WebR — Imposto sobre o Monopolista

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# ============================================
# Imposto sobre o monopolista
# Exercicio Resolvido 15.3
# ============================================

# --- Parametros ---
a <- 60   # demanda: p = a - q
c <- 12   # custo marginal
t <- 8    # imposto unitario

cat("====== IMPOSTO SOBRE O MONOPOLISTA ======\n")
cat("Demanda: p =", a, "- q\n")
cat("CMg =", c, "  Imposto t =", t, "\n\n")

# --- Antes do imposto ---
qm0 <- (a - c) / 2
pm0 <- a - qm0
lucro0 <- (pm0 - c) * qm0
EC0 <- 0.5 * (a - pm0) * qm0

cat("--- Antes do imposto ---\n")
cat("q^m =", qm0, "  p^m =", pm0, "\n")
cat("Lucro =", lucro0, "  EC =", EC0, "\n\n")

# --- Depois do imposto ---
c_eff <- c + t
qm1 <- (a - c_eff) / 2
pm1 <- a - qm1
lucro1 <- (pm1 - c_eff) * qm1
EC1 <- 0.5 * (a - pm1) * qm1
receita_fiscal <- t * qm1

cat("--- Depois do imposto ---\n")
cat("CMg efetivo =", c_eff, "\n")
cat("q^m(t) =", qm1, "  p^m(t) =", pm1, "\n")
cat("Lucro (liq. imposto) =", lucro1, "  EC =", EC1, "\n")
cat("Receita fiscal = t*q =", receita_fiscal, "\n\n")

# --- Analise do repasse ---
delta_p <- pm1 - pm0
repasse <- delta_p / t * 100
delta_EC <- EC1 - EC0
delta_lucro <- lucro1 - lucro0

cat("--- Analise do repasse ---\n")
cat("Delta p =", delta_p, " (repasse:", repasse, "%)\n")
cat("Delta EC =", delta_EC, "\n")
cat("Delta lucro =", delta_lucro, "\n")
cat("Receita fiscal =", receita_fiscal, "\n")

# PPM antes e depois
qc <- a - c
PPM0 <- 0.5 * (pm0 - c) * (qc - qm0)
qc1 <- a - c_eff
PPM1 <- 0.5 * (pm1 - c_eff) * (qc1 - qm1)
delta_PPM <- PPM1 - PPM0

cat("\nPPM antes =", PPM0, "  PPM depois =", PPM1, "\n")
cat("Delta PPM =", delta_PPM, "\n")
cat("Perda total (consumidor+produtor) =", abs(delta_EC) + abs(delta_lucro), "\n")
cat("Receita fiscal =", receita_fiscal, "\n")
cat("Diferenca =", abs(delta_EC) + abs(delta_lucro) - receita_fiscal, "= Delta PPM\n")

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

# Painel 1: Antes e depois
q_seq <- seq(0, 55, length = 300)
p_dem <- a - q_seq
RMg0 <- a - 2 * q_seq

plot(q_seq, p_dem, type = "l", lwd = 3, col = "#0d6efd",
     ylim = c(0, 65), xlim = c(0, 55),
     xlab = "q", ylab = "p",
     main = "Efeito do imposto unitario")
lines(q_seq, RMg0, lwd = 2, col = "#6f42c1", lty = 2)
abline(h = c, col = "#198754", lwd = 2)
abline(h = c_eff, col = "#dc3545", lwd = 2, lty = 3)

points(qm0, pm0, pch = 19, col = "#198754", cex = 1.8)
points(qm1, pm1, pch = 17, col = "#dc3545", cex = 1.8)
arrows(qm0 - 0.5, pm0 + 0.5, qm1 + 0.5, pm1 - 0.5,
       col = "#fd7e14", lwd = 2, length = 0.08)

text(qm0 + 1.5, pm0 - 2, "Antes", col = "#198754", cex = 0.8, font = 2)
text(qm1 - 1, pm1 + 2.5, "Depois", col = "#dc3545", cex = 0.8, font = 2)

legend("topright",
       legend = c("Demanda", "RMg", paste0("CMg = ", c),
                  paste0("CMg+t = ", c_eff)),
       col = c("#0d6efd", "#6f42c1", "#198754", "#dc3545"),
       lwd = c(3, 2, 2, 2), lty = c(1, 2, 1, 3),
       cex = 0.65, bg = "white")

# Painel 2: Repasse vs taxa
t_seq <- seq(0, a - c - 1, length = 200)
repasse_pct <- rep(50, length(t_seq))  # sempre 50% com demanda linear
lucro_seq <- ((a - c - t_seq) / 2)^2
receita_seq <- t_seq * (a - c - t_seq) / 2

plot(t_seq, receita_seq, type = "l", lwd = 3, col = "#0d6efd",
     xlab = "Imposto (t)", ylab = "R$ / %",
     main = "Receita fiscal e lucro",
     ylim = c(0, max(lucro_seq) * 1.1))
lines(t_seq, lucro_seq, lwd = 3, col = "#198754")
abline(v = t, col = "#fd7e14", lty = 2, lwd = 1.5)
abline(h = 50, col = "#adb5bd", lty = 3)
text(t + 1, max(lucro_seq) * 0.9, paste0("t = ", t),
     col = "#fd7e14", cex = 0.8, font = 2)

legend("topright",
       legend = c("Receita fiscal", "Lucro", "Repasse = 50%"),
       col = c("#0d6efd", "#198754", "#adb5bd"),
       lwd = c(3, 3, 1), lty = c(1, 1, 3),
       cex = 0.65, bg = "white")

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