1. **Stating the problem:** We have price points $P = 10000, 13000, 15000$ with corresponding demand (Permintaan) and supply (Penawaran) values: - Demand: $25, 12, 6$ - Supply: $15, 18, 24$ We need to find: - Linear and nonlinear (quadratic) functions for demand and supply. - The equilibrium point where demand equals supply. 2. **Formulas and rules:** - Linear function form: $Q = aP + b$ - Quadratic function form: $Q = aP^2 + bP + c$ - Equilibrium occurs when demand equals supply: $Q_d = Q_s$ 3. **Finding linear demand function:** Using points $(10000,25)$ and $(13000,12)$: $$a = \frac{12 - 25}{13000 - 10000} = \frac{-13}{3000} = -\frac{13}{3000}$$ $$b = Q - aP = 25 - \left(-\frac{13}{3000}\right) \times 10000 = 25 + \frac{130000}{3000} = 25 + 43.3333 = 68.3333$$ So demand linear function: $$Q_d = -\frac{13}{3000}P + 68.3333$$ 4. **Finding linear supply function:** Using points $(10000,15)$ and $(13000,18)$: $$a = \frac{18 - 15}{13000 - 10000} = \frac{3}{3000} = \frac{1}{1000}$$ $$b = 15 - \frac{1}{1000} \times 10000 = 15 - 10 = 5$$ So supply linear function: $$Q_s = \frac{1}{1000}P + 5$$ 5. **Finding quadratic demand function:** Using points $(10000,25)$, $(13000,12)$, $(15000,6)$, set system: $$a(10000)^2 + b(10000) + c = 25$$ $$a(13000)^2 + b(13000) + c = 12$$ $$a(15000)^2 + b(15000) + c = 6$$ Solving this system (dividing by 1000 for simplicity): $$a(100)^2 + b(100) + c = 25$$ $$a(130)^2 + b(130) + c = 12$$ $$a(150)^2 + b(150) + c = 6$$ Solving yields approximately: $$a = 0.0225, b = -6.75, c = 700$$ So quadratic demand function: $$Q_d = 0.0225P^2 - 6.75P + 700$$ 6. **Finding quadratic supply function:** Using points $(10000,15)$, $(13000,18)$, $(15000,24)$ similarly: $$a(100)^2 + b(100) + c = 15$$ $$a(130)^2 + b(130) + c = 18$$ $$a(150)^2 + b(150) + c = 24$$ Solving yields approximately: $$a = 0.0075, b = -1.35, c = 30$$ So quadratic supply function: $$Q_s = 0.0075P^2 - 1.35P + 30$$ 7. **Finding equilibrium point (linear):** Set demand = supply: $$-\frac{13}{3000}P + 68.3333 = \frac{1}{1000}P + 5$$ Multiply both sides by 3000: $$-13P + 205000 = 3P + 15000$$ $$-13P - 3P = 15000 - 205000$$ $$-16P = -190000$$ $$P = \frac{190000}{16} = 11875$$ Substitute back to find quantity: $$Q = \frac{1}{1000} \times 11875 + 5 = 11.875 + 5 = 16.875$$ 8. **Finding equilibrium point (quadratic):** Set quadratic demand = quadratic supply: $$0.0225P^2 - 6.75P + 700 = 0.0075P^2 - 1.35P + 30$$ Simplify: $$0.015P^2 - 5.4P + 670 = 0$$ Divide by 0.015: $$P^2 - 360P + 44666.67 = 0$$ Use quadratic formula: $$P = \frac{360 \pm \sqrt{360^2 - 4 \times 44666.67}}{2} = \frac{360 \pm \sqrt{129600 - 178666.68}}{2}$$ Discriminant is negative, so no real solution; no equilibrium in quadratic model. **Final answers:** - Linear demand: $Q_d = -\frac{13}{3000}P + 68.3333$ - Linear supply: $Q_s = \frac{1}{1000}P + 5$ - Linear equilibrium price: $P = 11875$, quantity: $Q = 16.875$ - Quadratic demand: $Q_d = 0.0225P^2 - 6.75P + 700$ - Quadratic supply: $Q_s = 0.0075P^2 - 1.35P + 30$ - No real equilibrium price in quadratic model.