EXAM
LUNDS UNJVERSITET
EkonornihOgskolan
I
NAME:
Course code: NEKG21
Course name:
Date: 2022-03-21
Time: 08:00-13:00
Examiner: Daniel Ekeblom
PERSONAL NUMBER:
Location: MA9
Department:
Allowed means of assistance: Ruler, calculator.
ID OK: lj;I
Other information:
Sign:
~
Please read the following instructions before you begin:
Mark the questions
you have answered
with an X
Check that you have got the right exam.
Question 1
1
You must not hand in the exam or leave the exam hall until one hour after the
start of the exam.
Question 2
I~.<;
.
Write clearly.
Question 3
Question 4
Grades: A= 85 %, B = 75 %, C = 65 %, D = 55 %, E = 50 %, U (Fail)< 50 %
Question 5
Points
l)'
1,
ii
Question 6
Question 7
Question 8
Question 9
Question 10
Question 11
Question 12
Home assignments
10
0 Blank
Total points
lt,~-
If you wish to leave a blank exam, only the cover page shall be handed in.
Tick the box and sign above. A blank exam gives you the grade Fail (U).
Grade
Receipt of exam
You sign a receipt for your exam when you collect it from the exam review or exam office.
I hereby certify that I have collected this exam
Date of receipt
Signature
"9
NEKG21
Daniel Ekeblom
2022-03-21
Instructions
There are 5 questions on the exam and the maximum number of points is 90. In addition,
the assignments can give a maximum of 10 points. A minimum of 50 points is required
for a passing grade (E).
- Read the questions carefully, and answer clearly and concisely. Do not scribble!
- Use the space assigned to each question.
- When drawing diagrams, be careful pointing out what the axes and the curves represent.
- Deductions will be made for unstructured answers, deficient in clarity of thought.
- Use additional sheets, if needed.
- Means of assistance: pencil, pen, ruler, eraser, calculator.
1
Question 1 (10p)
The Marshallian Demand can be expressed as
definitions for the following terms.
xi (p1, p2, m).
Provide the mathematical
x~ (f?) ,P~, w,)
a) Normal good (lp)
'P,
b) Ordinary good (1 p)
c) Inferior good (lp)
.
d) Substitute good (lp)
-- ·. < r,
x
I
e) Giffen good (lp)
) /' (f 1, fl t ~ )
f) Complement good (1 p)
.,....
'P2.
2
X,
)-/
g) preferences.
Write down and
.
( 4p) explain the properties that are required
for well behaved consumer
wdl ~euavevl. Ftdu-u1 c-e 5
tyo-MJl NV()
vvt,CWl
Co 11-1! 1-cJc rrekY-tNI ~ s
h~ lo~fP-r'~v(
.J-o
bu~Jl-eJ
Tr<M4SJ riv~
/b31ta(
+~
,.'°'(\
X >- -c-
T'-,M'
-t I,.,(
JAN~J.--
~O V
Av1
J
o I}l,4,uJ--
l u Sr
u-t,, tl
HA(,,#;~
u-r-
t -e- IA, 5 t;
1
~t,,lA,.f,L,V-(t,1
f re/C,,Y.(A/f tc'.J
e,j<IT(,v'I( J
lOt1
bw.vlk5
r
UJ#J
_,,{ {'!, ~ i ))
o: S
il
c o """(le,J-'-e.
'.ft/'t,itt
h-e+w?~
3
t,wt.vtJ
'1t ~
s n« f l•t
V"' &<M 1
~ ~-
C ovt vtX
&W"'f
1
S<J~wwr
-r(L- )
.,...,(M o frJ,'1
i-o
~
i'J- · _X >-
.su~« ya-~~ ~J
(Af'-(..
o
b(Jvitf/,es
x, JI 1.)
fr~r-cute J
J ''f«-,k ((~ tA
VVl or e,
0 or
((
,J-1A,ar
\,M.tA>M
( ()'II.$) JL,,/
~
( 0 Vl 1/t:,~ ~
tJ.II
f-utvJ-
j'Ytk:,H,.< w: ) ~
I~• · ~~
tvwt
r
a.vttA
~
<".._____..-:]
lo1,4o,tf'c.vt"l.,cl.!, k:,
5~J e
(
J
cue,ko ft.-t:Y
~J
TLl,1
~
;Vt. ovto+oYl ~· C
a. 5
CJ.-)Wdl.
ro.Ho-,.u.{ ( cov-1fleJ--e
0-N'e.
