F\f-
+
ff; x* Jy: JJvx_x
_9
f'
l\..t-
X
m** x= o
a
\ ]L,
(w -rt **
fe Jli J\;-
L'5
4,
V "/'i
v
g* o, rtL
t $ fJli -- x \ JVx {,x'
{?
{x V(Jqx * x) 2x= W
4xL Vn
x {vx -x A**Vxc0
=
SUMMER TER,M 2013
'X[+r-v l '
o
ECON2001: MICROECONOMICS
TIME ALLOWANCE: 3 hours
Answer ALL questi'ons from Part, A on the Multiple Choi,ce Questi,on sheet. Answer THREE questions
frorru Part B, including at least ONE from Part B.I and at teast ONE from Part B.II.
A carries
Prt'rt l0 per cent of the total mark and quest'ions in Pa,rt B carry 20 per cent of the total
rnark each.
In cases where a shtdent answers more questi,ons than requested by the eram,ination rabric, the poli,cy
of the Econom'ics Department is that the student's first set of answers up to the required. number will
be the ones that count (not the best answers). All remaini,ng &nswers wi.tl be,iqnored.
PART A
Answer ALL questions fron this section on the lVlultiple Choice Question sheet. For each question
there are four possible answers tabelled (u), (b), (c) and (d). Indicate which you think is correct by
placing a horizontal mark in the corresponding box on the answer sheet. To get full marks for this
section it is not necessary to provide any explanation for your answers.
(I)Firmlchoosesanadvertisingbudgetr)0andFirm2choosesanadvertisingbudgety>0.
The rnarket is worth V and the share of the market captured by each firrn is determinecl by their
advertising. Hence, Firm t has profits nr(*,y) and Firm 2 has the profits rz(r,y) where
rr\r,y):;,y r-Y-*, nz@,y):-!-v-u. - \
x+!/ t J t-!,',
!
A.1 Firm 1's reaction function is? L t) ( (
afr I
/-,v: t/v"-"
(.) Ax ({ ty )2 l
L(l}":t/vY-Y
(") v:JV-" = ,,
''
[,ttl I-
L G.ty 1,
,".1
(d)
": t/iry-y
A.2 This market has
I
@h," in V-
Nash equilibrium that is increasing
One Nash equilibriuur that is decreasing in V
(r t 7 ,v
Nash equilibria. 1
(d) No pure-strategy Nash equilibrium.
Jfx,Jq
U
trcoN2001
t@fr
W
JG
1
(xny)u-- \1$
TURN OVER :
lm*\
[4;': \l-L
s
t"\
,r "uJ ry rr
cl
Y m
, A.3 Suppose we now allow the firms to set / : 0 or y : 0 or both. (\Are assume that the firms
spiit the market 50:50 if no flrm advertises at all.) This market now has
(a) One Nash equilibrium that is increasing in L/.
One |'Iash equilibrium that is decreasing in V
Many Nash equilibria.
(d) No pure-strategy Nash equilibrium.
S{2. EV-{W Couat-* ff
1 fi*',r*t"'<s &t
(II) q: zf zl, where n > 0.(The input prices are w1,w2.)
There is a firm with a production function
Supposetbatz2isfixedintheshortrun. ,r1.,r t inr,.. A /;'i..
r_ AI
'***
I ,,.,.{
A.4 This firm has c:ost that of if
(a) a:2.
(b) a>2. 4ilr= Q *'et
(c) a:1. w, * y\ a Af
( a-712 rdrZp : 7A Z
C wr7' {wr?.u ts1
A.5 This firm's short-run average cost functi.on is
(")
7 Yr9
,19
"' lk
,* (T)= (H)'
(b)
L
q'l22
Lg
g 1
&
tt!
(") l--c(. (7-
Lr l":
w2z2 I wTQu Z2 - -.i
,
(d ) '/ i
'*.
..4'
" " +wtq;zi'
llbz, 1 a
i/-'!
q-
ge'€
(!l
ECON2001 2 CO TTINUED
I
,L € = (1" z7-2i\2, 'Wu r;:f
?r-w* c )c, + lilr 7
k\ba =
= )d Zf zf I zl
Ct
j
t:hor+W -) cx s..!
a(
, i)
\'0t (,oL l'o3
i. 0, @ s5) U, o1(t ,o\ ir
fr {.02 (o, 1) {!, L )(2, o )
t'gI i
{0, L) {o,.? )(' t, , *)
(III) Two firms, zl and B, are involved in Bertrand competition. There are 100 customers each willing
to pay up to f2 fbr one unit of output. The firms both have marginal costs of Xl. (You mav
assume the firrrrs share the customers equally if they set the sarne price.)
