_3 = 1 ## 1 ## 0.5 Corresponds to roughly 5 people convincing 10 other people per year on a 50k year budget
+## Dramatic if beta = 0.5, w_3 = 1000
+λ_1 = 0.5
+λ_3 = 0.5
+δ_3 = 0.44
+## k1_forward_shooting
+k1_forward_shooting = 3*10^(-7) ## 1*10^(-7) fails. 2*10^(-7) fails
+k1_reverse_shooting = k1_forward_shooting
+## Artfully guessed, such that s1 < 1
+stepsize = 0.1
+## stepsize = 0.1 => seconds (7s).
+## stepsize = 0.01 => minutes (3 mins).
+r1_stepsize = ((1+r_1)^stepsize)-1
+r3_stepsize = ((1+r_3)^stepsize)-1
+first = 0
+last = 1000
+times_forward_shooting = seq(from=first, to=last, by=stepsize)
+times_reverse_shooting = seq(from=last, to=first, by=-stepsize)
+### Initial conditions. Correspond to "year 0".
+x1_init = 10^10 ## 1 billion? 15 billion? 100 billion? Too much?
+x3_init = 10^5
+# Forward shooting
+options(digits=7)
+## Evolution
+x1_array_forward_shooting <- c()
+x3_array_forward_shooting <- c()
+a1_array_forward_shooting <- c()
+a3_array_forward_shooting <- c()
+s1_array_forward_shooting <- c()
+s3_array_forward_shooting <- c()
+x1_t = x1_init
+x3_t = x3_init
+#stepsize
+comienzo = Sys.time()
+max = max(times_forward_shooting)
+for(t in times_forward_shooting){
+if((100*t/max) %in% seq(from=0, to=100, by=1)){
+cat(paste(floor(100*t/max), "%", sep=""))
+cat("\n")
+}
+a1_t = a1(t)
+a3_t = a3(t)
+s1_t = s1(t)
+s3_t = s3(t)
+x1_t = x1_t*(1+r1_stepsize) + dx1(t)*stepsize
+x3_t = x3_t*(1+r3_stepsize) + dx3(t)*stepsize
+a1_array_forward_shooting <- c(a1_array_forward_shooting, a1_t)
+a3_array_forward_shooting <- c(a3_array_forward_shooting, a3_t)
+s1_array_forward_shooting <- c(s1_array_forward_shooting, s1_t)
+s3_array_forward_shooting <- c(s3_array_forward_shooting, s3_t)
+x1_array_forward_shooting <- c(x1_array_forward_shooting, x1_t)
+x3_array_forward_shooting <- c(x3_array_forward_shooting, x3_t)
+}
+fin = Sys.time()
+fin-comienzo
+## Checking condition
+options(digits=22)
+l = length(times_forward_shooting)
+x1_array_forward_shooting[l]
+x1_growth = (x1_array_forward_shooting[l]-x1_array_forward_shooting[l-1])/x1_array_forward_shooting[l-1]/(1*stepsize)
+x1_growth
+sum(x1_array_forward_shooting<0)
+x3_array_forward_shooting[l]
+x3_growth = (x3_array_forward_shooting[l]-x3_array_forward_shooting[l-1])/x3_array_forward_shooting[l-1]/(1*stepsize)
+x3_growth
+sum(x3_array_forward_shooting<0)
+a1_growth = (a1_array_forward_shooting[l]-a1_array_forward_shooting[l-1])/a1_array_forward_shooting[l-1]/stepsize
+a1_growth
+a3_growth = (a3_array_forward_shooting[l]-a3_array_forward_shooting[l-1])/a3_array_forward_shooting[l-1]/stepsize
+a3_growth
+a1_array_forward_shooting[l]/x1_array_forward_shooting[l]
+plot((a1_array_forward_shooting/x1_array_forward_shooting)[(l-100):l])
+# Plotting
+## install.packages("tidyverse") <- Not totally necessary.
