FE431: PUBLIC FINANCE
Fall 2012
Professor Schmitt
Homework 4 – due October 23rd
1. (50 points) The supply and demand for books are given by the following equations:
Demand: Q  2000  100 P
Supply: Q  400  100 P
a) Find the equilibrium price and quantity in this market.
2000 – 100P = -400 + 100P
2400 = 200P
P = 12
Plugging into Demand Q = 2000 – 100(12) = 800 (or into supply Q = –400 + 100(12))
b) If a $3 per unit tax is imposed in this market, then what will the consumer’s price be?
(Recall: While you can add the tax to supply or demand, you will have to find the
inverse demand.) What will the producer’s price be? How many books will be sold
in this market with the $3 tax in place?
Adding to Supply – we first need to have the supply as a function of Q (not Price)
100P = Q + 400  P = (1/100)*Q + 4
Adding tax
P = (1/100)*Q + 4 + 3 = 7 + (1/100)*Q
Setting S = D (both need to be in terms of P or Q)
-700 + 100P = 2000 – 100P
200P = 2700
P = 13.5
Plugging into D:
Q = 2000 – 100(13.5)
Q = 650
c) What are the price the producer receives and the price the consumer pays? Under this
per unit tax who pays a larger share of the tax – the producer or the consumer? Why?
Find the consumer and producer price first PC = 13.5
PP = PC – t = 10.5
Both share burden as the $3 tax increased price consumers pay by $1.5 and decreased price
producers receive by $1.5
d) What is the efficiency-loss ratio of this tax?
DWL = ½ T*Q = ½ $3 * 150 = 225
DWL/Revenue = 225/1950 = 0.115
e) Graph. Be sure to show the excess burden, total tax revenue, quantity with the tax,
producer price and consumer price.
MC + tax =4 + (1/100)Q + 3 = 7 + (1/100)Q
P
MC = 4 + (1/100)Q
13.5 = PC A
B
E
10.5 = PP C
D
MB=20 – (1/100)Q
650 800
ABCD is tax revenue = 1950 ($3 * 650)
BED is excess burden = 225
2. (50 points) What if instead an ad valorem (sales) tax was used, in which the tax
percentage was 25% of the price. What will the consumer price be? What will the
producer price be? How many books will be sold in this market?
Now need to change the tax to be (1 + 25%)*P
Adding the tax to supply, again we need to find the inverse demand
P = (1/100)*Q + 4, so P with ad valorem is:
PT = 1.25*[(1/100)Q + 4] = 1.25Q/100 + 5 = P
Solving for Q = (100P – 500)/1.25
QS = 80P – 400
Setting S = D (both need to be in terms of P or Q)
80P – 400 = 2000 – 100P
180P = 2400
PC = 2400/180 = 13.33
Q = 2000 – 100*13.33 = 666.67
At Q, what is PP = (1/100)*666.67 + 4 = 10.67
a) How much tax revenue is generated? Who pays a larger share of the tax?
T = $2.66
So total tax revenue (T*Q) is $2.66*666.67 = $1773
Here consumers pay (13.33 – 12) = 1.33 and producers pay (12 – 10.67) = 1.33, so again they
share the burden.
b) What is the efficiency-loss ratio of this tax?
DWL = ½ T Q
DWL = ½ 2.66(133.33) = 177.3
DWL/Revenue = 177.3/1773 = 0.1
c) Graph. Be sure to show the excess burden, total tax revenue, quantity with the tax,
producer price and consumer price.
P
S + tax
D
Pc = 13.33
S
Pe = 12
Pp = 10.67
666.67 800
Q
d) Which tax would you recommend? Why?
The ad valorem tax raises more revenue and has a lower DWL (lower efficiency-loss ratio),
therefore I would recommend this tax.