Let's solve the problem step-by-step. --- ## **Step 1: Write Down the Demand and Supply Equations** - **Demand:** \( Q_d = 200 - 4P \) - **Supply:** \( Q_s = 4P \) In equilibrium, \( Q_d = Q_s \). --- ## **Step 2: Set Demand Equal to Supply** \[ 200 - 4P = 4P \] --- ## **Step 3: Solve for \( P \)** Add \( 4P \) to both sides: \[ 200 = 8P \] \[ P = 25 \] --- ## **Step 4: Substitute \( P \) Back to Find \( Q \)** Use the supply equation: \[ Q_s = 4P = 4 \times 25 = 100 \] Or use the demand equation to check: \[ Q_d = 200 - 4 \times 25 = 200 - 100 = 100 \] --- ## **Step 5: Interpret the Answer** - \( Q = 100 \) million barrels will be extracted if the current generation does not consider the future. --- ## **Final Answer** \[ \boxed{100 \text{ million barrels}} \] However, this answer does **not** appear in the multiple-choice options provided. Let's double-check the supply function. ### Double-Check: - Supply: \( Q_s = 4P \) - Demand: \( Q_d = 200 - 4P \) Equilibrium: \[ Q_s = Q_d \implies 4P = 200 - 4P \implies 8P = 200 \implies P = 25 \] \[ Q = 4P = 4 \times 25 = 100 \] ### **Conclusion** - The correct answer is **100 million barrels**, but this is not listed. - If you must choose from the given options, none are correct based on the supply and demand equations provided. There may be a typo in the options or the problem. **Work shown is correct based on the given equations.**

## **Reasons Why Other Options are Not Correct** ### **1. 250 million barrels** - **Reason:** If we consider the supply equation \( Q_s = 4P \), with \( P \) calculated as 25, the maximum supply would be \( 4 \times 25 = 100 \) million barrels. Therefore, 250 million barrels is not feasible given the price and supply relationship. ### **2. 200 million barrels** - **Reason:** This value would imply a price \( P \) of 0, as seen from the demand equation: \[ Q_d = 200 - 4P \implies 200 = 200 - 4(0) \implies P = 0 \] A price of 0 does not reflect a realistic scenario in this context, as it would suggest no cost associated with extraction. ### **3. 4 million barrels** - **Reason:** This amount would suggest a very low price: \[ Q_s = 4P \implies 4 = 4P \implies P = 1 \] Substituting \( P = 1 \) into the demand function yields: \[ Q_d = 200 - 4(1) = 196 \text{ million barrels} \] Since demand far exceeds supply at this price, this option is also invalid. ### **4. 50 million barrels** - **Reason:** If we calculate the price at this supply level: \[ Q_s = 4P \implies 50 = 4P \implies P = 12.5 \] Substituting \( P = 12.5 \) into the demand equation gives: \[ Q_d = 200 - 4(12.5) = 150 \text{ million barrels} \] Again, here the demand exceeds supply, indicating that this option is not valid. ## **Summary** - The only calculated extraction amount is 100 million barrels, which is consistent with both demand and supply equations. The other options do not align with the equilibrium conditions derived from the given functions.