Question

Some residents of Smoketown (population 100) like to smoke, but all of them dislike the bad smell generated by others peoples’ cigarettes. Each pack of cigarettes purchased by a resident causes 2 cents worth of damage to each of the 100 residents. Ten residents are willing to pay a up to $20 for their first pack of cigarettes a day, and $10 for their second, and twenty residents are willing to pay a up to $15 for their first pack of cigarettes a day, and $5 for their second. The rest of the population dislike smoking. The supply of cigarettes is perfectly elastic at a price of $9 per pack. If we impose a tax on cigarettes equal to the external cost of smoking them, what would be the total tax collected?

Can you draw a graph for this?

a. $0

b. $2

c. $10

d. $60

e. $80

Answer 1

Consider the given problem here a pack of cigarette create a damage of “2 cent” to each of “100 residents”, => the “marginal damage by all the resident” is “$2” per pack. Now, there are two types of people the 1^st type willing to pay “$20” for the 1^st pack and “$10” for the 2^nd pack. So, the initial supply curve is “P=9”, => the type 1 people will choose to consume 2 packets of cigarette. Now, after the tax of “$2” the new supply curve is “P=11”, => type 1 people reduce their consumption to “1 packet”, => total tax paid is “2”. Now, there are 10 such residents, => total tax revenue is “$2*10=$20”.

Now, the 2^nd type willing to pay “$15” for the 1^st pack and “$5” for the 2^nd pack. So, the initial supply curve is “P=9”, => the type 2 people will choose to consume 1 packets of cigarette. Now, after the tax of “$2” the new supply curve is “P=11”, => type 2 people still continue to consume “1 packet”, => total tax paid is “2”. Now, there are 20 such residents, => total tax revenue is “$2*20=$40”.

So, here the total tax is given by, “$20 + $40 =$60”.So, here the correct answer is “D”.