ECON2001 1 Lecture Notes
ECO]\2001 Microeconomics
Lecture Notes
Terrn 2
Ian Preston
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ECON2001 2 Lecture Notes
Ea..
LpcruRp 1 : Buocpr coNSTRATNTS AND
CONSUMER DEMAND
w: - $Pt = 6o6stdpt , )- ,t c1 arad ,kt$l bt^d5e+
b1, b %
I \
Budget constraint
't t= \ I
'3/p+ Consumers purchase goods q frorn lvithiri a budget setB of affordable bun- %t
dles. In the standard model. prices p are constant and totai spendirrg has to
remain within budget so that p'q I A where y is total budget. Ma-ximum af- Pl
fordable cluantity of arry comriilffiis yfpi and slope )q"f )qilB: -pif pt is
constant and independerit of total budget.
r \
In practical appiications budget constraints are frequently kinked or discon-
tinuous as a consequence, for example. of ta,xtrtion or non-lirrear pricing. If the h
r-M
l
price of a good rises witli the quantity purchased (sa;u because of ta-xation above
a threshold) then the budget set is convex r,vhereas if it fails (sa1, because of a
bulk buying discount) theri the budget set is not convex.
Marshallian demands
1^ W'^L, The consumer's chosen quantities written as a function of y and p are the
Ma'rshalli,an, or urlcompensaled demands q : f fu,p)
(qbtr Consider the effects of charrges in y and p on demand for, say, the ith good:
4, = LYfqp\,
tl w ie j,{,,t*,., o total budget y
4-
r'L{ y - the path traced out by demands as g iricreases is called lhe ,inco,me
erpansion palh u,hereas the graph of fly,p) as a function of y is
e q= 4(#,f)
-
called the Engel cu,rue
we carr summarise dependence in the total budget elasticity
ri\r.l
VY'
,5
_ )Inq' ___\-- g,YYpl
' qi0g
''*!dq; 01ny
- if derrrand for a goocl rises with total budget, e; ) 0, then we say it
is a normal good and if it falls, ei ( 0, we say it is an infenor good
- if budget share of a good, 'wi : p,etla, rises wittr total budget , ei ) L,
then we say it is a l,ururg or i,ncorne ektstic and if it falls, e1 ( 1, we
say it is a necessi,tu or i'nconr,e inelastic
ffi
. own price p1
{! 6FF& L
- the path traced out by demands as lrr increases is called lhe offer
cu,rue whereas the graph of ft(y,,p) as a functiorr of p6 is calied the
demanrl curue
t1,
.ED
O lan Presron. 2OO7) 2009. 2011, 2013, 2tJ1S
?
, u
ECON2001 J Lecture Notes
Case Study 1 Budget constraints: Stamp Duty Land Tax
Residential property transactions in England are subject to a tax known as
stamp duty land tax. Prior to late 20L4, if the value of the transaction was
below X125K the transaction was exempt but, once it exceeded that value,
tax was due at LTo on the whole of the value of the transaction. This meant
that as the value passed f125K not only did the after-tax price of owner-
occupied housing increase but also the tax that was liable jumped by f,1.25K.
At f250K another threshold was passed at which the rate of tax increased to
37o, again on the whole of the value so that there was a jump of f5K in the
liability. There were further discrete jumps for similar reasons at higher values.
When translated into a budget constraint between housing and other wealth
this created jumps (or 'lnotches") at these points and there is evidence that
house sales showed bunching at values just below these notches. Objections
to the "badly designed" form of the tax led to the announcement of reforms
smoothing out the schedule in the Autumn Statement of 2014.