-4.6 If the firms can only adjust prices in_g-nl!s of one.pelny. then this market has the equilibrium
.P':"' '-i[ = (?^ * 1) tou i$ i'* ( F
(a) Xl only *
(b,) Either s1 or 11.01 = t?^ - t ) E0 ;e Y* Fs
@9rrO., f1 or f1.01 or f1.02
ffAitn", fl or 11.01 or f1.02 or f1.0J
ow suppos€r that the firnx r:arn adiust prices by arbitr:rrilv srnall arnounts. but the firrns
in order. firrn A sets its price then firm B set its price. Which of the following statements
is true.
a) This garne has orrl-v one Nash equilibrium.
This game ha*s rnanv subgame perfect equilibria.
c) Firm B can fbrce firm ;1 to set a high initial price at sorne Nash equilibria.
(d) There is no Nash equilibrium because firm B's optimal response is not defined
(IV) A firnr is sclling insurance to custourers with probability zr of experiencing a loss, where a- is
distributed uniformly on the interval 0 ( n' ( 1. If a customer experiences a loss, then they have
a weaith 15 whereas if a customer does not experience a loss they have wealth I10. Let p be
the price of insurance.
A.B Which of the foliowing is true if the customers are risk neutral
(a) If the price of insurance is flJ onc lifth of the customcrs buy insularrcc.
the price of insurance is f5 everyone buys insurance.
the price of insurance is "e2.50 haif the customers buy insurance.
80% of the customers buv insurance if the price is f4.
ECON2001 a- .,rr , TURN O\IER
CoIr i r
{UY}ul{ E
7"5.fi laJs = 6"ff
ffiflU-. : rD rr^.1 'J NIL -:- t'O(r- f")
ft$ \tr' /
+
ff; x* Jy: JJvx_x
_9
f'
l\..t-
X
m** x= o
a
\ ]L,
(w -rt **
fe Jli J\;-
L'5
4,
V "/'i
v
g* o, rtL
t $ fJli -- x \ JVx {,x'
{?
{x V(Jqx * x) 2x= W
4xL Vn
x {vx -x A**Vxc0
=
SUMMER TER,M 2013
'X[+r-v l '
o
ECON2001: MICROECONOMICS
TIME ALLOWANCE: 3 hours
Answer ALL questi'ons from Part, A on the Multiple Choi,ce Questi,on sheet. Answer THREE questions
frorru Part B, including at least ONE from Part B.I and at teast ONE from Part B.II.
A carries
Prt'rt l0 per cent of the total mark and quest'ions in Pa,rt B carry 20 per cent of the total
rnark each.
In cases where a shtdent answers more questi,ons than requested by the eram,ination rabric, the poli,cy
of the Econom'ics Department is that the student's first set of answers up to the required. number will
be the ones that count (not the best answers). All remaini,ng &nswers wi.tl be,iqnored.
PART A
Answer ALL questions fron this section on the lVlultiple Choice Question sheet. For each question
there are four possible answers tabelled (u), (b), (c) and (d). Indicate which you think is correct by
placing a horizontal mark in the corresponding box on the answer sheet. To get full marks for this
section it is not necessary to provide any explanation for your answers.
(I)Firmlchoosesanadvertisingbudgetr)0andFirm2choosesanadvertisingbudgety>0.
The rnarket is worth V and the share of the market captured by each firrn is determinecl by their
advertising. Hence, Firm t has profits nr(*,y) and Firm 2 has the profits rz(r,y) where
rr\r,y):;,y r-Y-*, nz@,y):-!-v-u. - \
x+!/ t J t-!,',
!
A.1 Firm 1's reaction function is? L t) ( (
afr I
/-,v: t/v"-"
(.) Ax ({ ty )2 l
L(l}":t/vY-Y
(") v:JV-" = ,,
''
[,ttl I-
L G.ty 1,
,".1
(d)
": t/iry-y
A.2 This market has
I
@h," in V-
Nash equilibrium that is increasing
One Nash equilibriuur that is decreasing in V
(r t 7 ,v
Nash equilibria. 1
(d) No pure-strategy Nash equilibrium.
