This R script uses gganimate to simulate and visualize how firms adapt their configurations—single-layer or two-layer, human or AI—as AI knowledge levels ( 𝑧 𝐴 𝐼 z AI ​ ) increase. Inspired by the Artificial Intelligence in the Knowledge Economy model, it calculates profits for each setup and dynamically displays the best configurations over tim…

ai_firm_config_simulation.R

library(tidyverse)
library(gganimate)

# Parameters
h <- 0.02 # Time cost per worker for the solver
r <- 2 # Rental rate for one unit of compute
worker_grid <- seq(0.2, 0.8, by = 0.1) # Range of human worker knowledge
solver_grid <- seq(0.3, 1.0, by = 0.1) # Range of human solver knowledge
zAI_values <- seq(0.25, 0.95, by = 0.05) # Range of AI knowledge levels

# Functions
productivity_h <- function(z) 10 * z
wage_h <- function(z) 0.6 * productivity_h(z)
n_workers <- function(z) {
  val <- 1 / (h * (1 - z))
  return(pmin(val, 100)) # Cap at 100 workers
}
profit_single_human <- function(z) 4 * z
profit_single_ai <- function(zAI) 10 * zAI - r
profit_two_layer_hh <- function(s, z) {
  n_z <- n_workers(z)
  return(n_z * (s - wage_h(z)) - wage_h(s))
}
profit_two_layer_tA <- function(z, zAI) {
  n_z <- n_workers(z)
  return(n_z * (zAI * 10 - wage_h(z)) - r)
}
profit_two_layer_bA <- function(s, zAI) {
  n_AI <- n_workers(zAI)
  return(n_AI * (s * 10 - r) - wage_h(s))
}

# Create a dataset with varying zAI
df <- expand.grid(
  z_worker = worker_grid,
  s_solver = solver_grid,
  zAI = zAI_values
) |>
  mutate(
    # 1) Single-layer HUMAN
    pi_single_h = profit_single_human(z_worker),

    # 2) Single-layer AI
    pi_single_ai = profit_single_ai(zAI),

    # 3) Two-layer, human-human
    pi_hh = if_else(s_solver >= z_worker,
      profit_two_layer_hh(s_solver * 10, z_worker),
      NA_real_
    ),

    # 4) Two-layer, AI as solver
    pi_tA = profit_two_layer_tA(z_worker, zAI),

    # 5) Two-layer, AI as worker
    pi_bA = if_else(s_solver >= zAI,
      profit_two_layer_bA(s_solver, zAI),
      NA_real_
    )
  ) |>
  rowwise() |>
  mutate(
    best_profit = max(c_across(starts_with("pi_")), na.rm = TRUE),
    best_config = case_when(
      best_profit == pi_single_h ~ "Single-Layer Human",
      best_profit == pi_single_ai ~ "Single-Layer AI",
      best_profit == pi_hh ~ "Two-Layer Human-Human",
      best_profit == pi_tA ~ "Two-Layer AI as Solver",
      best_profit == pi_bA ~ "Two-Layer AI as Worker",
      TRUE ~ NA_character_
    )
  ) |>
  ungroup()

# Animate the plot
p <- ggplot(df, aes(x = z_worker, y = s_solver, fill = best_config)) +
  geom_tile(color = "white") +
  labs(
    title = "Best Firm Configuration by Worker & Solver Knowledge<br>",
    subtitle = "AI Knowledge Level: {closest_state}<br>",
    x = "Worker Knowledge (z)",
    y = "Solver Knowledge (s)<br>",
    fill = "Best Config:"
  ) +
  theme_wl_void() +
  theme(
    legend.title = element_markdown(size = 12),
    legend.text = element_markdown(size = 12),
    axis.text = element_markdown(size = 12),
    axis.title = element_markdown(size = 12),
    axis.title.y = element_markdown(angle = 90),
    plot.title = element_markdown(hjust = 0.5),
    plot.subtitle = element_markdown(size = 12, hjust = 0.5),
    plot.caption = element_markdown(size = 12),
    panel.grid = element_blank(),
    panel.grid.major = element_blank(),
    panel.grid.minor = element_blank()
  ) +
  transition_states(zAI, transition_length = 2, state_length = 1) +
  ease_aes("linear")

# Save/render animation
animate(p, fps = 10, width = 800, height = 600)
anim_save("best_firm_config.gif", animation = last_animation())