WebR — Monopsônio no Mercado de Trabalho

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# ============================================
# Monopsonio no Mercado de Trabalho
# Exercicio Resolvido 17.2
# ============================================

# Oferta de trabalho: w = a + b*H
# VPMgL = d - e*H
a <- 4; b <- 2     # w(H) = 4 + 2H
d <- 100; e <- 2   # VPMgL = 100 - 2H

cat("====== MONOPSONIO ======\n")
cat("Oferta: w =", a, "+", b, "* H\n")
cat("VPMgL =", d, "-", e, "* H\n\n")

# --- Equilibrio competitivo ---
# VPMgL = w => d - e*H = a + b*H
Hc <- (d - a) / (e + b)
wc <- a + b * Hc
cat("--- Equilibrio competitivo ---\n")
cat(sprintf("H_c = %.1f   w_c = %.1f\n\n", Hc, wc))

# --- Monopsonio ---
# CMgL = a + 2b*H (derivada do custo total wH = (a+bH)H)
# VPMgL = CMgL => d - e*H = a + 2b*H
Hm <- (d - a) / (e + 2*b)
wm <- a + b * Hm
VPMg_m <- d - e * Hm
exploração <- VPMg_m - wm

cat("--- Monopsonio ---\n")
cat(sprintf("H_m = %.1f   w_m = %.1f\n", Hm, wm))
cat(sprintf("VPMgL(H_m) = %.1f\n", VPMg_m))
cat(sprintf("Exploracao monopsonistica = %.1f\n\n", exploração))

# --- Salario minimo = w_c ---
w_min <- wc
# CMgL = w_min ate onde oferta = w_min, depois CMgL normal
# VPMgL = w_min => d - e*H = w_min
H_min <- (d - w_min) / e
cat("--- Salario minimo = w_c ---\n")
cat(sprintf("w_min = %.1f => H = %.1f\n", w_min, H_min))
cat(sprintf("Variacao emprego: %.1f -> %.1f (+%.0f%%)\n",
    Hm, H_min, (H_min/Hm - 1)*100))
cat(sprintf("Variacao salario: %.1f -> %.1f (+%.0f%%)\n\n",
    wm, w_min, (w_min/wm - 1)*100))

# --- Comparacao ---
cat("--- Resumo ---\n")
cat(sprintf("%-20s %-10s %-10s\n", "", "Monopsonio", "Competitivo"))
cat(strrep("-", 42), "\n")
cat(sprintf("%-20s %-10.1f %-10.1f\n", "Emprego (H)", Hm, Hc))
cat(sprintf("%-20s %-10.1f %-10.1f\n", "Salario (w)", wm, wc))
cat(sprintf("%-20s %-10.1f %-10.1f\n", "VPMgL", VPMg_m, wc))
cat(sprintf("%-20s %-10.1f %-10.1f\n", "Exploracao", exploração, 0))

# --- Grafico ---
par(mar = c(4.5, 4.5, 3, 2), bg = "#f8f9fa")
H_seq <- seq(0, 30, length = 300)
w_oferta <- a + b * H_seq
CMgL <- a + 2*b * H_seq
VPMgL <- d - e * H_seq

plot(H_seq, VPMgL, type = "l", lwd = 3, col = "#0d6efd",
     xlim = c(0, 30), ylim = c(0, 110),
     xlab = "Emprego (H)", ylab = "w, VPMgL, CMgL",
     main = "Monopsonio vs. Competitivo")
lines(H_seq, w_oferta, lwd = 3, col = "#198754")
lines(H_seq, CMgL, lwd = 3, col = "#dc3545", lty = 2)

# Salario minimo
segments(0, w_min, H_min, w_min, lwd = 2, col = "#fd7e14", lty = 4)

# Pontos
points(Hm, wm, pch = 19, col = "#dc3545", cex = 2)
text(Hm + 1, wm + 3, paste0("Monop. (", Hm, ", ", wm, ")"),
     col = "#dc3545", cex = 0.7, font = 2)

points(Hc, wc, pch = 17, col = "#198754", cex = 2)
text(Hc + 1, wc + 3, paste0("Compet. (", Hc, ", ", wc, ")"),
     col = "#198754", cex = 0.7, font = 2)

# Exploracao (segmento vertical)
segments(Hm, wm, Hm, VPMg_m, lwd = 2, col = "#6f42c1", lty = 3)
text(Hm - 2, (wm + VPMg_m)/2, paste0("Expl. = ", exploração),
     col = "#6f42c1", cex = 0.7, font = 2)

# PPM (triangulo)
polygon(c(Hm, Hc, Hc, Hm),
        c(wm, wc, VPMg_m, VPMg_m),
        col = rgb(0.85, 0.2, 0.2, 0.1), border = NA)

legend("topright",
       legend = c("VPMgL (demanda)", "Oferta (w)",
                  "CMgL", "Salario minimo"),
       col = c("#0d6efd", "#198754", "#dc3545", "#fd7e14"),
       lwd = 3, lty = c(1, 1, 2, 4),
       cex = 0.65, bg = "white")

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