Unformatted text preview: Solutions to Excercise in CH2 Slides
Bin Xie
2/1/2015
Question on Chapter 2  Page 18 : What if the tax is collected from consumers? (Hint:
consumers have to pay p + τ when the market price is still p.
Solution: After the tax is implemented, consumers eectively experience a higher price p+τ
than the market price p because the tax is collected from consumers. Therefore, the demand
function becomes D = D(p + τ ) and the supply function remains S = S(p).Meanwhile, the market
equilibrium price becomes an implicit function of τ , as we discussed in the lecture. It nally yields
the equilibrium condition D(p(τ ) + τ ) = S(p(τ )).
dD
dS
Next, do the derivatives of both sides with respect to τ :
= dτ
dτ
dD(p(τ ) + τ )
dD d(p(τ ) + τ )
dD dp
=
=
(
+ 1)
dτ
dp
dτ
dp dτ
dS
dS dp
Right hand side:
=
.
dτ
dp dτ
dD
dD dp
dS dp
dp
dp
dp
So
(
+ 1) =
. Rearrange the terms:
=
<0
. Be cautious here
dS
dD
dp dτ
dp dτ
dτ
dr
−
dp
dp Left hand side: because when there is a tax on consumers, the demand curve will shift to the left driving the market
equilibrium price DOWN.
dp
This
seems to be not identical to the result we derive from the case where the tax is collected
dτ
from suppliers (call it case 1). However, remember what we want to nd out is the tax incidence on
consumers and suppliers. In this case, the tax incidence of consumers is the tax τ plus the change
of the price (which is negative), instead of the pure change of price in case 1. So consumers' tax dD
dS
dp
dp
dp
incidence is τ + τ = (1 +
)τ =
τ (THIS is identical to the result on the
dS
dD
dS
dD
dτ
−
−
dp
dp
dp
dp
dD
−
dp
dp
slides.) The tax incidence on suppliers is the (absolute) change of the price − τ =
τ
dS
dD
dr
−
dp
dp
dp
(because
is negative!!!). Till now, you can see that the solutions of tax incidences are exactly
dr the same as case 1.
From the solution, the conclusion is clear: the tax incidences are irrelevant to whether the tax
1 is collected from consumers or suppliers and they only depend on the elasticities of demand and
supply. 2...
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 Fall '10
 Raven
 Supply And Demand, DP, Bin Xie

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