Jfx,Jq
U
trcoN2001
t@fr
W
JG
1
(xny)u-- \1$
TURN OVER :
lm*\
[4;': \l-L
s
t"\
,r "uJ ry rr
cl
Y m
, A.3 Suppose we now allow the firms to set / : 0 or y : 0 or both. (\Are assume that the firms
spiit the market 50:50 if no flrm advertises at all.) This market now has
(a) One Nash equilibrium that is increasing in L/.
One |'Iash equilibrium that is decreasing in V
Many Nash equilibria.
(d) No pure-strategy Nash equilibrium.
S{2. EV-{W Couat-* ff
1 fi*',r*t"'<s &t
(II) q: zf zl, where n > 0.(The input prices are w1,w2.)
There is a firm with a production function
Supposetbatz2isfixedintheshortrun. ,r1.,r t inr,.. A /;'i..
r_ AI
'***
I ,,.,.{
A.4 This firm has c:ost that of if
(a) a:2.
(b) a>2. 4ilr= Q *'et
(c) a:1. w, * y\ a Af
( a-712 rdrZp : 7A Z
C wr7' {wr?.u ts1
A.5 This firm's short-run average cost functi.on is
(")
7 Yr9
,19
"' lk
,* (T)= (H)'
(b)
L
q'l22
Lg
g 1
&
tt!
(") l--c(. (7-
Lr l":
w2z2 I wTQu Z2 - -.i
,
(d ) '/ i
'*.
..4'
" " +wtq;zi'
llbz, 1 a
i/-'!
q-
ge'€
(!l
ECON2001 2 CO TTINUED
I
,L € = (1" z7-2i\2, 'Wu r;:f
?r-w* c )c, + lilr 7
k\ba =
= )d Zf zf I zl
Ct
j
t:hor+W -) cx s..!
a(
, i)
\'0t (,oL l'o3
i. 0, @ s5) U, o1(t ,o\ ir
fr {.02 (o, 1) {!, L )(2, o )
t'gI i
{0, L) {o,.? )(' t, , *)
(III) Two firms, zl and B, are involved in Bertrand competition. There are 100 customers each willing
to pay up to f2 fbr one unit of output. The firms both have marginal costs of Xl. (You mav
assume the firrrrs share the customers equally if they set the sarne price.)
-4.6 If the firms can only adjust prices in_g-nl!s of one.pelny. then this market has the equilibrium
.P':"' '-i[ = (?^ * 1) tou i$ i'* ( F
(a) Xl only *
(b,) Either s1 or 11.01 = t?^ - t ) E0 ;e Y* Fs
@9rrO., f1 or f1.01 or f1.02
ffAitn", fl or 11.01 or f1.02 or f1.0J
ow suppos€r that the firnx r:arn adiust prices by arbitr:rrilv srnall arnounts. but the firrns
in order. firrn A sets its price then firm B set its price. Which of the following statements
is true.
a) This garne has orrl-v one Nash equilibrium.
This game ha*s rnanv subgame perfect equilibria.
c) Firm B can fbrce firm ;1 to set a high initial price at sorne Nash equilibria.
(d) There is no Nash equilibrium because firm B's optimal response is not defined
(IV) A firnr is sclling insurance to custourers with probability zr of experiencing a loss, where a- is
distributed uniformly on the interval 0 ( n' ( 1. If a customer experiences a loss, then they have
a weaith 15 whereas if a customer does not experience a loss they have wealth I10. Let p be
the price of insurance.
A.B Which of the foliowing is true if the customers are risk neutral
(a) If the price of insurance is flJ onc lifth of the customcrs buy insularrcc.
the price of insurance is f5 everyone buys insurance.
the price of insurance is "e2.50 haif the customers buy insurance.
80% of the customers buv insurance if the price is f4.
ECON2001 a- .,rr , TURN O\IER
CoIr i r
{UY}ul{ E
7"5.fi laJs = 6"ff
ffiflU-. : rD rr^.1 'J NIL -:- t'O(r- f")
ft$ \tr' /
