Carregando WebR...
# ============================================ # Inovacao sob monopolio vs. concorrencia # Exercicio Resolvido 15.8 (Hipotese Schumpeteriana) # ============================================ # --- Parametros --- a <- 100 # demanda: p = a - q c0 <- 40 # CMg inicial # Investimento I reduz CMg: c(I) = c0 - sqrt(I) cat("====== HIPOTESE SCHUMPETERIANA ======\n") cat("Demanda: p =", a, "- q\n") cat("CMg inicial =", c0, "\n") cat("CMg apos P&D: c(I) =", c0, "- sqrt(I)\n\n") # --- Monopolista --- # Lucro(s) = (30 + s/2)^2 - s^2, onde s = sqrt(I) # FOC: 30 - 3s/2 = 0 => s = 20 => I = 400 s_star <- 20 I_star <- s_star^2 c_new <- c0 - s_star qm_new <- (a - c_new) / 2 pm_new <- a - qm_new lucro_bruto <- (pm_new - c_new) * qm_new lucro_liq <- lucro_bruto - I_star # Sem inovacao qm_old <- (a - c0) / 2 pm_old <- a - qm_old lucro_old <- (pm_old - c0) * qm_old cat("--- Monopolista ---\n") cat("Sem P&D: q =", qm_old, " p =", pm_old, " lucro =", lucro_old, "\n") cat("Investimento otimo: I* =", I_star, "\n") cat("CMg novo:", c_new, " (reducao de", round((1 - c_new/c0)*100), "%)\n") cat("Com P&D: q =", qm_new, " p =", pm_new, "\n") cat("Lucro bruto =", lucro_bruto, " Lucro liquido =", lucro_liq, "\n") cat("Ganho: +", lucro_liq - lucro_old, "\n\n") # --- Concorrencia com spillover total --- cat("--- Concorrencia (spillover total) ---\n") cat("p = CMg => lucro = 0 para qualquer nivel de CMg\n") cat("Investimento otimo: I* = 0 (ninguem recupera o custo)\n\n") # --- Bem-estar social --- qc_old <- a - c0 W_old_comp <- 0.5 * (a - c0) * qc_old # EC = W sob competicao qc_new <- a - c_new W_new_mono <- 0.5*(a - pm_new)*qm_new + lucro_bruto # EC + EP PPM_old <- 0.5 * (pm_old - c0) * (qc_old - qm_old) PPM_new <- 0.5 * (pm_new - c_new) * (qc_new - qm_new) cat("--- Bem-estar social ---\n") cat("Concorrencia sem inovacao: W =", W_old_comp, "\n") cat("Monopolio sem inovacao: W =", W_old_comp - PPM_old, " (PPM =", PPM_old, ")\n") cat("Monopolio com inovacao: W =", W_new_mono - I_star, " (PPM =", PPM_new, ", I =", I_star, ")\n\n") cat("CONCLUSAO: O monopolista investe I* =", I_star, "em P&D,\n") cat("reduzindo CMg de", c0, "para", c_new, ".\n") cat("Sob concorrencia com spillover total, I* = 0.\n") cat("Trade-off schumpeteriano: PPM vs. inovacao.\n") # --- Grafico --- par(mfrow = c(1, 2), mar = c(4.5, 4.5, 3, 1), bg = "#f8f9fa") # Painel 1: Lucro vs investimento I_seq <- seq(0, 1200, length = 300) s_seq <- sqrt(I_seq) lucro_seq <- (30 + s_seq/2)^2 - s_seq^2 plot(I_seq, lucro_seq, type = "l", lwd = 3, col = "#0d6efd", xlab = "Investimento em P&D (I)", ylab = "Lucro liquido", main = "Lucro do monopolista vs. P&D") abline(v = I_star, col = "#dc3545", lty = 2, lwd = 1.5) abline(h = lucro_old, col = "#adb5bd", lty = 3) points(I_star, lucro_liq, pch = 19, col = "#dc3545", cex = 2) text(I_star + 30, lucro_liq + 30, paste0("I* = ", I_star), col = "#dc3545", cex = 0.85, font = 2) text(50, lucro_old + 30, "Sem P&D", col = "#adb5bd", cex = 0.75, font = 3) # Painel 2: Antes vs depois q_seq <- seq(0, 90, length = 300) plot(q_seq, a - q_seq, type = "l", lwd = 3, col = "#0d6efd", ylim = c(0, 105), xlim = c(0, 90), xlab = "q", ylab = "p", main = "Equilibrio: antes e depois de P&D") lines(q_seq, a - 2*q_seq, lwd = 2, col = "#6f42c1", lty = 2) abline(h = c0, col = "#fd7e14", lwd = 2, lty = 3) abline(h = c_new, col = "#198754", lwd = 2) points(qm_old, pm_old, pch = 1, col = "#fd7e14", cex = 1.8) points(qm_new, pm_new, pch = 19, col = "#198754", cex = 2) arrows(qm_old + 1, pm_old - 1, qm_new - 1, pm_new + 1, col = "#dc3545", lwd = 2, length = 0.08) text(qm_old + 3, pm_old + 3, "Antes", col = "#fd7e14", cex = 0.8, font = 2) text(qm_new + 3, pm_new - 3, "Depois", col = "#198754", cex = 0.8, font = 2) legend("topright", legend = c("Demanda", "RMg", paste0("CMg antes = ", c0), paste0("CMg depois = ", c_new)), col = c("#0d6efd", "#6f42c1", "#fd7e14", "#198754"), lwd = c(3, 2, 2, 2), lty = c(1, 2, 3, 1), cex = 0.6, bg = "white")
▶ Executar
↻ Resetar
(Aguardando WebR...)