WebR — Custo de Uso do Capital e Demanda por K

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# ============================================
# Custo de Uso do Capital e Demanda por K
# Secao 18.8 — Cobb-Douglas
# ============================================

# Y = A * K^alpha * L^(1-alpha)
A <- 10; alpha <- 0.35; L <- 100
p <- 1       # preco do produto
pK <- 1      # preco do bem de capital
delta <- 0.10  # depreciacao

cat("====== CUSTO DE USO DO CAPITAL ======\n")
cat(sprintf("Y = %.0f * K^%.2f * L^%.2f\n", A, alpha, 1-alpha))
cat(sprintf("p = %.0f  pK = %.0f  delta = %.0f%%\n\n", p, pK, delta*100))

# cK = pK * (r + delta)
# Condicao: p * PMgK = cK => p * alpha * A * K^(alpha-1) * L^(1-alpha) = pK*(r+delta)
# K* = (p*alpha*A / (pK*(r+delta)))^(1/(1-alpha)) * L

cat("--- Custo de uso e demanda por capital ---\n")
cat(sprintf("%-8s %-10s %-12s %-12s\n",
    "r(%)", "cK", "K*", "PMgK"))
cat(strrep("-", 46), "\n")

r_vals <- c(0.02, 0.04, 0.06, 0.08, 0.10, 0.15, 0.20)
K_vals <- numeric(length(r_vals))
for (k in seq_along(r_vals)) {
  ri <- r_vals[k]
  cK <- pK * (ri + delta)
  K_star <- (p * alpha * A / cK)^(1/(1-alpha)) * L
  PMgK <- alpha * A * K_star^(alpha-1) * L^(1-alpha)
  K_vals[k] <- K_star
  cat(sprintf("%-8.0f %-10.3f %-12.1f %-12.4f\n",
      ri*100, cK, K_star, PMgK))
}

# --- Exemplo do caminhao ---
cat("\n--- Exemplo: caminhao ---\n")
pK_cam <- 400000
delta_cam <- 0.15
frete_mensal <- 10000

for (ri in c(0.12, 0.18)) {
  cK_mensal <- pK_cam * (ri + delta_cam) / 12
  lucro <- frete_mensal - cK_mensal
  cat(sprintf("r = %.0f%%: cK mensal = R$ %s  Lucro = R$ %s => %s\n",
      ri*100,
      format(round(cK_mensal), big.mark="."),
      format(round(lucro), big.mark="."),
      ifelse(lucro > 0, "COMPRA", "NAO COMPRA")))
}

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

# Painel 1: Demanda por capital
r_fine <- seq(0.01, 0.25, length = 300)
K_fine <- (p * alpha * A / (pK*(r_fine + delta)))^(1/(1-alpha)) * L

plot(K_fine, r_fine * 100, type = "l", lwd = 3, col = "#0d6efd",
     xlab = "Capital (K)", ylab = "Taxa de juros real (%)",
     main = "Demanda por capital")

# Marcar pontos
for (k in seq_along(r_vals)) {
  points(K_vals[k], r_vals[k]*100, pch = 19, col = "#dc3545", cex = 1.2)
}

# Duas taxas de referencia
abline(h = 4, col = "#198754", lty = 3, lwd = 1.5)
text(max(K_fine)*0.6, 4.8, "r = 4% (EUA)", col = "#198754", cex = 0.7, font = 2)
abline(h = 8, col = "#dc3545", lty = 3, lwd = 1.5)
text(max(K_fine)*0.6, 8.8, "r = 8% (Brasil)", col = "#dc3545", cex = 0.7, font = 2)

# Painel 2: Custo de uso vs taxa de juros
r_seq2 <- seq(0, 0.25, length = 200)
cK_seq <- pK * (r_seq2 + delta)

plot(r_seq2 * 100, cK_seq, type = "l", lwd = 3, col = "#dc3545",
     xlab = "Taxa de juros real (%)",
     ylab = expression(c[K] == p[K](r + delta)),
     main = "Custo de uso do capital")

# Componentes
lines(r_seq2 * 100, pK * r_seq2, lwd = 2, col = "#0d6efd", lty = 2)
abline(h = pK * delta, col = "#fd7e14", lty = 3, lwd = 2)

legend("topleft",
       legend = c(expression(c[K] == p[K](r+delta)),
                  expression(p[K] %.% r ~ "(oportunidade)"),
                  expression(p[K] %.% delta ~ "(depreciacao)")),
       col = c("#dc3545", "#0d6efd", "#fd7e14"),
       lwd = c(3, 2, 2), lty = c(1, 2, 3),
       cex = 0.6, bg = "white")

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