WebR — Renda Ricardiana e Industria de Custos Crescentes

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# ============================================
# Renda ricardiana em industria de custos crescentes
# Exercicio Resolvido 13.1
# ============================================

# --- Oferta de longo prazo e demanda ---
# Oferta LP: p = 20 + 0.05*Q
# Demanda 1: Q = 800 - 10*p
# Demanda 2: Q = 1000 - 10*p (choque positivo)

p_S <- function(Q) 20 + 0.05 * Q
Q_D1 <- function(p) 800 - 10 * p
Q_D2 <- function(p) 1000 - 10 * p

# --- Equilibrio 1 ---
# 800 - 10p = (p - 20)/0.05 = 20p - 400
# 1200 = 30p => p = 40
Q1 <- 400; p1 <- 40

# --- Equilibrio 2 ---
# 1000 - 10p = 20p - 400 => 1400 = 30p => p = 46.67
p2 <- 1400/30; Q2 <- Q_D2(p2)

# --- Renda ricardiana (area acima da oferta LP) ---
RR1 <- 0.5 * (p1 - 20) * Q1
RR2 <- 0.5 * (p2 - 20) * Q2

cat("====== RENDA RICARDIANA ======\n")
cat("Oferta LP: p = 20 + 0.05Q\n")
cat("Demanda 1: Q = 800 - 10p\n")
cat("Demanda 2: Q = 1000 - 10p\n\n")

cat("--- Equilibrio 1 ---\n")
cat("p* =", p1, " Q* =", Q1, "\n")
cat("Renda ricardiana = 0.5*(", p1, "- 20)*", Q1, "=", RR1, "\n\n")

cat("--- Equilibrio 2 (pos-choque de demanda) ---\n")
cat("p* =", round(p2, 2), " Q* =", round(Q2, 2), "\n")
cat("Renda ricardiana =", round(RR2, 1), "\n")
cat("Variacao =", round(RR2 - RR1, 1), " (+", round((RR2/RR1 - 1)*100, 1), "%)\n\n")

cat("--- Interpretacao ---\n")
cat("A renda ricardiana e' o pagamento aos fatores inframarginais\n")
cat("(terras ferteis, localizacao privilegiada, etc.).\n")
cat("NAO e' lucro da firma — e' custo de oportunidade do fator escasso.\n")
cat("Ricardo: 'Nao e' porque os alugueis sao altos que o trigo e' caro;\n")
cat("          e' porque o trigo e' caro que os alugueis sao altos.'\n")

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

Q_seq <- seq(0, 700, length = 300)
p_seq <- seq(0, 70, length = 300)

# Painel 1: Equilibrio 1
plot(Q_seq, p_S(Q_seq), type = "l", lwd = 3, col = "#dc3545",
     ylim = c(0, 70), xlim = c(0, 700),
     xlab = "Q", ylab = "p",
     main = "Equilibrio 1: demanda original")
lines(Q_D1(p_seq), p_seq, lwd = 3, col = "#0d6efd")

# Area de renda ricardiana
Q_rr <- seq(0, Q1, length = 200)
polygon(c(Q_rr, rev(Q_rr)),
        c(rep(p1, length(Q_rr)), p_S(rev(Q_rr))),
        col = rgb(0.1, 0.53, 0.33, 0.2), border = NA)
text(Q1/2, (p1 + 20)/2, paste0("RR = ", RR1),
     col = "#198754", cex = 1, font = 2)

points(Q1, p1, pch = 19, col = "#6f42c1", cex = 1.8)
text(Q1, p1, paste0("  E1"), pos = 4, cex = 0.8, col = "#6f42c1", font = 2)

legend("topright", legend = c("Oferta LP", "Demanda", "Renda ricardiana"),
       col = c("#dc3545", "#0d6efd", rgb(0.1, 0.53, 0.33, 0.5)),
       lwd = c(3, 3, NA), pch = c(NA, NA, 15), cex = 0.7, bg = "white")

# Painel 2: Equilibrio 2 (pos-choque)
plot(Q_seq, p_S(Q_seq), type = "l", lwd = 3, col = "#dc3545",
     ylim = c(0, 70), xlim = c(0, 700),
     xlab = "Q", ylab = "p",
     main = "Equilibrio 2: demanda expandida")
lines(Q_D1(p_seq), p_seq, lwd = 1.5, col = "#0d6efd", lty = 2)
lines(Q_D2(p_seq), p_seq, lwd = 3, col = "#0d6efd")

# Area de renda ricardiana 2
Q_rr2 <- seq(0, Q2, length = 200)
polygon(c(Q_rr2, rev(Q_rr2)),
        c(rep(p2, length(Q_rr2)), p_S(rev(Q_rr2))),
        col = rgb(0.1, 0.53, 0.33, 0.2), border = NA)
text(Q2/2, (p2 + 20)/2, paste0("RR = ", round(RR2)),
     col = "#198754", cex = 1, font = 2)

points(Q1, p1, pch = 1, col = "#adb5bd", cex = 1.5)
points(Q2, p2, pch = 19, col = "#6f42c1", cex = 1.8)
text(Q2, p2, paste0("  E2"), pos = 4, cex = 0.8, col = "#6f42c1", font = 2)

# Seta de transicao
arrows(Q1 + 5, p1 + 1, Q2 - 5, p2 - 1,
       col = "#fd7e14", lwd = 2, length = 0.08)

legend("topright", legend = c("Oferta LP", "D (nova)", "D (antiga)", "RR"),
       col = c("#dc3545", "#0d6efd", "#0d6efd", rgb(0.1, 0.53, 0.33, 0.5)),
       lwd = c(3, 3, 1.5, NA), lty = c(1, 1, 2, NA),
       pch = c(NA, NA, NA, 15), cex = 0.7, bg = "white")

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