WebR — Agregacao de Demandas Individuais

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# ============================================
# Agregacao de demandas individuais
# Soma horizontal => demanda de mercado
# ============================================

# --- Tres tipos de consumidores ---
# Tipo A: 100 consumidores, x_A(p) = 20 - 2p  (p <= 10)
# Tipo B:  50 consumidores, x_B(p) = 15 - p    (p <= 15)
# Tipo C:  30 consumidores, x_C(p) = 30 - 3p   (p <= 10)

n_A <- 100; n_B <- 50; n_C <- 30

x_A <- function(p) pmax(20 - 2*p, 0)
x_B <- function(p) pmax(15 - p, 0)
x_C <- function(p) pmax(30 - 3*p, 0)

# Demanda de mercado: soma horizontal
X_mkt <- function(p) n_A * x_A(p) + n_B * x_B(p) + n_C * x_C(p)

# --- Oferta de mercado (40 firmas identicas) ---
# s_j(p) = 4p - 10  para p >= 2.5
n_f <- 40
s_j <- function(p) ifelse(p >= 2.5, 4*p - 10, 0)
S_mkt <- function(p) n_f * s_j(p)

# --- Equilibrio ---
# Resolver X(p*) = S(p*) numericamente
f_eq <- function(p) X_mkt(p) - S_mkt(p)
p_star <- uniroot(f_eq, c(0.1, 15))$root
Q_star <- X_mkt(p_star)

cat("====== AGREGACAO DE DEMANDAS ======\n")
cat("Tipo A:", n_A, "consumidores, x_A = 20 - 2p\n")
cat("Tipo B:", n_B, "consumidores, x_B = 15 - p\n")
cat("Tipo C:", n_C, "consumidores, x_C = 30 - 3p\n\n")

cat("--- Demanda de mercado em p = 5 ---\n")
cat("  A:", n_A, "x", x_A(5), "=", n_A*x_A(5), "\n")
cat("  B:", n_B, "x", x_B(5), "=", n_B*x_B(5), "\n")
cat("  C:", n_C, "x", x_C(5), "=", n_C*x_C(5), "\n")
cat("  X(5) =", X_mkt(5), "\n\n")

cat("--- Equilibrio ---\n")
cat("p* =", round(p_star, 2), "\n")
cat("Q* =", round(Q_star, 2), "\n")

# Elasticidade de mercado no equilibrio
eps <- 1e-6
elast_mkt <- ((X_mkt(p_star+eps) - X_mkt(p_star-eps))/(2*eps)) * p_star / Q_star
cat("|e_D| =", round(abs(elast_mkt), 3), "\n\n")

# Elasticidade ponderada
e_A <- -2 * p_star / x_A(p_star)
e_B <- -1 * p_star / x_B(p_star)
e_C <- -3 * p_star / x_C(p_star)
w_A <- n_A * x_A(p_star) / Q_star
w_B <- n_B * x_B(p_star) / Q_star
w_C <- n_C * x_C(p_star) / Q_star
e_pond <- w_A * e_A + w_B * e_B + w_C * e_C
cat("Verificacao (media ponderada):\n")
cat("  e_pond =", round(e_pond, 3), " = e_mkt? ",
    abs(e_pond - elast_mkt) < 0.01, "\n")

# --- Grafico ---
par(mfrow = c(1, 2), mar = c(4.5, 4.5, 3, 1), bg = "#f8f9fa")
p_seq <- seq(0, 16, length = 500)

# Painel 1: Demandas individuais
plot(n_A*x_A(p_seq), p_seq, type = "l", lwd = 2, col = "#0d6efd",
     xlim = c(0, max(X_mkt(0))*1.1), ylim = c(0, 16),
     xlab = "Q", ylab = "p",
     main = "Demandas individuais (agregadas por tipo)")
lines(n_B*x_B(p_seq), p_seq, lwd = 2, col = "#dc3545")
lines(n_C*x_C(p_seq), p_seq, lwd = 2, col = "#198754")
legend("topright",
       legend = c(paste0("100 x A"), paste0("50 x B"), paste0("30 x C")),
       col = c("#0d6efd", "#dc3545", "#198754"),
       lwd = 2, cex = 0.75, bg = "white")

# Painel 2: Mercado
plot(X_mkt(p_seq), p_seq, type = "l", lwd = 3, col = "#0d6efd",
     xlim = c(0, max(X_mkt(0))*1.1), ylim = c(0, 16),
     xlab = "Q", ylab = "p",
     main = "Equilibrio de mercado")
lines(S_mkt(p_seq), p_seq, lwd = 3, col = "#dc3545")

# Equilibrio
points(Q_star, p_star, pch = 19, col = "#6f42c1", cex = 2)
text(Q_star, p_star,
     paste0("  E: p*=", round(p_star,1), ", Q*=", round(Q_star,0)),
     pos = 4, cex = 0.8, col = "#6f42c1", font = 2)

# EC (area acima de p* abaixo da demanda)
q_ec <- seq(0, Q_star, length = 200)
# Inverter: para cada q, achar p tal que X(p) = q
p_inv <- sapply(q_ec, function(q) {
  if (q <= 0) return(15)
  tryCatch(uniroot(function(p) X_mkt(p) - q, c(0, 16))$root, error = function(e) NA)
})
p_inv[is.na(p_inv)] <- p_star
polygon(c(q_ec, rev(q_ec)),
        c(p_inv, rep(p_star, length(q_ec))),
        col = rgb(0.05, 0.43, 0.99, 0.15), border = NA)

# EP (area abaixo de p* acima da oferta)
q_ep <- seq(0, Q_star, length = 200)
p_s_inv <- sapply(q_ep, function(q) {
  if (q <= 0) return(2.5)
  (q / n_f + 10) / 4
})
polygon(c(q_ep, rev(q_ep)),
        c(rep(p_star, length(q_ep)), p_s_inv),
        col = rgb(0.1, 0.53, 0.33, 0.15), border = NA)

text(Q_star*0.3, p_star + 2, "EC", col = "#0d6efd", cex = 1, font = 2)
text(Q_star*0.3, p_star - 1.5, "EP", col = "#198754", cex = 1, font = 2)

legend("topright",
       legend = c("Demanda (X)", "Oferta (S)"),
       col = c("#0d6efd", "#dc3545"),
       lwd = 3, cex = 0.75, bg = "white")

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