ECOIV 200 I : Intermediate lVlicroeconom'ics
Dem.onstration erercises Terrn 2
Demonstration lecture 1: Choice and revealed preference
1. You are studying demand for a low quality staple food in a low income country. Consumers allocate
total buclget gr between this good q1 at price p1 and a better quality substitute g2 at price p2. You
find that consunlers' demand for the good is viell captured empirically by a double log e<luation
ln q1 : Ar -i rrr lny * 0t I*p, + ppllrtp2.
(i) What restrictions on thc coefficients l.: 1, 3fi and ll12 are implied by homogeneitv?
(ii) Explain why it is only under very strong restrictions on o1, p11 and 912 that the other good
(iii) Your estimates suggest that o1 is negative arrd p11 is positive. fise the Sh.rtsky equatiol to
show that this is compatible with optimising behaviour by corrsurners only if the trudget share of
the good is greater than -[31 f a,1 . Explain.
2. You have data frorn the Root Vegetable Association of Great Britain on average consumption of
carrots and turnips in three J-ears as suntrnarised in the table below
Year Price Consumption
Carrots
970 0.100 0.025
1980 0.025 0.100
1990 0.050 0.050
are in 1990 pence per kilogram.
Consumptions are in kilograms per person per
lveek
Denote the burrdles choserr in the three years by qrn, qss and qeg. Let .R clenote weak revealed
preference.
(tr) Drau' budget constraints for the three years and identi$r choices made on each budget co1-
straint.
(b) Use the choice made in 1970 to shou, that qzo.Rqgg.
(c) Use the choice rnade in 1980 to siror.r, that qao/?qzo.
(d) Given your previous ans\\,ers r.hat pro.blern is raised bv the choice in 1990?
(e) Should we conclude that individual .behaviour in this econornv fails to satisfy WARP?
1
,No Date: ?3 ( 1-/- ?p!7.
li,{,c^\l?.ool Danr.o l,stu,e
(;t ,l_^ != Ar+ o( lLn + ln + l^
tt L )= ) v\>o
^
{(
t" 4 (.1 A, + d, t^( + b^ (-t + !"( )
A, + qt l^ )+ rl !"n ,) + ,z ,(.n
r c(, Ln (l) + u l,n (r) + ln '()
fu. l,\,o 4. h"ole| ,
I ty. 4 (oU,\ ,,-x
A * d, lw t !-n ,* !n A,* d,ln + f,,/,n r* !-^
+( + t d,\9n )
( d\+ ,,*
dr+ tr* o
(i,\ o v\ag dwanol e+ Aaublz 6,"^
Lnt z= /\> + & Ln + !-" + ,L^
lriow, Jz+ + a
z /.z*
z = Az + d, ln 1- 2l ,Q*, (o, r ,\ ,0",
lr^ r = A, r A,,[^ + 2 l^ (o, n \tn z
i'*S urt
,No. Date
Laa 4, L
U B
+n" cb,r,vtnols 4^^ don llr'l,zrhh^Qg .firrt t
ior< 4., BWtt€
4l o(1-l p,t+t drl u)
L
4
e
Az
e
\low actd 4,\r4z '1, - l
*
o
A, d,-l t'"+r
+
+
-l (2
I f,,
l,t-o-s 40 Vo,",l !-- a(l b vatrN-S o&
'r^ */.*r "&'' ,Nl^/- L- l't 's - W l: or{ w 4 c|T,' J. L
v@ eu(
._--_1
c, dr*l o
d, = 4z = (
+( 2t = o
=) (= -t o r=O
* 0{r- = D \ -dL - 2\ =Q
4r
) t\ + [n q, =
tl Az+h,
Sl*i
, No Date
d'l A>-
ft Pz
) D{o L(/osc LWfu 2t -o
) on calh ouc\ +"
A1 At
u 8'
\ten-r.4p" , eAt + d'
'i
.a. t[ vv( lo{ a = eh'
8 a
iil sltk e1,r-atiVn '. hr,LoWS Kubcfutfin e{,("-{* d\ W calcwlodccl 4*^
Ntawatil.rqn e&.{}<
a{,
a a
a"
P,
+"\^L f( +q
Z
U o/r
,.,*g:rd
Dem.onstration erercises Terrn 2
Demonstration lecture 1: Choice and revealed preference
1. You are studying demand for a low quality staple food in a low income country. Consumers allocate
total buclget gr between this good q1 at price p1 and a better quality substitute g2 at price p2. You
find that consunlers' demand for the good is viell captured empirically by a double log e<luation
ln q1 : Ar -i rrr lny * 0t I*p, + ppllrtp2.
