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
The government imposes a Pigouvian tax designed to correct the externality - Who bears the tax burden on this tax, why?

Question

BlackTom AI · Accepted Answer

Because the marginal external cost equals $300, the Pigouvian tax is $300 per unit. This tax shifts the firms’ supply upward by $300 (they must remit $300 for every unit sold), changing the market equilibrium and splitting the tax burden between consumers (higher price paid) and producers (lower net price received).

Relevant concepts:
- Market equilibrium: set inverse demand equal to inverse supply.
- Pigouvian tax: a per-unit tax equal to the marginal external cost, implemented to internalize the externality by shifting supply upward by the tax amount.
- Tax incidence: the division of the tax burden depends on the relative responsiveness (steepness) of supply and demand.

Step-by-step algebra and intermediate calculations:
1. Pre-tax equilibrium:
   Inverse demand: P = 900 − Q
   Inverse supply: P = 2Q
   Set equal: 900 − Q = 2Q → 900 = 3Q → Q0 = 300
   Price: P0 = 900 − 300 = $600

2. With a $300 Pigouvian tax, supply shifts up by 300:
   New inverse supply faced by consumers: P = 2Q + 300
   New equilibrium: 900 − Q = 2Q + 300 → 900 − 300 = 3Q → 600 = 3Q → Q1 = 200

3. Prices after tax:
   Price paid by consumers Pc = 900 − Q1 = 900 − 200 = $700
   Price received by producers Pp = Pc − tax = 700 − 300 = $400

4. Changes (tax incidence):
   Consumers: Pc − P0 = 700 − 600 = +$100 (consumers pay $100 more)
   Producers: P0 − Pp = 600 − 400 = $200 (producers receive $200 less)
   Total tax per unit = $300 = $100 (consumer) + $200 (producer)

Why the correct answer is correct:
Producers bear more of the tax ($200 vs $100 for consumers). Algebraic equilibrium calculations show consumers’ price rises by only $100 while producers’ net price falls by $200. Intuitively, the supply curve here is steeper (less responsive) than demand, so producers cannot avoid much of the tax and therefore absorb the larger share.

Why other answers would be wrong:
- Saying consumers bear most is incorrect because calculations show consumers pay only $100 of the $300 tax.
- Saying incidence is equal is wrong because the price changes are not symmetric ($100 vs $200).

Conclusion: The producers bear more of the $300 Pigouvian tax (producers $200, consumers $100), matching the provided answer.

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