Harold smokes cigarettes but his office mate Kumar hates smoking. Harold and Kumar have the following utility functions: UH = 100 + 10z – 0.1z2 UK = 100 – 10z, where z is the number of cigarettes smoked by Harold (and UH includes the cost of cigarettes). Determine: a. The number of cigarettes smoked by Harold when the external effect on Kumar is ignored; b. The socially optimal number of cigarettes smoked. To find the socially optimal number of cigarettes smoked, we create a social welfare function (SWF). The SWF is defined as the sum of Harold’s utility and Kumar’s utility. Using this approach, find the socially optimal level of cigarettes that should be smoked by Harold; c. The Pigouvian tax needed to reach this social optimum;
Harold smokes cigarettes but his office mate Kumar hates smoking. Harold and Kumar have
the following utility functions:
UH = 100 + 10z – 0.1z2
UK = 100 – 10z,
where z is the number of cigarettes smoked by Harold (and UH includes the cost of cigarettes).
Determine:
a. The number of cigarettes smoked by Harold when the external effect on Kumar is ignored;
b. The socially optimal number of cigarettes smoked. To find the socially optimal number
of cigarettes smoked, we create a social welfare function (SWF). The SWF is defined
as the sum of Harold’s utility and Kumar’s utility. Using this approach, find the socially
optimal level of cigarettes that should be smoked by Harold;
c. The Pigouvian tax needed to reach this social optimum;
d. The outcome with Coasian bargaining when the property right is assigned Harold;
e. The outcome with Coasian bargaining when the property right is assigned to Kumar.
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