A large commercial laundry service supplies industrial cleaning to hotels and hospitals. The cleaning process uses chemical solvents that generate wastewater pollution, imposing costs on downstream users who rely on the river for recreation and drinking water. It is estimated that each additional unit of cleaning service provided generates an external cost of $300.
Inverse Demand: P=900-Q and Inverse Supply: P=2Q
Compute the market clearing price at the private equilibrium, round your answer to two decimal places, do not include any units.

Question

BlackTom AI · Accepted Answer

900 - Q = 2Q

1. Relevant knowledge points and concepts
- Market (private) equilibrium occurs where private marginal benefit (inverse demand) equals private marginal cost (inverse supply). External costs from pollution are ignored in the private equilibrium calculation. Inverse demand: P = 900 − Q; inverse supply: P = 2Q.

2. Step-by-step reasoning
- At private equilibrium set inverse demand equal to inverse supply because price adjusts so quantity demanded equals quantity supplied:
  900 − Q = 2Q.

3. Calculations with intermediate steps
- Solve for Q:
  900 − Q = 2Q
  900 = 3Q
  Q = 900 / 3
  Q = 300.
- Compute the market-clearing price by substituting Q into either the demand or supply function:
  Using supply: P = 2Q = 2 × 300 = 600.
  Using demand check: P = 900 − Q = 900 − 300 = 600.
- Round to two decimal places: 600.00.

4. Why the correct answer is correct
- The private equilibrium is determined solely by private supply and demand; solving those equations yields Q = 300 and the corresponding market price P = 600. The external cost of $300 per unit does not enter the private equilibrium calculation, so the market-clearing price remains 600.00.

5. Why other options are incorrect
- Any price other than 600 would not equate quantity supplied and demanded given the provided functions. If one incorrectly tried to internalize the external cost, the social optimum would instead satisfy 900 − Q = 2Q + 300, giving Q = 200 and consumer price 700 — but that is the social, not the private, equilibrium.

6. Conclusion
- The computed private market-clearing price is 600.00, which matches the provided answer.

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