:rovl ,
Pj
fo
,t-,1,c,.~
vVe
~
ffo(}t/ls
{,Oll{UV"l-vV
Question 2 (20p)
Mephisto enjoys coffee (x1) with milk (x2) in accordance with the following utility function:
1/3 2/3)
u(x1, x2) = 3e ( x1 x2
(1)
He has an income of 20, and buys them at the following prices:
Questions to answer:
a) Calculate the Marshallian demands xi (p1, p2, m) and x2 (p1, p2, m). ( 4p)
Hint: ln( e) = 1.
b) Calculate the MRS at xi(2,4,20) and xH2,4,20). (2p)
c) Prices change to (p1, p;) = (2, 13°). What is the new optimal consumption? (2p)
d) What are the income and substitution effects on Mephisto's optimal consumption?
(4p)
e) Show the income and substitution effects in a graph. (4p)
f) What kind of goods are xi (p1, p2, m) and xHp1, p2, m) judging by their marginal
price effects? (2p)
g) Draw the Price Expansion path for xi (p1, p2, m) in a second graph for the following -;,
0 0
prices: (p1, p~, pn = (
,
). Assume p2 = 2 and m = 20. (2p)
i, \ t
4
Question 3 (20p)
Anna and Bill also enjoy coffee (x1) with milk (x2). However, Anna wants to have exactly
equal proportions of milk and coffee, if she is to enjoy her (Italian) cup of coffee. Meanwhile, Bill is perfectly happy substituting one unit of milk for one unit of coffee, or vice
versa, as he does not prefer the one to the other. They are considering barter and their
initial endowments are:
Y = (YA, YB)= {(yf = 8,yt = 1), (yf = 2,yf = 7)}
(2)
Questions to answer:
a) Choose Anna's and Bill's utility functions over coffee and milk. (4p)
Hint: Perfect substitutes and perfect complements ..
b) Draw a complete Edgeworth box, mark the initial endowment Y, show the set of
possible utility improving allocations, and show the Contract Curve. (6p)
Hint: Show the "tense" in the diagram.
c) What are the i) maximum and ii) minimum level of relative prices -;~ that are
consistent with a Walrasian equilibrium in trade between the two? (2p)
d) Bill offers to trade two milk for one coffee. Is the offer rational?
Motivate your answer. (2p)
e) Anna offers to trade two coffee for one milk. Is the offer rational?
Motivate your answer. (2p)
f) After trading back and forth for a while, Anna and Bill settle on the following allocation:
(3)
X = (XA,XB) = {(xf = 4,xf = 5), (xf = 6,xf = 3)}
Is the allocation X a Pareto improvement? Motivate your answer. (2p)
g) Is the allocation X Pareto efficient? Motivate your answer. (2p)
5
Question 4 (20p)
A power producer enjoys a monopoly on power production, using input factors natural
gas x1 and power turbines Xz. The production function is:
(4)
The input factor prices are (w1, w 2) = (2, 1). The market power demand can be modelled
using the aggregate Marshallian demand:
y(p) = 4-2p
(5)
Questions to answer:
a) Calculate the amount of power y* that the profit maximizing monopoly chooses in
the Jong term. (12p)
b) Calculate the profit tt: (2p)
c) Calculate the markup over marginal cost. (2p)
d) Is the monopolist producing according to profit maximizing theory? (2p)
. . _ ax(P) p
Hmt.
E - ~ X(P) .
e) What kind of returns to scale does the production technology exhibit? (2p)
6
Question 5 (20p)
A firm managing a radio station has a business model in which it profits from selling
advertisements. However, in order to attract listeners, it regularly broadcasts popular interviews with various celebrities. The firm has discovered that the better the interviews
are combined with advertisement segments, the higher the number of listeners and the
higher the revenues become from sales of advertisements.