+## install.packages("ggplot2")
+## install.packages("ggsci")
+library(ggplot2)
+library(ggsci)
+## General variables
+saveplots=TRUE
+times = times_forward_shooting
+## Also for reverse shooting plots; time in reverse shooting is inverted
+shootingtype="reverse"#"forward"#
+shootingtype="forward"#"reverse"#
+directory = paste("/home/nuno/Documents/core/SRF/BackShooting/RCode/plots/satisfactory3/", shootingtype, "shooting", "/", last, "years", sep="")
+directory
+setwd(directory)
+if(shootingtype=="forward"){
+x1_array_plotting <- x1_array_forward_shooting
+x3_array_plotting <- x3_array_forward_shooting
+a1_array_plotting <- a1_array_forward_shooting
+a3_array_plotting <- a3_array_forward_shooting
+s1_array_plotting <- s1_array_forward_shooting
+s3_array_plotting <- s3_array_forward_shooting
+} else if(shootingtype=="reverse"){
+x1_array_plotting <- x1_array_reverse_shooting
+x3_array_plotting <- x3_array_reverse_shooting
+a1_array_plotting <- a1_array_reverse_shooting
+a3_array_plotting <- a3_array_reverse_shooting
+s1_array_plotting <- s1_array_reverse_shooting
+s3_array_plotting <- s3_array_reverse_shooting
+}
+height = 5
+width = floor(height*(1+sqrt(5))/2)
+imagenumbercounter = 1
+saveplot = function(imagename){
+if(saveplots){
+ggsave(paste(imagenumbercounter,"_", imagename, "_",shootingtype, "shooting",".png", sep =""), units="in", width=width, height=height)
+imagenumbercounter <<- imagenumbercounter+1
+## https://stackoverflow.com/questions/1236620/global-variables-in-r
+}
+}
+options(digits=1) ## Just for display
+xs <- list()
+xs$values <- c(x1_array_plotting, x3_array_plotting)
+xs$var <- c(rep("x1", length(x1_array_plotting)), rep("x3", length(x3_array_plotting)))
+xs$times = rep(times,2)
+xs <- as.data.frame(xs)
+title_text = "Evolution of state variables"
+(ggplot(data = xs, aes(x = times, y= values, color = var)) +
+geom_line(size = 0.5)
++ labs(
+title=title_text,
+#subtitle="n =303",
+x="Year since start",
+y="Capital and labor"
+#caption="@EA Mental Health Survey"
+)
++theme(
+legend.title = element_blank(),
+#plot.subtitle = element_text(hjust = 0.5),
+plot.title = element_text(hjust = 0.5),
+#axis.text.y = element_blank(),
+legend.position="bottom",
+legend.box="vertical"
+)
++ scale_color_lancet(
+breaks=c("x1", "x3"),
+labels=c("Capital", "Labor")
+)
++ scale_y_continuous(breaks = seq(min(x1_array_plotting), max(x1_array_plotting), length.out=5))
+)
+saveplot("StateVariablesX1X3")
+## x1 and x3: log plot
+title_text = "Evolution of state variables"
+(ggplot(data = xs, aes(x = times, y= values, color = var)) +
+geom_line(size = 0.5)
++labs(
+title=title_text,
+subtitle="(logarithmic scale)",
+#subtitle="n =303",
+x="Year since start",
+y="Capital and labor"
+#caption="@EA Mental Health Survey"
+)
++theme(
+legend.title = element_blank(),
+#plot.subtitle = element_text(hjust = 0.5),
+plot.title = element_text(hjust = 0.5),
+plot.subtitle = element_text(hjust = 0.5),
+#axis.text.y = element_blank(),
+legend.position="bottom",
+legend.box="vertical"
+)
++ scale_color_lancet(
+breaks=c("x1", "x3"),
+labels=c("Capital", "Labor")
+)
++ scale_y_continuous(trans = 'log2')
+)
+saveplot("StateVariablesX1X3logplot")
+## Only x3
+equis3 <- list()
+equis3$values <- c(x3_array_plotting)
+equis3$times = times
+equis3 <- as.data.frame(equis3)
+title_text = "Evolution of movement size"
+(ggplot(data = equis3, aes(x = times, y= values))
++geom_line(size = 0.5)
++labs(
+title=title_text,
+#subtitle="n =303",
+x="Year since start",
+y="Labor"
+#caption="@EA Mental Health Survey"
+)
++theme(
+legend.title = element_blank(),
+#plot.subtitle = element_text(hjust = 0.5),
+plot.title = element_text(hjust = 0.5),
+#axis.text.y = element_blank(),
+legend.position="bottom",
+legend.box="vertical"
+)
+##+ scale_color_lancet()
+)
+saveplot("StateVariableX3")
+## s1, s3, s4
+sigmas <- list()
+s4_array_plotting=1-s1_array_plotting-s3_array_plotting
+sigmas$values <- c(s1_array_plotting, s3_array_plotting,s4_array_plotting)
+sigmas$fraction <- c(rep("s1", length(s1_array_plotting)), rep("s3", length(s3_array_plotting)),rep("s4", length(s3_array_plotting)))
+sigmas$times = rep(times,3)
+sigmas <- as.data.frame(sigmas)
+title_text = "Evolution of labor fractions"
+(ggplot(data = sigmas, aes(x = times, y= values, color = fraction)) +
+geom_line(size = 0.5)
++labs(
+title=title_text,
+#subtitle="n =303",
+x="Year since start",
+y="Fraction of total labor"
+#caption="@EA Mental Health Survey"
+)
++theme(
+legend.title = element_blank(),
+#plot.subtitle = element_text(hjust = 0.5),
+plot.title = element_text(hjust = 0.5),
+#axis.text.y = element_blank(),
+legend.position="bottom",
+legend.direction="vertical"
+)
++ scale_color_lancet(
+breaks=c("s1", "s3", "s4"),
+labels=c("Direct work", "Movement building", "Money-making")
+)
+)