WebR — Barganha Sindical de Nash

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# ============================================
# Barganha Sindical de Nash
# Baseado no Exercicio 17.9
# ============================================

# Lucro da firma: pi = (100 - H)*H - w*H
# Utilidade do sindicato: U_S = (w - w0)*H
# Demanda por trabalho: H^d(w) = (100 - w)/2

w0 <- 10  # salario de reserva

cat("====== BARGANHA SINDICAL DE NASH ======\n")
cat("Lucro: pi = (100 - H)*H - w*H\n")
cat("Utilidade sindical: U_S = (w - w0)*H\n")
cat("Demanda: H^d(w) = (100 - w)/2\n")
cat("Salario de reserva: w0 =", w0, "\n\n")

# Demanda por trabalho
Hd <- function(w) (100 - w) / 2

# Lucro na demanda
pi_func <- function(w) {
  H <- Hd(w)
  (100 - H) * H - w * H
}

# Utilidade do sindicato na demanda
Us_func <- function(w) (w - w0) * Hd(w)

# Produto de Nash: max [(w-w0)*H]^beta * [pi]^(1-beta)
# Substituindo H = (100-w)/2:
# U_S = (w-w0)*(100-w)/2
# pi = (100-w)^2/4
# Nash: max [(w-w0)(100-w)/2]^beta * [(100-w)^2/4]^(1-beta)
# Tomando log e derivando:
# beta/(w-w0) - beta/(100-w) - 2(1-beta)/(100-w) = 0
# beta/(w-w0) = (beta + 2 - 2*beta)/(100-w) = (2-beta)/(100-w)
# beta*(100-w) = (2-beta)*(w-w0)
# w* = (beta*(100-w0) + 2*w0) / 2 = w0 + beta*(100-w0)/2

cat("--- Salario negociado por beta ---\n")
cat(sprintf("%-8s %-10s %-10s %-10s %-10s\n",
    "beta", "w*", "H*", "pi*", "U_S*"))
cat(strrep("-", 50), "\n")

beta_vals <- seq(0, 1, by = 0.1)
w_neg <- w0 + beta_vals * (100 - w0) / 2
H_neg <- Hd(w_neg)
pi_neg <- sapply(w_neg, pi_func)
Us_neg <- sapply(w_neg, Us_func)

for (i in seq_along(beta_vals)) {
  cat(sprintf("%-8.1f %-10.1f %-10.1f %-10.0f %-10.0f\n",
      beta_vals[i], w_neg[i], H_neg[i], pi_neg[i], Us_neg[i]))
}

cat("\nFormula: w* = w0 + beta*(100-w0)/2\n")
cat("beta=0: competitivo (w=w0, firma tem todo o poder)\n")
cat("beta=1: monopolio sindical (w=55, sindicato tem todo o poder)\n")

# --- Caso especifico beta = 0.5 ---
beta_ex <- 0.5
w_ex <- w0 + beta_ex * (100 - w0) / 2
H_ex <- Hd(w_ex)
pi_ex <- pi_func(w_ex)
Us_ex <- Us_func(w_ex)

cat(sprintf("\n--- Caso beta = %.1f ---\n", beta_ex))
cat(sprintf("w* = %.1f  H* = %.1f  pi* = %.0f  U_S* = %.0f\n",
    w_ex, H_ex, pi_ex, Us_ex))

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

# Painel 1: Salario e emprego vs beta
plot(beta_vals, w_neg, type = "l", lwd = 3, col = "#dc3545",
     xlab = expression(beta ~ "(poder do sindicato)"),
     ylab = "",
     main = "Salario e emprego vs. poder sindical",
     ylim = c(0, 60))
par(new = TRUE)
plot(beta_vals, H_neg, type = "l", lwd = 3, col = "#0d6efd",
     lty = 2, axes = FALSE, xlab = "", ylab = "",
     ylim = c(0, 60))
axis(4, col = "#0d6efd", col.axis = "#0d6efd")
mtext("H*", side = 4, line = 2.5, col = "#0d6efd")

# beta = 0.5
abline(v = 0.5, col = "#adb5bd", lty = 3)
points(0.5, w_ex, pch = 19, col = "#dc3545", cex = 1.5)
points(0.5, H_ex, pch = 17, col = "#0d6efd", cex = 1.5)

legend("left",
       legend = c("w* (eixo esq.)", "H* (eixo dir.)"),
       col = c("#dc3545", "#0d6efd"),
       lwd = 3, lty = c(1, 2), cex = 0.65, bg = "white")

# Painel 2: Curva de contrato no espaco (w, H)
w_range <- seq(w0, 55, length = 200)
H_range <- Hd(w_range)

plot(H_range, w_range, type = "l", lwd = 3, col = "#6f42c1",
     xlab = "Emprego (H)", ylab = "Salario (w)",
     main = "Curva de demanda e equilibrios",
     xlim = c(0, 50), ylim = c(0, 60))

# Marcar pontos para beta = 0, 0.25, 0.5, 0.75, 1
beta_marks <- c(0, 0.25, 0.5, 0.75, 1)
w_marks <- w0 + beta_marks * (100 - w0) / 2
H_marks <- Hd(w_marks)
points(H_marks, w_marks, pch = 19,
       col = c("#198754", "#0d6efd", "#fd7e14", "#dc3545", "#6f42c1"),
       cex = 1.8)
for (i in seq_along(beta_marks)) {
  pos <- ifelse(i <= 3, 4, 2)
  text(H_marks[i], w_marks[i],
       paste0(" b=", beta_marks[i]),
       col = c("#198754", "#0d6efd", "#fd7e14", "#dc3545", "#6f42c1")[i],
       cex = 0.65, font = 2, pos = pos)
}

abline(h = w0, col = "#adb5bd", lty = 3)
text(5, w0 + 2, paste0("w0 = ", w0), col = "#adb5bd",
     cex = 0.7, font = 2)

legend("topright",
       legend = "Demanda H^d(w)",
       col = "#6f42c1", lwd = 3, cex = 0.65, bg = "white")

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