The firm wants to optimize its pricing using a second degree price discriminating strategy. By using popular A-celebrities and lesser known B-celebrities, the firm wants to
capture as much consumer surplus as possible.
Question to answer:
a) Explain how the firm should optimize the pricing by the use of A celebrities (xA) for
high demand listeners and B celebrities (xB) for low demand listeners.
(Hint: Measure Willingness to Pay by the time that a listener spends tuned in to the radio
station. Use graphs to illustrate the reasoning.) (Sp)
Takeover situation
The pricing strategy of the radio station has made the firm F very profitable. A private
equity firm PE wants to acquire the target firm Fin a hostile takeover. The PE can choose
between making a high offer Hor a low offer L. The firm F can respond by accepting (A)
or rejecting (R) the offer. (Hint: Assume rational and fully informed players.)
- If F accepts the first high offer, the payoff will be 2 for F, and 1 for PE.
- If F rejects the first high offer, the payoff will be O for F, and -1 for PE.
- If F accepts the first low offer, the payoff will be 1 for F, and 3 for PE.
- If PE is making a low offer L, and F rejects, PE will make a second attempt.
- In the second attempt, all rejected offers incur a payoff of O for F, and -1 for PE.
- In the second attempt, an accepted high offer incur a payoff of 3 for F, and 1 for PE.
- In the second attempt, an accepted low offer incur an equal payoff of 2 for both
firms.
Question to answer:
b) Model the take over situation using sequential game theory. Draw the game in
extensive form, then i) identify all strategies, ii) identify all subgames, and finally
iii) identify subgame perfect equilibria. (12p)
7
,l(
J ?,--
TA
-=-
Zo - '- X,
t.o
J)
Mi5
»
ix,
-1:/x--i -z.
J-'j Xi.
XL ( 2,, :~
7,(.))-:
1
2•
J
b
-===
Z X-z +~X1. :: 6X1..
"
~,,;=
Xi ~ Ju/1,
-z -
ttV,
f'\Uz.,
c)u...
J') I
JlA.
c)~1,
;I
_,,
'Y-z' r3
j 'X Il/-1:,
I/-}
2._l:_ X1
.:J Xz •J~
)(, ,1J
'Iil./3
. JC
J-,
7
z.-
X-<.
. X J/J Z/3
• e·, t
X 1,
'3-
'I. I z l!,
. Je
2
~ 1/~
I
1
><1
== -
l3
')( 7.
.
2 )(.,
--
•J,
2. )( /
'X l. 1/3
X1 i/5 Xz l/3
e
X1
"'-
xz.( Z, 'vf>, 1.0)
-z
I. "2.
v,
f; \J
,-_ Y'
l'q
;:
2 )' I ..f
).. t -=-
M
1
= 2
'(. -i, ::
Al~w
)/ .:: llf
lo .
+ .!.!d.. Xi.. :::
~I
)1 ~
'1
10/3
-
3
J
tov
-f-
1
/0
J
IO/,
fz.', =7 · Jb0
2.
_
-,-
)<1
r ~ (1,t
v
-x,) -:. 6 X1
'I- r ~ ~o
?. ';/-
I, 2 · ~ "- ~
l< i-:.
S<.J~ e/leel-; ) 1
/'1{.
/vi
1
P1 ,
1
X1
gt5
-
z.
i-r, FL) : : !~ - 3" ~
1
~#t:tl- !
/(J
J
I l.Al
P~) -
e/larJ
)z
(V1
I
Z?-
P
) I
Pi')--:-
Xl (.,._,',
-z,,..
/(J
P,,Pi} -
4/"\
~- JZ.
Tz T'1
I 14{
u~ ,_
e~t,r
,
,
"
..
/\ I ..
z/0r
) 1,
"f
o/
~ -
.,
JJ.J.1
fo/J ~ - - :,;\~~s::;::::::::,_
~~9~
~-
I
j
'J
it 1- ~ ..
~.x--'i---~--1 I.
11 l
/ to/5
fO/t'),
SO/'f
:
~-
ji,!7 eflt;e ,-.
~?
t<At
Xe
'lfk(I
el-f.ec#,
· ·,ootA .
