2009ps4 - answer key - BUAD 351 Economic Analysis for...

BUAD 351 - Economic Analysis for Business Decisions
Homework 4
PART (i): multiple choice
question 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
answer d c d b b a b b c a d b b c d
PART (ii): Longer questions
1. Suppose the demand for cars is given by Q
d
= 12 ° P; and the supply of cars is given by
Q
s
= 4 P ° 3 :
(i) Find the equilibrium of this market and calculate the consumer and producer surpluses associated
with this equilibrium
In equilibrium, demand equals supply so
12 ° P = 4 P ° 3 ! P = 3 and Q = 9 :
To calculate the consumer and producer surpluses, we have
CS =
1
2
( P
max
° P ) Q =
1
2
(12 ° 3) 9 = 40 : 5
PS =
1
2
°
P ° P min
±
Q =
1
2
°
3 °
3
4
±
9 = 10 : 125
(ii) Suppose that the government imposes a tax T = 5 that has to be paid by the buyers when
buying a car. What is the new equilibrium quantity traded, together with the price paid by the
buyers ( P
B
) and the price received by the sellers ( P
S
) ?
12 °
°
P S + 5
±
= 4 P S ° 3 ! P S = 2 and P B = 7 ; with Q ° = 5
(iii) Under the tax, what are the new consumer and producer surpluses, tax revenue and the dead-
weight loss associated with the tax?
CS =
1
2
(12 ° 7) 5 = 12 : 5
PS =
1
2
(2 °
3
4
)5 = 3 : 125
Tax Revenue = 5 ± 5 = 25
deadweight loss = 40 : 5 + 10 : 125 ° 12 : 5 ° 3 : 125 ° 25 = 10
Thus, by raising $25 in tax revenue, the government destroys $10 of surplus
(iv) How much of the tax is paid by the consumers and the producers, respectively. How would
your answer change if the tax would have been imposed on the sellers instead?