ECO3320-001
Spring2015
Instructor:Rui He
Name
R#
Quiz 1
1.Thedemandfor goodXis givenby Qd*: 6,000- (ll2)P*- Pv* 9P,+ (l/10)M. Research
shows
thatthepricesof relatedgoodsaregivenby Pr: $6,500andP,: $100,while the average
incomeof individualsconsumingthis productis M : $7.0,000.
a. Indicatewhethergoods)zandX aresubstitutes
for goodX.
or complements
b. Is X an inferior or a normalgood?
c. How manyunitsof goodXwill bepurchased
whenP*: $5,230?
d. Determinethe demandfunctionfor goodX.
/ Determinethe inversedemandfunctionfor goodX.
g. If Qs': (Tlz)P*,what is the equilibriumpriceandQuantity?(Otherthingsconstant)
b'
ctl-^7ln*'e*ts
-2
< o
*1
a,
Jr'a >o
c.
O;(
,
'T q*
&od=
7?^,
6g'..' + 2ao I
j p,
6,,,-
-
TorD
o-s l2x
a-sxf)3o:
+7*s
= 7<t.'"' - o'5Pr
ze* : tf 8o6- P*
J ..
&"
&=
d=
,
>)
to&d-
>4.5
&^t
74^ - o-er116: e o-spx
P"= 7V*.
&*.
p 17^
ECO3320-001 Spring2015
Quiz2
Instructor:Rui He
L The demandcurve for a productis given by
e*d: 7_0.5p,.
a' How much would the firm's revenuechangeif it lowered
the price from $12 to
$ l0? Is demandelasticor inelasticin this range?
b' How muchwould the firm's revenuechangeif it lowered
the pricefrom $4 to $2?
Is demandelasticor inelasticin this range?
c' What price maximizesthe firm's total revenue?What
is the elasticityof demand
at this point on the demandcurve?
gl=7?r=ro,
6,
Oj-
P,=t
P- =2
o-sr,. :
I
7-_o.s,#:-(-
,A!--
& .rl , 7_ o.l- /< - =6
44P=o)
P'
( o.
=
"t* E
:>
)
7_ o.jx/o3
TRr =
>)
*> 7lr
T'R-.
,exl:
a-.
- )o
:)14>--tL
Px
-o.j '<,
G-
=
tZ
=)
Px :
-
l/
: ( 7- o.spx)--
lV - P r = )
2' Thedemand
curv€for a productis givenby e*d=I200-3p"-0.rp,
wherep,=$300.
a. Whatis tfr"l@aggJelasticity of demand
whenp*:g140?Is demandelasticor
inelasticat this point?what wouldhgRRen
to the firm's -revenueif it decidedto
Qr - 7- o.rr',
:3-,!=)l*R=
-
chargea pricebelow$140?
&^d . /r.I'u- 3x,go - o.tx3ru' 7JD
b' What is the own price elasticityof demandwhen p*:g240?
Is demandelasticor
inelasticat this point?what would happento the
firm,s revenueif it decidedto
chargeapriceabove
9240? C Sl : ,r.6) - zxz4o-o.fxg^. 4-6
a.:
Px
t*!, = c{*- e*
I .l
lt*
t(o
= -) x15--
p^=)
)xl,
'9.J-
- o.\-L
:
L"-ul-oot',-CJncne*p\.b
le't cLu.
P\,
4
fr-*=
| ,,:*
Px
--
d"
oi
|
l9o
-lx
=)
+sp
_
.eAo.+t"
,'f@-r rRo L
_/- 6
(
&rte4,.
P .r
4eu+ cLt
ReviewQuestions
ECO3320-001Spring
!015
lnsfructor:Rui He
l.
Thedemandcurvefor productX is given
by e*L 300_2p*
a. Findthe inversedemandcurve.
b. How muchconsumersurplus
do consumers
receivewhenp.:452
c' In generar,whathappensto the
leverof consumersurprusastheprice
of a goodfails?
s> zPx = 3,-&'$ = ,^-.Px
px= rfp - j ej
C,f =)
rIt
tl ->
4r
( t5o -<fli)
Lfo*
CS=j
Q* = 2-ro
:.)
Px.?i,
"
---ozs-
1'"r
:-':-.7'? (
f-=
&= ?o
lq*o
&y'=r
@f=4o.
ttz\
@p=cu.o*s.z
\d
i1l
a.
es. Ps
cs + Ps
J-, d,q^ea"^..
fr.
3'
/ro.J-
"t'l
2. Considera market where
supply -a A"rnunAare given by
e.o-t6+&, and e_d:92_2&.
Supposethegovernmentimposes|ffif$40,andagreestopurchaseanyandallunits
r". v'eewqv aru inrru
consumers
do not by at the floor of $40per
unit.
l
a. Determinethe costto thegovernment
= cl
o-i
of buyingfirms,unsoldunits.
b' computethelostsocialwelfare(DwL)ttutrt".rfromthe$40pricefloor.