XI - \V\ k,-Mo[ j [)Ou\ .
!Acrasc
'f}~f#//
~('-fl-l 'C
~
vV~
ewJ ~~
'>(:.,
frvt~
~
l(lcv~c.J~.
l,,v\
t /l C. "H,U'<,e
0/1-.
I'--
)
@ .~)
0\4A/U..t
~~Ill
i
~
-
v"1
,\4 { 't''
x, f 'Xz..
9-fl.:/O
x0
x,
X2.
4
/~
c.,')
ti c
wJ f4
(!OOJ
{)vi~
,~
~/v:J
/3/tl
+o
Dvt:-
rv1,,JJfW~,4J-
711/J s ,-1 hJ ~
o VJ,, e
Jff.t'/t:-0-5<
5. ThU>r
ck,l./vl-cvf
.s~~WlA&<J-
.ftrr
~-ev'l
jyll-e
<~
t1Jo ,
-fktM-
wHI
Jt?'ft{,fSe
~-C::,11,t(/ ~
-r~
e) 1 lAciJJ-.rx~J
( (J..
IA
or
0
J-
equll/t,(IVl/"1
w./1-1
r1A.,-1VJ1vl
Jr
fl/JI
TO
uHHh.-;
b'1
DAd
tloi~
So
hrJt~
X,; f-Xi
;: 1.
W,tVfA
d---tA-t
~
l).J-kt 1-
k,(/())
bur
•l:, ~
du
'5)'11
( /-f.c
c e:
11'"J
C>VJ ly
~(:,~
..
.s~
.J-d
Jv
s /ttt-t:,
(;v\,t,J
i,,
~u
/'11irer,,,Je)
( t~.5.5
tfvve5
Lt t. 5
V\.vV
J-e
/ (I ( '( e,Gl
vV J vi
-r.:.,
t()
H-t:.
¼
~7- = '1
1
V
'x I t Xz -:. 6
+- 3
z:.
q
• 11
<-t ,
5"
i t1 jf/!ur,e,vl-
t W'.e-5 e. 1-, UVJ-
~k
w1U ~v l h) re
,'n ~ts vW~
t= ..:-
Lil~
1/a_
rwo i.300JJ
V"t () ('--G
Wfve 5
/0 ;:, I?" . g
::::- 7_7'7:-z:.
P, -T$'o
_
r,
v /-
CDfk
0 ~
of
e7ull/Jy/l)VVI
f,1
r
,j-'l,,,,.t:,.
o}:
t'H·
Ill
S
1-1 (JV/ ,J
w~
VHtl~
J
'Pt ✓t t:
lll,/Jlfer-ev7L~
+vvf/ ,J M -t,,l J
t,4A/'101/lt1 }-J
,vlt, (JY'(,,,
J.o&5
~V'-t'
(NVt-0 tu n 1--
f~
vt<>r
t 5
; I-
b7; ,;M-1,NaJ
-- ....,
~
o~
1---~
yooJ5
-twv
~
j-£: Z.~
W1'X1-I-
WI ")(
(!)...
c?x,
I
()07)~'1-ZP
f(J)-.
Wt,'f..l,
z-1:-1f
1r
+ W l ')( 2 + _>. ( 'j - (. \0( 1 ")(_.;_)
, W1 - A
·
U-i.VXi
Jx,..) ~
0
x,
X2.
jt_;; W1.,o 'j.2.,
/"
2
( ~\ ?-0
7.,J X1- }
r)J..
dA ~ ;- zJx,~
~o
:;~,zJ;11x2
=
z Jx,. (~)-x
W'Z.
~ z[f'
l
=
-~,
lV--:
2 XI
;: :.
.,
.
b)
~
-:: 01 B Z 3 '1
I
,,
I ' 2-
-, 1.
~ ::::>-
t4U su-5,j~S
?i)
A
_,
J
1
0
)
L
<. .
'3
r
-1
.J
( fl I A A}
{L, ARI
~
(!)
