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Principles of Microeconomics – Econ1014
Tax and Subsidy Study Sheet - Ryan
1. Taxing Cigarette Buyers
Governments place taxes on both consumers and producers in order to raise tax revenue
to be used to run the government and to finance programs, such as national defense,
transportation systems, poverty reduction, education, and so on. These taxes distort the
market price signal and lead to a reduction in consumption and production. This
reduction in market activity, in the absence of market failure, causes resource
misallocation and Deadweight Loss. Sometimes, governments place taxes on markets to
intentionally reduce market activity because the government feels the good or service
being consumed is ethically or morally bad for people and it doesn’t trust people to make
their own choices. In this case, we call the tax a sin tax. In November, Missourians will
be asked to vote to increase the tax on cigarette purchases from 17¢ to 97¢, a 470%
increase. The proponents of the new higher tax argue that the tax is necessary both to
discourage smoking (they realize that people respond negatively to price changes) and to
raise more government tax revenue. Suppose the following graph represents the adult
cigarette market.
P
5.5
S
5
4.5
4
Pb=3.9
3.5
Pe=3.4
Ps=new
Pe=3.1 3
80¢ tax
2.5
2
RM
0
1
2
3
4
5
6
7
New Qe=6.3 Qe=7
8
D
New D
9
10
11 Q
in thousands
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a. Show how the market changes when the government places this new 80¢ tax on
cigarettes buyers. Suppose the equilibrium price of cigarettes is currently $3.40
and 7 thousand packs of cigarettes are being purchased. Show and estimate the
new price paid by buyers (buyer’s price) and the new amount actually received by
sellers (seller’s price). Show and estimate as well the new equilibrium price and
quantity.
The demand curve shifts down by the amount of the new tax because this lowers
your willingness-to-pay to the seller by the tax if you have to pay this to the
government. This is a demand shift to the left or a decrease in the demand for
cigarettes. Show the students how to shift it down by the amount of the new tax.
The new equilibrium price will not decrease by 80 cents since sellers are
responsive to price changes and won’t sell as much at this lower price, this means
the price will need to be renegotiated. Since sellers are so responsive and buyers
are not, it looks like the price does not get negotiated down much. The new
equilibrium price seems to be about $3.1 (30 cents lower). It looks like sales and
purchases fall to about 6300 (700 fewer)
b. Who is actually bearing the burden of this tax? Explain why the tax burden is
being shared in this way.
The burden is being shared by buyers and sellers. Sellers have to accept a 30 cent
price decrease (so they are paying 30/80=37.5% of the tax) and buyers end up
paying out of pocket 50 cents more than before (so they are paying 50/80=62.5%
of the tax). Buyers pay more simply because they are less responsive to price
changes and find it harder to change their cigarette purchase decisions to “get
away from the tax.” This means sellers don’t have to lower their prices very much
to keep sales relatively high.
Give them the Tax Sharing Rule: Whoever is least responsive to price changes
pays more of the tax share.
c. Suppose the price elasticity of demand among adult smokers is -0.5. If the
equilibrium price of cigarettes did not change (just the tax added to the cost to
buyers), what would be the new level of quantity demanded?
Qnew − Qold
%ΔQd
Qold
Εd =
=
Pnew − Pold
%ΔP
Pold
− 0.5 x0.235 x7 = Q − 7
Qnew − 7
− 0.5 =
4.2 − 3.4
6.1775 = Q
7
3.4
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Quantity demanded would fall to 6178 cigarettes. This is a bigger fall than we
actually observed graphically, because the equilibrium price was renegotiated
down so that the actual cost to buyers did not increase as much as the new tax.
d. Can you give any prediction at all about the size of the price elasticity of supply?
How did you arrive at your prediction?
It must be bigger than 0.5 because we can clearly see that buyers paid more of the
tax so they must be less responsive to price changes than sellers.
e. Do you think this tax will have more or less impact on teenage smokers? Why?
We would expect a bigger impact on teenagers since they are usually more
responsive to price changes than adult smokers. This is probably due to their
lower income (so cigarette price changes seem more significant to them) and
because they are less addicted (so it is easier to stop). They might also have less
stress and more substitutes for stress release if they have more free time and fewer
work and family responsibilities.
f. What is the privately optimum level of smoking?
This is the negotiated equilibrium quantity of 7000. This is best for me personally
because according to my demand curve, I believe each of those first 7000
cigarettes is worth more than the price of 3.40, so I am better off by buying them.
This gives me the maximum consumer surplus I can earn. This is also the best for
sellers, because according to the supply curve, each of these first 7000 cigarettes
costs less than 3.40 to offer for sale, so I am better off by selling them and earn
the maximum producer surplus I can.
g. If this market is not in market failure (before the tax increase), what is the socially
optimum level of smoking?
