WebR — Cournot com n Firmas

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# ============================================
# Cournot com n firmas: convergencia
# para concorrencia perfeita
# ============================================

a <- 100; b <- 1; c <- 20  # Demanda: p = a - b*Q, CMg = c

cat("====== COURNOT COM n FIRMAS ======\n")
cat("Demanda: p =", a, "-", b, "* Q\n")
cat("CMg =", c, "\n\n")

# Formulas gerais:
# q* = (a - c) / [b(n+1)]
# Q* = n(a - c) / [b(n+1)]
# p* = (a + nc) / (n+1)
# pi* = (a - c)^2 / [b(n+1)^2]

n_vec <- c(1, 2, 3, 5, 10, 20, 50, 100)

cat(sprintf("%-5s %-8s %-8s %-8s %-10s %-8s %-10s\n",
    "n", "q*", "Q*", "p*", "pi*", "HHI", "Markup%"))
cat(strrep("-", 62), "\n")

for (n in n_vec) {
  q_star <- (a - c) / (b * (n + 1))
  Q_star <- n * q_star
  p_star <- (a + n * c) / (n + 1)
  pi_star <- (a - c)^2 / (b * (n + 1)^2)
  HHI <- n * (100/n)^2  # = 10000/n
  markup <- (p_star - c) / p_star * 100
  cat(sprintf("%-5d %-8.2f %-8.2f %-8.2f %-10.1f %-8.0f %-10.1f\n",
      n, q_star, Q_star, p_star, pi_star, HHI, markup))
}

# Limites
Q_comp <- (a - c) / b
p_comp <- c
cat(sprintf("\n%-5s %-8s %-8.1f %-8.1f %-10s %-8s %-10.1f\n",
    "inf", "--", Q_comp, p_comp, "0", "0", 0.0))
cat("\nConvergencia: p* -> c, Q* -> (a-c)/b, pi* -> 0\n")

# --- Grafico ---
par(mfrow = c(1, 2), mar = c(4.5, 4.5, 3, 1), bg = "#f8f9fa")

n_fine <- 1:50
p_seq <- (a + n_fine * c) / (n_fine + 1)
Q_seq <- n_fine * (a - c) / (b * (n_fine + 1))
pi_seq <- (a - c)^2 / (b * (n_fine + 1)^2)

# Painel 1: Preco e quantidade vs n
plot(n_fine, p_seq, type = "l", lwd = 3, col = "#dc3545",
     xlab = "Numero de firmas (n)",
     ylab = "",
     main = "Convergencia para concorrencia",
     ylim = c(0, max(a)))
abline(h = c, col = "#198754", lty = 2, lwd = 2)
text(40, c + 3, "p = CMg (conc. perfeita)",
     col = "#198754", cex = 0.7, font = 2)

# Monopolio
points(1, (a + c) / 2, pch = 19, col = "#6f42c1", cex = 1.8)
text(3, (a + c) / 2 + 3, "Monopolio", col = "#6f42c1", cex = 0.7, font = 2)

# Eixo secundario para Q (sobreposto)
par(new = TRUE)
plot(n_fine, Q_seq, type = "l", lwd = 3, col = "#0d6efd", lty = 2,
     axes = FALSE, xlab = "", ylab = "", ylim = c(0, max(a)))
axis(4, col = "#0d6efd", col.axis = "#0d6efd")
mtext("Q*", side = 4, line = 2.5, col = "#0d6efd")
abline(h = Q_comp, col = "#0d6efd", lty = 3, lwd = 1)

legend("right",
       legend = c("p* (eixo esq.)", "Q* (eixo dir.)",
                  "p = CMg", "Q competitivo"),
       col = c("#dc3545", "#0d6efd", "#198754", "#0d6efd"),
       lwd = c(3, 3, 2, 1), lty = c(1, 2, 2, 3),
       cex = 0.6, bg = "white")

# Painel 2: Lucro individual e HHI
plot(n_fine, pi_seq, type = "l", lwd = 3, col = "#fd7e14",
     xlab = "Numero de firmas (n)",
     ylab = "Lucro individual",
     main = "Lucro e concentracao vs. n")

par(new = TRUE)
HHI_seq <- 10000 / n_fine
plot(n_fine, HHI_seq, type = "l", lwd = 3, col = "#6f42c1", lty = 2,
     axes = FALSE, xlab = "", ylab = "",
     ylim = c(0, 10000))
axis(4, col = "#6f42c1", col.axis = "#6f42c1")
mtext("HHI", side = 4, line = 2.5, col = "#6f42c1")

# Faixas CADE/DOJ
abline(h = 2500, col = "#dc3545", lty = 3)
abline(h = 1500, col = "#fd7e14", lty = 3)
text(35, 2700, "HHI = 2500", col = "#dc3545", cex = 0.6)
text(35, 1700, "HHI = 1500", col = "#fd7e14", cex = 0.6)

legend("topright",
       legend = c("Lucro (eixo esq.)", "HHI (eixo dir.)"),
       col = c("#fd7e14", "#6f42c1"),
       lwd = 3, lty = c(1, 2), cex = 0.6, bg = "white")

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