'RA
(i I)
(1 ,1)
(-1,0)
r '/ o)
(], 1)
(f, 1:)
(3_, 1)
(I,
A- A-
t
i(
1-f
L
1'R
A~ I
AA,·
I
ff~
1 "-
1
I
-Y·
L
(1 , 2)
~,,.1
--
'l0
0
('•l/' R) { -t! I I\") \ ,t I 1( R) ' ( L 1 p. p. ){LI 11 A,) '
J+ ,.A-A) {L/'R.1 ~ /fP1) (L,M\', r,;_;~A) {L/11-?l,R)
ff i'\,A, ) '( l, It, /#; !W.] ( Lr llGl-1 '(,, j>,) ( L P,l's L', ~ R)
1
~~
)
I
( L , 1. R
(r-~
:
)
A n..
\
I\
I
.
--·o)
{iI,) )
(- I 1
f
61.A-
, (- I
I ())
· (' 2; 2)
--
.
I)
R. R
I u/o)-f -J 1 0)
I
I3 y o!i<-fi'llj
'!i "'-)
,,,,._,A
11 ~l-r1G-V 7
- 1 ,___
c,
w /'U
~rJ,vu,Y
-/'ltro~
-'I
l,V o V [ i)_
ro:« P(x o) ~
!jJ1v{Mlj
, A
IM. ~
A
) e 5)
L
V3 ~
Wj
-
IJV-,G,lv;
1-v
!,~
bu-<f i'aj
~
"" r 1/21
c,,i. tc
JJ-S Cf Iv.< /t1 "' k'
i-o
6"" 11<'.
oJo
I 1I ow
f-a s r .kfj-,,,e
.
JrM4
'f"-'A'v'
·,f,JW
J()~(/1
f
lv:fVI CifUa 111--f :J o o cJ(
c5
"'
b tJ '1
k)
13 ( ov-<K
W<J"t
j 00-J,
~)
~ ' ~ f3
w-J,I{. ~ a-tic
r-:
wt vf o
~
tt)1,.;'V(
h)(
1-o
Jdr "-
h:,
~i..ev 11(-'L-t:.
,J.~,/ w JU M<J HJ' f 0 . l-<)(' t,dH,<!
'(OW '1 Ut,, Ltl-1 , '1 oll'.J! · B · {-1-0
I ti W • ,J&<A,,,,,,J)
I.A t,7V1
.w.Jlt
pt:lt~.-. 7t,iJ.)
r"fl,lyct<-J.l'
frcJvu-v
'.. Ii< P tv 5
JJ~ f!oJ_U ce« ~ , ...,~ ~ HJ . /9-I 5,c,~r,, ,-e,
7m,z, ~ +v,r.t ' los W>"'-W J
~ <>"'C f ""'1 .....,.....::
I\
1
\
,J.l V't" ! e,
P~Ut4~-, C
!; '1
'
, I .
"
' /
✓
p5
·5V{Wyi,
, - j t<A1
-f'lwWv~L\
~--1//vij
p.,,,t-t,
o!+<AMJ.
"'·,rrw
4--0
Xt)
7{ /ftlWI
[dW .~~,,
JelV'tuJG. n/r uJV41/rM-Ja~I
,
A,/-r(), 1,1 , , ,~,.,. ·/k,mp,;
Ps
(A
J,-<Hw (ll'otfvtl-
pl ,,-e
I
---7.x~
v~
Xi1r---~~_;~ )(1
~'1
1--v
s t ~IJ,/-1 u,1
(1,1.1, k.
l,-<,
c eW.,5 ,-,1--<>
'. •·-
.
6 f-
t(A,-ftvr<
froJ/Jtc,Y
fO
(Jrr,,W V 1--
\,U~ fr,..
S
WW.G{
r,r-n .e
~ 1,-l,{
IMJV\ J..wi 1.vntl
.IQIA
vi
k
=: "-
6
0 ~ ..
13 Y
;~,J
P.)
AJow
·
lo=
i---c)
wjW - / 1-
"-
J ooJ ( s /
IU<,<t~
,.,,.,.,(
'fV/J, ui-; :rad
low
-rvt,-c frock~ I
b'j lJ;tj i,_ ~,,,,_,;/
,
JO-Ok.A
P.
"'-
¼
.,