Q7. (a) Show that neither the unanimity relationship nor the strict Pareto ordering is necessarily negatively transitive, even if individual preferences are negatively transitive.

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Q7.
(a) Show that neither the unanimity relationship nor the strict Pareto ordering is
necessarily negatively transitive, even if individual preferences are negatively
transitive.
(b) Two textile mills located across a river from each other are polluting the
river. The marginal costs for pollution reduction for each firm are
MCE₁ 4E₁+ 4 and MCE₂ 4/3 E₂ + 4/3,
Where E is the reduction in pollution from unregulated levels. The
associated marginal social benefit is estimated to be MSB 10-E, where
El+ E2= E.
(1) What is the socially optimal level of water pollution reduction?
What level of per-unit pollution tax, r, will achieve this optimal
level of pollution reduction?
Transcribed Image Text:Q7. (a) Show that neither the unanimity relationship nor the strict Pareto ordering is necessarily negatively transitive, even if individual preferences are negatively transitive. (b) Two textile mills located across a river from each other are polluting the river. The marginal costs for pollution reduction for each firm are MCE₁ 4E₁+ 4 and MCE₂ 4/3 E₂ + 4/3, Where E is the reduction in pollution from unregulated levels. The associated marginal social benefit is estimated to be MSB 10-E, where El+ E2= E. (1) What is the socially optimal level of water pollution reduction? What level of per-unit pollution tax, r, will achieve this optimal level of pollution reduction?
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