The Diamond model
19. There are 6 widget factories clustered into an industrial zone upwind of a city. Each
factory emits 1 unit of particulate matter into the air for each widget it produces.
These emissions travel to the city and cause harm to two groups of city residents.
The first are school children, who receive $2 worth of damages for each unit of
pollution. The second group are nursing home residents, who receive $5 worth of
damages for each unit of pollution.
True or False: The Diamond model indicates that if the government can place a
uniform tax on each factory per unit of emissions, the resulting allocation will not be
fully efficient (it will only be “second best”) because the damages are heterogeneous.
Explain briefly. (1 point)
We introduced the Diamond model as a case where the Pigouvian prescription needs
to be amended. This problem walks you through a closely related problem. In class,
we motivated the model thinking about heterogeneous consumers, but here I ask
you to think about two different firms.
Two local mines, named Asscher and Oval, extract identical diamonds. Suppose
that the mines are small operations and are therefore price takers in the global
diamond market, where the price per unit is currently $50. The Asscher mine
is located in a low population part of Napa County where the mine creates an
externality by using up fresh water supplies. The private cost of Asscher extraction
is equal to MCA = QA, while the social damages from water use are equal to
MEDA = 1. The Oval mine is located in Richmond, and the mine leaches chemicals
into the Bay that cause significant problems. The private cost of Oval extraction
is MCO = 4QO and the social damages from the chemical leakage is MEDO = 2.

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