Contagion
Week 10
Ch 10.1-10.4
Recap
No aggregate liquidity
A competitive bank in a single region maximises:
maxXulc.ltl tlulcels.t.xtyet.Xaey I1HczeRxtlytc.l.Oex.y.c c
Essential bank run: each late consumer optimally runs even when other late consumers do not run
This never occurs under the e cient solution because no essential bank run condition always holds
C c as FOCu'letRule
Expected aggregate uncertainty
S
g
5
5
D
If
to 2 1 1 8
5 17 5
Max 5t.uk.ltl tlulcal t 57uulanltllt.lucal s.t.xtye1 Ascisey.lltskesekxtlyAsaslts
H Oex.y
c.sczstsHL
IUH.A.la IulIl
Unexpected aggregate liquidity uncertainty, single region
Pr Early late Max AHAvk.ltltilukalltTtzulal litlule
S l tie to.z this O
S TO X 8 1ta 2 e.g ulcklogle R 2
5 D 5 17 5 C 1c 2 x y't 5
Suppose
Stoccurs
A eg r 5
Xp0.8ratty 75 onlye arlyconsumerscomeat EI
Bankdefaultse venwhen
ill
lateconsumersruntact tale 1 ratty 75 each gets75att1
c onsumer Oatto
B e.g r 7
andliquidate 37oflongasset
1 tact 8 rl y't
Xp 8 ratty 85 Bankdoesn'tdefault
Iltalc 4Rbc1.1 17 Att2late
Essentialbank still
run ascites
occurs
geta
consumers
1411 57act1
c e.g re 9
Tac 8crafty 95 Bankliquidates Its Aac 8rlity
ldulcet 4 Rft I173 e 145,11 53 c 1 NBsunspotbankrun
can
occurascicest still
Noessentialb ankrunascic
Week 10
Ch 10.1-10.4
Recap
No aggregate liquidity
A competitive bank in a single region maximises:
maxXulc.ltl tlulcels.t.xtyet.Xaey I1HczeRxtlytc.l.Oex.y.c c
Essential bank run: each late consumer optimally runs even when other late consumers do not run
This never occurs under the e cient solution because no essential bank run condition always holds
C c as FOCu'letRule
Expected aggregate uncertainty
S
g
5
5
D
If
to 2 1 1 8
5 17 5
Max 5t.uk.ltl tlulcal t 57uulanltllt.lucal s.t.xtye1 Ascisey.lltskesekxtlyAsaslts
H Oex.y
c.sczstsHL
IUH.A.la IulIl
Unexpected aggregate liquidity uncertainty, single region
Pr Early late Max AHAvk.ltltilukalltTtzulal litlule
S l tie to.z this O
S TO X 8 1ta 2 e.g ulcklogle R 2
5 D 5 17 5 C 1c 2 x y't 5
Suppose
Stoccurs
A eg r 5
Xp0.8ratty 75 onlye arlyconsumerscomeat EI
Bankdefaultse venwhen
ill
lateconsumersruntact tale 1 ratty 75 each gets75att1
c onsumer Oatto
B e.g r 7
andliquidate 37oflongasset
1 tact 8 rl y't
Xp 8 ratty 85 Bankdoesn'tdefault
Iltalc 4Rbc1.1 17 Att2late
Essentialbank still
run ascites
occurs
geta
consumers
1411 57act1
c e.g re 9
Tac 8crafty 95 Bankliquidates Its Aac 8rlity
ldulcet 4 Rft I173 e 145,11 53 c 1 NBsunspotbankrun
can
occurascicest still
Noessentialb ankrunascic