(i) What restrictions on thc coefficients l.: 1, 3fi and ll12 are implied by homogeneitv?
(ii) Explain why it is only under very strong restrictions on o1, p11 and 912 that the other good
(iii) Your estimates suggest that o1 is negative arrd p11 is positive. fise the Sh.rtsky equatiol to
show that this is compatible with optimising behaviour by corrsurners only if the trudget share of
the good is greater than -[31 f a,1 . Explain.
2. You have data frorn the Root Vegetable Association of Great Britain on average consumption of
carrots and turnips in three J-ears as suntrnarised in the table below
Year Price Consumption
Carrots
970 0.100 0.025
1980 0.025 0.100
1990 0.050 0.050
are in 1990 pence per kilogram.
Consumptions are in kilograms per person per
lveek
Denote the burrdles choserr in the three years by qrn, qss and qeg. Let .R clenote weak revealed
preference.
(tr) Drau' budget constraints for the three years and identi$r choices made on each budget co1-
straint.
(b) Use the choice made in 1970 to shou, that qzo.Rqgg.
(c) Use the choice rnade in 1980 to siror.r, that qao/?qzo.
(d) Given your previous ans\\,ers r.hat pro.blern is raised bv the choice in 1990?
(e) Should we conclude that individual .behaviour in this econornv fails to satisfy WARP?
1
,No Date: ?3 ( 1-/- ?p!7.
li,{,c^\l?.ool Danr.o l,stu,e
(;t ,l_^ != Ar+ o( lLn + ln + l^
tt L )= ) v\>o
^
{(
t" 4 (.1 A, + d, t^( + b^ (-t + !"( )
A, + qt l^ )+ rl !"n ,) + ,z ,(.n
r c(, Ln (l) + u l,n (r) + ln '()
fu. l,\,o 4. h"ole| ,
I ty. 4 (oU,\ ,,-x
A * d, lw t !-n ,* !n A,* d,ln + f,,/,n r* !-^
+( + t d,\9n )
( d\+ ,,*
dr+ tr* o
(i,\ o v\ag dwanol e+ Aaublz 6,"^
Lnt z= /\> + & Ln + !-" + ,L^
lriow, Jz+ + a
z /.z*
z = Az + d, ln 1- 2l ,Q*, (o, r ,\ ,0",
lr^ r = A, r A,,[^ + 2 l^ (o, n \tn z
i'*S urt
,No. Date
Laa 4, L
U B
+n" cb,r,vtnols 4^^ don llr'l,zrhh^Qg .firrt t
ior< 4., BWtt€
4l o(1-l p,t+t drl u)
L
4
e
Az
e
\low actd 4,\r4z '1, - l
*
o
A, d,-l t'"+r
+
+
-l (2
I f,,
l,t-o-s 40 Vo,",l !-- a(l b vatrN-S o&
'r^ */.*r "&'' ,Nl^/- L- l't 's - W l: or{ w 4 c|T,' J. L
v@ eu(
._--_1
c, dr*l o
d, = 4z = (
+( 2t = o
=) (= -t o r=O
* 0{r- = D \ -dL - 2\ =Q
4r
) t\ + [n q, =
tl Az+h,
Sl*i
, No Date
d'l A>-
ft Pz
) D{o L(/osc LWfu 2t -o
) on calh ouc\ +"
A1 At
u 8'
\ten-r.4p" , eAt + d'
'i
.a. t[ vv( lo{ a = eh'
8 a
iil sltk e1,r-atiVn '. hr,LoWS Kubcfutfin e{,("-{* d\ W calcwlodccl 4*^
Ntawatil.rqn e&.{}<
a{,
a a
a"
P,
+"\^L f( +q
Z
U o/r
,.,*g:rd