ifl(+ I\i+ iiili++ .i\{.++ i\+ Ii-
aJ'=
r) 1l!{.}!xi}i
[Source: M. Best and H. Ktevel,2O13, HousiDa Nlarket Responses to Transaction Taxes: Ewidence Fror! Notches
arlil Stimulus ir the UK, LSE \&'orkins Paper. I
I
O lan Preston, 2OO7, 2009) 2O11j 2013, 2015
, ECON2001 4 Lecture Notes
- we can surrrrnarise dependerrce in the (urrcompensated) own price
elasticity
tt,, : Loq; - ol',q; 7-"
qi 0P; ?lnPi tt
- if uncompensated demand for a good rises with own price, \;t ) 0,
then we say it is a Giffen good
- if budget share of a good rises with price, 4;; ) -1, then we say it is
price i,nelastdc and if it falls, \.ii 1 -1, we say it is price elastic
. otlrer price p1. jI i
- we can summarise dependence in the (uncompensated) cross price
elasticity
pi 0q; ?hq;i-1,
,tii-iApj-0W1
- if uricompensated demand for a good rises rvith the price of another,
ryi.j > 0. then we can say it is an (uncompensated) subslzfzte whereas
if it falls with the price of another, \.ii { 0, then we can say it is
arr (uncompensated) com,plement These are rrot the best definitions
of cornplernerrtarity and substitutabiiity ho.nvever since they rnay not
be syrnnretric, in other words q; could be a substitute for qi while
(; is a complement for qi. A better defi.nition, guaranteed to be
symmetric, is one based on tlie concept of compensated demands to
be introduced beiow.
Adding up
We know that demands must lie within the budget set:
p'f (y,p) a a.
If consumer spending exhausts the total budget then tliis holds as an equalitv,
p'f (a,p):'a,
which is known as adding up.
By adding up
o rrot all goods can be inferior
o rrot all goods carr be luxuries
o not all goods can be necessities
O lan Presion, 2O07j 2009, 2011, 2013, 2015
ECO]\2001 Microeconomics
Lecture Notes
Terrn 2
Ian Preston
),[qw .toa, lv\L Lruay,l ert- ,My
ctl nkxW
y t:.{.i y e,h**p,
1, 1,
,,u/?"
V ^f
{ou pu - pi pi} t,,
t)
a 7*10
3,r,
?uElr.S lasy*o|av1 Ot,"+
n
ll(,-l Cb,A,,r.y ivr ,fl,*pc
i drx *,*b,* "l["zsn"rat - wk*.* &*ed &* u/{tt.d\t lt,xg.A \ < ,, t}v\
&, ",.,t,rp
{e od
ft f. i6 11,
,E
ol
;i
$teu"d.wry
^o*'il ,1 ?_1r'
of 41n"x'#qLfi E
91v,
'1-
L( X,, - tr) 9/o-
*i{"riri
fr\
V)
fuvu> $r.l €
,,i
, *
U'
), tr,
c'lt
:".
@ Ian Preston, 2007, 2009, 2011, 2013, 2015
LrM,rtv {,r.rn'*'rga ,tr'l
t
[rn l. {,orrtrie d *-+i' I
I
I
I
Ju, nr 4: hdo i' &^ c,,*rpd*: -ffJ
iI
1
, Ph3*col vtrha#iU*. [ru rv $rtr*nc c/otr^rll,. $.{ -) Y**
l>o
L(anawtc 'r*rh&Aura r tira. wilu* *lw- 'pa,Agat p+ &
r+ *[orda*b- bu"dtas
ECON2001 2 Lecture Notes
Ea..
LpcruRp 1 : Buocpr coNSTRATNTS AND
CONSUMER DEMAND
w: - $Pt = 6o6stdpt , )- ,t c1 arad ,kt$l bt^d5e+
b1, b %
I \
Budget constraint
't t= \ I
'3/p+ Consumers purchase goods q frorn lvithiri a budget setB of affordable bun- %t
dles. In the standard model. prices p are constant and totai spendirrg has to
remain within budget so that p'q I A where y is total budget. Ma-ximum af- Pl
fordable cluantity of arry comriilffiis yfpi and slope )q"f )qilB: -pif pt is
constant and independerit of total budget.
r \
In practical appiications budget constraints are frequently kinked or discon-
tinuous as a consequence, for example. of ta,xtrtion or non-lirrear pricing. If the h
r-M
l
price of a good rises witli the quantity purchased (sa;u because of ta-xation above
a threshold) then the budget set is convex r,vhereas if it fails (sa1, because of a
bulk buying discount) theri the budget set is not convex.