'e> -/(t P
,rf
-
Supposedemandandsupplyaregivenby
1t.. P"w.fltv
Q"d:14-0'5P-and Q*L0.25P*-I
a' Determine the equilibrium
price and quantity.
gwl =
= j t ee-lc;r z. --)
.! 1 cr -zr) x(Lv- rL )
t( t z * g z 4e
,j
"
a $12excisetax is imposed
on thegood.Determine
rhenewequilibrium
priceand
ilffi
c' If a priceceilingof $6is imposed,
whataretheresurting
shortage
andfulreconomic
price?
b'
.>>
I
[(- o.s P -* o."s P- /
P> >o.
"8
b,
l^,
.l
Pru*, - A U + l =
&^' :
C'
wgi'rd
S
a-d
O{= = tg- o.rr 6= t I
a.asx6-f
Qrs=
Ne'Lt
F.vl
Pr"tl
&o..r*i
.
:
a.s
* (
Prr-e ,o
t?J
- 3 *,
l--
>>
,a :
rio.5
I
P.a *tt
o'rs ( Pra- - rz)
*r
p
=) &:
I :
rv24
I V- o. r P..,,
Jp
- l
&:L
4. Supposethe demandfunctionfor a firm's productis givenby
hQ"d:7-l.5lnP*+2lnpy-0.5lnM+lnA
.--\
a. Determinethe own price elasticityof demand,and statewhetherdemandi( elastic/inelastic,
\-/
or unitaryelastic.
b. Determinethe cross-gllglQlticity of demandbetWeen
goodX andgoodY, andstatewhether
thesetwo goodsaretrrbstitut".b, complements.
c. Determinethe incomeelasticityof demand,and statewhethergood X is a normal good or
6E[or-vooa.
\'----z
'^'\
t*
: -/'s
b,
2,5 :>
c.
f,{ : _,.,
5. Thedemandfor companyX's productis givenby Q*o:I2-3P*+4Pv..
SupposegoodX sellsfor
4
$3 per unit andgoodY sellsfor $1..5per unit.
a. Calculatethe cross-price
elasticityof demandbetweengoodsX andY at the givenprices.
b. Are goodsX andY Q@r
complements?
c. Whatis the own priceelasticityof demandat theseprices?
d. How wouldyou answersto partsa andc changeif thepriceof X droppedto $2.5per unit?
t--O
d.$. tL-
3,<3+4xt-s=
J - r 3 ' ' ) - zJ J
.^,J -
J.
E
:
7
**T:
3
l,o -- '-;
5{=
*.#=
t*u
€^!r:
-'x
f'
+"}'#
xp
ECO3320-001Spring20l5
Quiz4
Instructor:Rui He
l. A consumerhas$300to spendon goodsX andY. The marketpricesof thesetwo goodsare
P-:$15andPr=$5.
a. What is ttremarketrateof substitutionbetweengoodsandy?
b. Illustratetheconsumer's
opportunitysetin a carefullylabeleddiagram.
c. Showhow the consumer'sopportunitysetchangesif incomeincreasesby $300.How doesthe
$300in incomealterthe marketrateof substitutionbetweengoodsX andy.
Showhow the consumer's
opportunitysetchanges
whentheprice of goodY increases
to $10.
How doesthis changealterthe marketrateof substitutionbetweengoodsX andy?
6[,r. >- ]f\
g
r.l
r
a.
b.
c.
d.
.Pg
A consumermustspendall of her incomeon two goods(X and \). In eachof the following
scenarios,
indicatewhetherthe equilibriumconsumption
of goodsX and Y will increaseor
decrease.
Assumegood
Y is a inferior good.
Incomedoubles.
Incomequadruples
andall pricesdouble
A
rvl
Incomeandall pricesquadruple )
TJ
T"
Incomeis halvedandall pricesdouble t"t
Y1'
XL
{,
a
3. In the following figure, a consumeris initially in equilibriumat point C. The consumer,s
incomeis $400,andthe budgetline throughpoint C is givenby l00X+200y=400.Whenthe
consumeris given a $100 gift certificatethat is good only at storeX, shemovesto a new
equilibriumat point D.
a. Determinethepriceof goodsX andy.
b.
c.
d.
e.
f.
How manyunitsof productYcouldbe purchased
atpointA?
How manyunitsof productX couldbe purchasedat point E?
How muchunitesof productX couldbe purchased
at pointB?
How muchunitesofproductX couldbe purchased
at pointF?
Basedon this consumer'spreferences,
rank bundlesA, B, c, and D in order from most
Tt
X
preferredto leastpreferred.
Is productX a normalor an inferiorgood?
z!,.rx +
Y
ij\
iI
E
D > i1 >
X
F
c
2'+Y
o*'>>