WebR — Estatica Comparativa: Choques de Oferta e Demanda

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# ============================================
# Estatica Comparativa: choques de oferta e demanda
# Exemplo: mercado de petroleo (ANPEC 2023)
# ============================================

# --- Parametros iniciais ---
p0 <- 80; Q0 <- 100  # equilibrio inicial
e_D <- -0.4          # elasticidade demanda
e_S <- 0.2           # elasticidade oferta

# Derivar curvas lineares
b <- -e_D * Q0 / p0  # |dQd/dp| = 0.5
d <-  e_S * Q0 / p0  # dQs/dp  = 0.25

a_d <- Q0 + b * p0   # intercepto demanda = 140
c_s <- Q0 - d * p0   # intercepto oferta  = 80

cat("====== ESTATICA COMPARATIVA ======\n")
cat("Demanda: Qd =", a_d, "-", b, "p\n")
cat("Oferta:  Qs =", c_s, "+", d, "p\n")
cat("Equilibrio inicial: p* =", p0, " Q* =", Q0, "\n\n")

# --- Choque 1: embargo reduz oferta em 30 ---
delta_S <- -30
c_s2 <- c_s + delta_S

p1 <- (a_d - c_s2) / (b + d)
Q1 <- a_d - b * p1

cat("--- Choque de oferta: embargo (-30 MM barris) ---\n")
cat("Nova oferta: Qs' =", c_s2, "+", d, "p\n")
cat("Novo equilibrio: p =", round(p1, 1), " Q =", round(Q1, 1), "\n")
cat("Variacao: dp = +", round(p1 - p0, 1),
    " dQ = ", round(Q1 - Q0, 1), "\n\n")

# --- Choque 2: embargo + queda de demanda de 20 ---
delta_D <- -20
a_d2 <- a_d + delta_D

p2 <- (a_d2 - c_s2) / (b + d)
Q2 <- a_d2 - b * p2

cat("--- Choque duplo: embargo + novas tecnologias (-20 MM) ---\n")
cat("Nova demanda: Qd' =", a_d2, "-", b, "p\n")
cat("Novo equilibrio: p =", round(p2, 1), " Q =", round(Q2, 1), "\n")
cat("p2 =", round(p2, 1), "> p0 =", p0,
    "=> preco SUBIU mesmo com queda na demanda!\n\n")

cat("--- Regra geral ---\n")
cat("dp/d(choque_demanda) > 0 (demanda sobe => preco sobe)\n")
cat("dp/d(choque_oferta)  < 0 (oferta cai  => preco sobe)\n")
cat("Magnitude depende das elasticidades!\n")

# --- Grafico ---
par(mar = c(4.5, 4.5, 3, 2), bg = "#f8f9fa")
p_seq <- seq(0, 200, length = 500)

Qd0 <- a_d - b * p_seq
Qs0 <- c_s + d * p_seq
Qs1 <- c_s2 + d * p_seq
Qd2 <- a_d2 - b * p_seq

plot(Qd0, p_seq, type = "l", lwd = 3, col = "#0d6efd",
     xlim = c(0, 180), ylim = c(0, 180),
     xlab = "Q (milhoes barris/dia)", ylab = "p (US$/barril)",
     main = "Estatica comparativa: mercado de petroleo")
lines(Qs0, p_seq, lwd = 3, col = "#dc3545")
lines(Qs1, p_seq, lwd = 2, col = "#dc3545", lty = 2)
lines(Qd2, p_seq, lwd = 2, col = "#0d6efd", lty = 2)

# Equilibrios
points(Q0, p0, pch = 19, col = "#198754", cex = 2)
points(Q1, p1, pch = 17, col = "#fd7e14", cex = 1.8)
points(Q2, p2, pch = 15, col = "#6f42c1", cex = 1.5)

text(Q0, p0, paste0("  A: p=", p0, ", Q=", Q0),
     pos = 4, cex = 0.75, col = "#198754", font = 2)
text(Q1, p1, paste0("  B: p=", round(p1), ", Q=", round(Q1)),
     pos = 4, cex = 0.75, col = "#fd7e14", font = 2)
text(Q2, p2, paste0("  C: p=", round(p2,1), ", Q=", round(Q2,1)),
     pos = 2, cex = 0.75, col = "#6f42c1", font = 2)

# Setas
arrows(Q0, p0 + 3, Q1, p1 - 3, col = "#fd7e14", lwd = 1.5, length = 0.08)
arrows(Q1, p1 + 3, Q2, p2 - 3, col = "#6f42c1", lwd = 1.5, length = 0.08)

legend("topright",
       legend = c("Demanda (D)", "Oferta (S)",
                  "Oferta pos-embargo (S')", "Demanda pos-tecnologia (D')"),
       col = c("#0d6efd", "#dc3545", "#dc3545", "#0d6efd"),
       lwd = c(3, 3, 2, 2), lty = c(1, 1, 2, 2),
       cex = 0.7, bg = "white")

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