Certainly! Here is your answer, restructured for clarity and flow, with each step clearly delineated and concise explanations for each scenario. --- # **Greaze Extraction Problem: Structured Solution** ## **Step 1: Problem Recap & Key Information** - **Greaze Stock:** 400 million gallons (must be sold within 4 years) - **Annual Demand:** \( Q_t = 225 - P_t \) - **Marginal Cost:** 0 - **Interest Rate:** 0 (so Hotelling's rule applies: constant scarcity rent over time) - **Poodz Entry:** In Years 3–4, Poodz provides unlimited supply at MC = \$75 ⇒ **Price ceiling at \$75** in those years --- ## **Step 2: Perfect Competition, No Poodz** **Logic:** With no interest and limited stock, competitive equilibrium spreads the resource evenly over 4 years. **Calculation:** \[ Q_t = \frac{400}{4} = 100 \text{ million gallons per year} \] **Year 1 Sales:** **100 million gallons** --- ## **Step 3: Monopoly, No Poodz** **Logic:** Monopolist also faces no incentive to shift sales across years due to zero interest rate and finite horizon. The monopoly quantity is allocated evenly. **Calculation:** \[ Q_t = \frac{400}{4} = 100 \text{ million gallons per year} \] **Year 1 Sales:** **100 million gallons** --- ## **Step 4: Perfect Competition, Poodz Arrives in Years 3–4** **Logic:** Once Poodz arrives, price is capped at \$75. Greaze suppliers will want to sell all their stock before competition erodes the scarcity rent. **Demand at \$75:** \[ Q = 225 - 75 = 150 \text{ million gallons} \] But Greaze cannot price above \$75 after Year 2, so all 400 million gallons are sold in Years 1–2. **Calculation:** \[ Q_1 = Q_2 = \frac{400}{2} = 200 \text{ million gallons per year} \] **Year 1 Sales:** **200 million gallons** --- ## **Step 5: Monopoly, Poodz Arrives in Years 3–4** **Logic:** Monopolist can sell above \$75 only in Years 1–2. In Years 3–4, marginal revenue for Greaze cannot exceed \$75 (Poodz's price). Monopolist sets Year 1 sales where marginal revenue equals \$75. **Demand Curve:** \( Q = 225 - P \) **Revenue:** \( R = P \cdot Q = (225 - Q)Q = 225Q - Q^2 \) **Marginal Revenue:** \( MR = \frac{dR}{dQ} = 225 - 2Q \) **Set \( MR = 75 \):** \[ 225 - 2Q = 75 \implies Q = 75 \] **Corresponding Price:** \[ P = 225 - Q = 150 \] **Year 1 Sales:** **75 million gallons** --- ## **Step 6: Summary Table** | Scenario | Year 1 Sales (million gallons) | | ----------------------------------------- | ------------------------------ | | Perfect Competition (no Poodz) | **100** | | Monopoly (no Poodz) | **100** | | Perfect Competition (with Poodz looming) | **200** | | Monopoly (with Poodz looming) | **75** | --- ## **Key Takeaways** - **No Poodz:** Both perfect competition and monopoly spread sales evenly over the 4 years. - **With Poodz:** Competition front-loads sales before Poodz arrives. A monopolist restricts quantity to maximize price before the price cap binds. ---