Marshallian demands
1^ W'^L, The consumer's chosen quantities written as a function of y and p are the
Ma'rshalli,an, or urlcompensaled demands q : f fu,p)
(qbtr Consider the effects of charrges in y and p on demand for, say, the ith good:
4, = LYfqp\,
tl w ie j,{,,t*,., o total budget y
4-
r'L{ y - the path traced out by demands as g iricreases is called lhe ,inco,me
erpansion palh u,hereas the graph of fly,p) as a function of y is
e q= 4(#,f)
-
called the Engel cu,rue
we carr summarise dependence in the total budget elasticity
ri\r.l
VY'
,5
_ )Inq' ___\-- g,YYpl
' qi0g
''*!dq; 01ny
- if derrrand for a goocl rises with total budget, e; ) 0, then we say it
is a normal good and if it falls, ei ( 0, we say it is an infenor good
- if budget share of a good, 'wi : p,etla, rises wittr total budget , ei ) L,
then we say it is a l,ururg or i,ncorne ektstic and if it falls, e1 ( 1, we
say it is a necessi,tu or i'nconr,e inelastic
ffi
. own price p1
{! 6FF& L
- the path traced out by demands as lrr increases is called lhe offer
cu,rue whereas the graph of ft(y,,p) as a functiorr of p6 is calied the
demanrl curue
t1,
.ED
O lan Presron. 2OO7) 2009. 2011, 2013, 2tJ1S
?
, u
ECON2001 J Lecture Notes
Case Study 1 Budget constraints: Stamp Duty Land Tax
Residential property transactions in England are subject to a tax known as
stamp duty land tax. Prior to late 20L4, if the value of the transaction was
below X125K the transaction was exempt but, once it exceeded that value,
tax was due at LTo on the whole of the value of the transaction. This meant
that as the value passed f125K not only did the after-tax price of owner-
occupied housing increase but also the tax that was liable jumped by f,1.25K.
At f250K another threshold was passed at which the rate of tax increased to
37o, again on the whole of the value so that there was a jump of f5K in the
liability. There were further discrete jumps for similar reasons at higher values.
When translated into a budget constraint between housing and other wealth
this created jumps (or 'lnotches") at these points and there is evidence that
house sales showed bunching at values just below these notches. Objections
to the "badly designed" form of the tax led to the announcement of reforms
smoothing out the schedule in the Autumn Statement of 2014.
ifl(+ I\i+ iiili++ .i\{.++ i\+ Ii-
aJ'=
r) 1l!{.}!xi}i
[Source: M. Best and H. Ktevel,2O13, HousiDa Nlarket Responses to Transaction Taxes: Ewidence Fror! Notches
arlil Stimulus ir the UK, LSE \&'orkins Paper. I
I
O lan Preston, 2OO7, 2009) 2O11j 2013, 2015
, ECON2001 4 Lecture Notes
- we can surrrrnarise dependerrce in the (urrcompensated) own price
elasticity
tt,, : Loq; - ol',q; 7-"
qi 0P; ?lnPi tt
- if uncompensated demand for a good rises with own price, \;t ) 0,
then we say it is a Giffen good
- if budget share of a good rises with price, 4;; ) -1, then we say it is
price i,nelastdc and if it falls, \.ii 1 -1, we say it is price elastic
. otlrer price p1. jI i
- we can summarise dependence in the (uncompensated) cross price
elasticity
pi 0q; ?hq;i-1,
,tii-iApj-0W1
- if uricompensated demand for a good rises rvith the price of another,
ryi.j > 0. then we can say it is an (uncompensated) subslzfzte whereas
if it falls with the price of another, \.ii { 0, then we can say it is
arr (uncompensated) com,plement These are rrot the best definitions
of cornplernerrtarity and substitutabiiity ho.nvever since they rnay not
be syrnnretric, in other words q; could be a substitute for qi while
(; is a complement for qi. A better defi.nition, guaranteed to be
symmetric, is one based on tlie concept of compensated demands to
be introduced beiow.
Adding up
We know that demands must lie within the budget set:
p'f (y,p) a a.
If consumer spending exhausts the total budget then tliis holds as an equalitv,
p'f (a,p):'a,
which is known as adding up.
By adding up
o rrot all goods can be inferior
o rrot all goods carr be luxuries
o not all goods can be necessities
O lan Presion, 2O07j 2009, 2011, 2013, 2015
