Let's solve the problem step by step: --- ## **Step 1: Understanding the Problem** - **MPC (Marginal Private Cost)**: This is the supply curve (orange squares). - **MPB (Marginal Private Benefit)**: This is the demand curve (blue circles). - **MEC (Marginal External Cost)**: This is a constant $70 per ton. - **MSC (Marginal Social Cost)**: This is MPC + MEC. --- ## **Step 2: Plotting the MSC Curve** To get the MSC curve, **add $70 to each MPC value** at every quantity. Let's extract the MPC (Supply) points from the graph: - Q = 1: MPC = $20 - Q = 2: MPC = $40 - Q = 3: MPC = $60 - Q = 4: MPC = $80 - Q = 5: MPC = $100 - Q = 6: MPC = $120 Now, add $70 to each: - Q = 1: MSC = $20 + $70 = $90 - Q = 2: MSC = $40 + $70 = $110 - Q = 3: MSC = $60 + $70 = $130 - Q = 4: MSC = $80 + $70 = $150 - Q = 5: MSC = $100 + $70 = $170 - Q = 6: MSC = $120 + $70 = $190 --- ## **Step 3: Finding Market Equilibrium Quantity** Market equilibrium is where MPC = MPB. Look for the quantity where the orange square (MPC) and blue circle (MPB) intersect. From the graph: - At Q = 4: MPC = $80, MPB = $80 **Market equilibrium quantity is 4 tons.** --- ## **Step 4: Finding Socially Optimal Quantity** Social optimum is where **MSC = MPB**. From our earlier MSC values: | Q | MSC | MPB | |---|-----|-----| | 1 | 90 | 180 | | 2 | 110 | 140 | | 3 | 130 | 100 | | 4 | 150 | 80 | | 5 | 170 | 60 | | 6 | 190 | 40 | Find where MSC = MPB. At Q = 2: MSC = 110, MPB = 140 At Q = 3: MSC = 130, MPB = 100 So, the intersection is **between Q = 2 and Q = 3**. Let's interpolate: Let \( Q^* \) be the optimal quantity. \[ \text{MSC at } Q^* = \text{MPB at } Q^* \] MSC increases by 20 per unit, MPB decreases by 40 per unit between Q=2 and Q=3. Let Q = 2 + x, where 0 < x < 1. \[ MSC = 110 + 20x \\ MPB = 140 - 40x \\ \] Set equal: \[ 110 + 20x = 140 - 40x \\ 60x = 30 \\ x = 0.5 \\ \] So, **Q = 2.5 tons** (socially optimal quantity). --- ## **Step 5: Government Policy** To make firms internalize the externality, the government should impose a **tax equal to the external cost**, which is **$70 per ton**. --- ## **Step 6: Final Answers** Fill in the blanks: > The market equilibrium quantity is **4** tons of bolts, but the socially optimal quantity of bolt production is **2.5** tons. > > To create an incentive for the firm to produce the socially optimal quantity of bolts, the government could impose a **tax** of **$70** per ton of bolts. --- ## **Summary Table** | Quantity (tons) | MPC | MSC (MPC+70) | MPB | |-----------------|-----|--------------|-----| | 1 | 20 | 90 | 180 | | 2 | 40 | 110 | 140 | | 3 | 60 | 130 | 100 | | 4 | 80 | 150 | 80 | | 5 | 100 | 170 | 60 | | 6 | 120 | 190 | 40 | --- ## **Final Answers** - Market equilibrium quantity: **4** tons - Socially optimal quantity: **2.5** tons - Government could impose a **tax** of **$70** per ton --- Let me know if you need the plotted points for MSC or any other details!