WebR — Funções Custo por Tipo de Tecnologia

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# ============================================
# Funcoes Custo: CD, Linear, Leontief, CES
# Comparacao lado a lado
# ============================================

w <- 4;  v <- 1  # precos dos insumos
q_seq <- seq(0.1, 10, length = 500)

# --- 1. Cobb-Douglas ---
# (a) CRS: q = K^0.5 * L^0.5  (alpha+beta = 1)
C_cd_crs <- function(q) {
  kappa <- 2 * (0.5^(-0.5) * 0.5^(-0.5))
  kappa * w^0.5 * v^0.5 * q   # linear em q
}

# (b) DRS: q = K^0.25 * L^0.25  (alpha+beta = 0.5)
C_cd_drs <- function(q) {
  # C = kappa * w^0.5 * v^0.5 * q^2
  kappa <- 1 * (0.25^(-0.25) * 0.25^(-0.25))^2
  kappa * w^0.5 * v^0.5 * q^2
}

# (c) IRS: q = K^0.4 * L^0.6  com alpha+beta = 1 mas A > 1
# Usaremos alpha=0.6, beta=0.9 => s=1.5
C_cd_irs <- function(q) {
  a <- 0.6; b <- 0.9; s <- a + b
  kappa <- s * (a^(-a) * b^(-b))^(1/s)
  kappa * w^(b/s) * v^(a/s) * q^(1/s)  # q^(2/3), concava
}

# --- 2. Linear: q = 2K + L ---
C_linear <- function(q) {
  q * min(v/2, w/1)  # min{v/alpha, w/beta}
}

# --- 3. Leontief: q = min{K, 2L} ---
C_leontief <- function(q) {
  (1 * v + 0.5 * w) * q   # alpha*v + beta*w (com K/1 = L/0.5)
}

# --- Calculos ---
C1 <- C_cd_crs(q_seq)
C2 <- sapply(q_seq, C_cd_drs)
C3 <- C_cd_irs(q_seq)
C4 <- sapply(q_seq, C_linear)
C5 <- sapply(q_seq, C_leontief)

# --- Tabela resumo ---
cat("====== FUNCOES CUSTO: CATALOGO ======\n")
cat("Precos: w =", w, " v =", v, "\n\n")

cat("1. CD (CRS): q = K^0.5 L^0.5\n")
cat("   C(q) =", round(C_cd_crs(1), 2), "* q  |  CMg = CMe =", round(C_cd_crs(1), 2), "\n\n")

cat("2. CD (DRS): q = K^0.25 L^0.25\n")
cat("   C(q) ~ q^2  |  CMg crescente  |  CMe crescente\n\n")

cat("3. CD (IRS): q = K^0.6 L^0.9\n")
cat("   C(q) ~ q^(2/3)  |  CMg decrescente  |  CMe decrescente\n\n")

cat("4. Linear: q = 2K + L\n")
cat("   C(q) = min{v/2, w/1}*q = min{", v/2, ",", w, "}*q =", min(v/2, w)*1, "*q\n")
cat("   Firma usa so capital (v/alpha < w/beta)\n\n")

cat("5. Leontief: q = min{K, 2L}\n")
cat("   C(q) = (v + w/2)*q =", (v + w/2), "*q  |  Independe dos precos!\n")

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

# Painel 1: Custo Total
plot(q_seq, C1, type = "l", lwd = 3, col = "#0d6efd",
     xlab = "q", ylab = "C(q)", main = "Custo Total",
     ylim = c(0, max(C2) * 0.6), cex.lab = 1.1)
lines(q_seq, C2, lwd = 2, col = "#dc3545")
lines(q_seq, C3, lwd = 2, col = "#198754")
lines(q_seq, C4, lwd = 2, col = "#fd7e14", lty = 2)
lines(q_seq, C5, lwd = 2, col = "#6f42c1", lty = 3)

legend("topleft",
       legend = c("CD (CRS)", "CD (DRS)", "CD (IRS)", "Linear", "Leontief"),
       col = c("#0d6efd", "#dc3545", "#198754", "#fd7e14", "#6f42c1"),
       lwd = c(3, 2, 2, 2, 2), lty = c(1, 1, 1, 2, 3),
       cex = 0.75, bg = "white")

# Painel 2: Custo Medio
CMe1 <- C1 / q_seq
CMe2 <- C2 / q_seq
CMe3 <- C3 / q_seq
CMe4 <- C4 / q_seq
CMe5 <- C5 / q_seq

plot(q_seq, CMe1, type = "l", lwd = 3, col = "#0d6efd",
     xlab = "q", ylab = "CMe(q)", main = "Custo Medio",
     ylim = c(0, max(CMe2[q_seq > 1]) * 1.2), cex.lab = 1.1)
lines(q_seq, CMe2, lwd = 2, col = "#dc3545")
lines(q_seq, CMe3, lwd = 2, col = "#198754")
lines(q_seq, CMe4, lwd = 2, col = "#fd7e14", lty = 2)
lines(q_seq, CMe5, lwd = 2, col = "#6f42c1", lty = 3)

legend("topright",
       legend = c("CD (CRS) - const.", "CD (DRS) - cresc.",
                  "CD (IRS) - decresc.", "Linear - const.", "Leontief - const."),
       col = c("#0d6efd", "#dc3545", "#198754", "#fd7e14", "#6f42c1"),
       lwd = c(3, 2, 2, 2, 2), lty = c(1, 1, 1, 2, 3),
       cex = 0.7, bg = "white")

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