Download Assignment 2

University of Hong Kong
1st semester 2009-10
ECON1001 Introduction to Economics I, Subclasses I
Assignment 2
Due time: 5:30pm, November 9 (Monday), 2009
Answer all questions. While you are encouraged to discuss with your classmates, you must write
up your own script. (The answer to each question should not exceed one page.) Please hand in
your script to your TA (Miss Titi Hung) on or before the deadline via her pageon box on the 9th
floor of K.K. Leung Building.
1. (5 marks)The market for CD's has supply and demand curves given by:
Demand: P = 20 - Q
Supply: P = 4 + 3Q
a. Calculate the equilibrium quantity and price of CD's.
At equilibrium, Q* = QD = QS ; P* = PD = PS
20 – QD = 4+3QS
Q* = 4
P* = 16
b. If price is $19, what is the quantity demanded? quantity supplied? Is there a surplus or
a shortage?
At price $19, QD is:
19 = 20 - QD
QD = 1
QS is:
19 = 4 + 3QS
QS = 5
This price is above the equilibrium price, $16, there is an excess supply (surplus) of 4
CD’s.
c. If price is $10, what is the quantity demanded? quantity supplied? Is there a surplus or
a shortage?
At price $10, QD is:
10 = 20 - QD
QD = 10
QS is:
10 = 4 + 3QS
QS = 2
This price is below the equilibrium price, $16, there is an excess demand (shortage) of 8
CD’s.
2. (6 marks) You have been hired by the government to audit a dead economist's
consulting
firm. He left his records incomplete so that only a student trained in economics could fill
the blanks.
Fixed cost is a sunk cost. It is independent of output.
Marginal cost is the change in TC/the change in quantity; or the change in VC/the change
in quantity.
Clients
Total
Fixed
Variable Average Average Average Marginal
cost
cost
cost
total cost variable fixed
cost
cost
cost
0
100
100
0
0
0
0
0
1
175
100
75
175
75
100
75
2
240
100
140
120
70
50
65
3
330
100
230
110
76.67
33.33
90
4
450
100
350
112.5
87.5
25
120
5
600
100
500
120
100
20
150
6
800
100
700
133.33
116.67
16.67
200
7
1100
100
1000
157.14
142.86
14.29
300
Does the consulting firm exhibit diminishing returns for any number of clients between 0
and 7?
Yes. MC is decreasing until Q = 2, then MC is increasing until Q = 7. This reflects the
fact that VC, or TC increases by a decreasing amount and then TC increases by an
increasing amount.
3. (4 marks) John wants to go into the donut business. For $500 per month he can rent a
bakery complete with all the equipment he needs to make a dozen different kinds of
donuts (K=1). He must pay unionized donut bakers a monthly salary of $400 each. He
projects that his output level Q equals 2KL (where Q is tons of donuts and L is the
number of bakers hired).
a. What is John's monthly total cost function, variable cost function, and marginal
cost?
TC(Q) = 500 + 400*L
TC(Q) = 500 + 400(Q/2K)
TC(Q) = 500 + 200Q
VC(Q) = 200Q
MC(Q) = 200
b. How many bakers will John hire to make 25 tons of donuts?
Q = 2KL
25= 2(1)(L)
L = 12.5
4. (5 marks) A monopolist can produce at constant average and marginal costs of AC =
MC = 6. It faces a market demand curve given by Q = 54 – P and MR = 54 – 2Q.
a) Calculate the profit-maximizing price-quantity combination. Also calculate the
monopolist's profits and consumer surplus.
MR = MC
54 – 2Q = 6
Q = 24, P = 30
Profit = TR – TC
Profit = (24*30) – (24*6)
Profit = 576
Consumer surplus = [(54 – 30)*24]/2 = 288
b) What output level would be produced by this industry under perfect competition
(where price = marginal cost)? Calculate the consumer surplus.
P = MC = 6
Q = 54 – P
Q = 48
Consumer surplus = [(54 – 6)*48]/2 = 1,152