If the market is not in market failure, then what is best for private individuals is
also best for society. If my consumption or production decision doesn’t hurt you,
then by doing what is best for me, I am doing what is best for society.
h. If this market is not in market failure (before the tax increase), what is the amount
of resource misallocation induced by the tax? Show this on your graph.
In this case, since the tax discourages market activity and sales and purchases fall
to 6300, we have 700 cigarettes too few being produced and consumed and
resource misallocation of 700 cigarettes too few.
i. What is the economic cost of the tax? Show this on your graph.
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The economic cost comes about because of the loss of consumer and producer
surplus from those lost 700 cigarettes. This is measured as Deadweight Loss
(DWL) and is the area of the triangle between the original demand and original
supply curves above the RM.
⎛1⎞
⎛1⎞
DWL = ⎜ ⎟(tax)( RM ) = ⎜ ⎟(0.80)(700) = $280
⎝2⎠
⎝2⎠
2. Taxing Cigarette Sellers
Suppose the same situation exists as in the graph in the above question, but the
government decides to place the tax on cigarette sellers instead of cigarette buyers.
P
5.5
New S
S
5
4.5
4
Pb=new
Pe=3.9
3.5
Pe=3.4
Ps=3.1
3
80¢ tax
2.5
2
RM
0
1
2
3
4
5
6
7
New Qe=6.3 Qe=7
D
8
9
10
11 Q
in thousands
a. Show how the market changes when the government places this new 80¢ tax on
cigarettes sellers. Suppose the equilibrium price of cigarettes is currently $3.40
and 7 thousand packs of cigarettes are being purchased. Show and estimate the
new price paid by buyers (buyer’s price) and the new amount actually received by
sellers (seller’s price). Show and estimate as well the new equilibrium price and
quantity.
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The only change will be that the supply curve shifts up by the amount of the tax on
sellers since their MC of selling cigarettes has now increased. This is a shift of the
supply left or a decrease in supply.
Also the new equilibrium price is now the buyers price instead of the sellers price.
b. Who is actually bearing the burden of this tax? Explain why the tax burden is
being shared in this way.
Same as before. Sharing does not depend on who the tax is officially placed on
but on the relative responsiveness to price changes.
c. If this market is not in market failure (before the tax increase), what is the amount
of resource misallocation induced by the tax? Show this on your graph.
Same as before.
d. What is the economic cost of the tax? Show this on your graph.
Same as before.
e. How do your results compare to the results of the tax placed on the buyers? Are
there any differences? Does it matter who the tax is placed on? Can the
government really determine who pays the burden of a tax?
See above for answers to this.
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3. Encouraging the Use of Vaccinations
a. Suppose the U.S. government wants to encourage as many people as possible to get
immunized against influenza. Show that it doesn’t matter whether they do this by offering
a $100 per vaccination subsidy to vaccine producers, a $100 per vaccination subsidy to
vaccine consumers or a combination of subsidies of $50 to vaccine producers and $50 to
vaccine consumers. Using three separate graphs, show that the subsidy will be shared
between the two groups the same way in all three cases.
P
S
Ps= new Pe=$560
$100
Pe=$500
Pb=$460
D (subsidy offered)
D (no subsidy offered)
Qe
new Qe
Q
$100 Subsidy Offered to Buyers
Subsidy of $100 is shared by buyers and sellers with buyers getting $40 in the form of a
decrease in their out-of-pocket costs and with sellers getting $60 in the form of a $60
increase in the market equilibrium price as a result of this demand increase for vaccine.
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P
S (no subsidy)
S (subsidy offered)
Ps=$560
$100
Pe=$500
Pb= new Pe=$460
D
Qe
new Qe
Q
$100 Subsidy Offered to Sellers:
Subsidy of $100 is shared by buyers and sellers with buyers getting $40 in the form of a
decrease in the market equilibrium price of $40 and with sellers getting $60 in the form
of an increase in their take home earnings.
P
S
S (subsidy offered)
Ps=$560
new Pe=$510
Pe=$500
Pb=$460
D (subsidy offered)
D (no subsidy offered)
Qe
new Qe
Q
$50 Subsidy to Buyers and $50 Subsidy to Sellers:
Subsidy of $100 is shared by buyers and sellers with buyers getting $40 in the form of a
decrease in their out-of-pocket costs (they collect $50 from the government but have to
pay an extra $10 for the vaccine, so their net gain is $40) and with sellers getting $60
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(they collect $50 from the government and get an extra $10 from the increase in the
selling price).
See if you can explain how buyer’s price and seller’s price are found above on the graph.
b. Now explain what the sharing of this subsidy tells us about the responsive of these
vaccine buyers and sellers to price changes.
We can see that the seller in each case ended up with the bigger share of the subsidy ($60
versus $40), this must mean that buyers are more responsive to price changes than are
sellers at the equilibrium price.