Summary Credit & Banking
,Table of Contents
Chapter 1: Why do banks exist? Why are banks special? ........................................... 4
What do banks do & what is special about banks?.............................................................. 4
Bank ................................................................................................................................................ 4
Functions and role of banks............................................................................................................... 4
Who borrows from banks? ................................................................................................ 6
Basics of credit rationing: fixed investment model .............................................................................. 6
Lenders’ credit analysis ..................................................................................................................... 7
Debt overhang ................................................................................................................................ 10
Investor activism: active role of banks/other financial intermediaries............................... 12
Introduction ................................................................................................................................... 12
Basics of investor activism .............................................................................................................. 13
Advising ......................................................................................................................................... 15
Empirics ......................................................................................................................................... 17
Chapter 2: Asymmetric Information – problems and solutions ................................. 20
Equilibrium credit rationing ............................................................................................ 20
Definition ....................................................................................................................................... 20
Credit rationing due to adverse selection ......................................................................................... 21
Collateral ....................................................................................................................... 23
Ex-ante theories: Screening versus Rationing ................................................................................... 23
Ex-post theories regarding collateral: solving ex-post frictions ........................................................... 25
Empirics ........................................................................................................................ 25
Berger, Frame and Ioannidou (2011) ................................................................................................. 25
Collateral and Credit (Degryse, De Jonghe, Laeven and Zhao (2025)) ................................................. 27
Chapter 3: Information sharing in banking markets ................................................. 29
Information sharing ........................................................................................................ 29
Model 1: information sharing Padillo & Pagano RFS 1997 .................................................................. 29
Extension of model 1: Padilla and Pagana (2000) .............................................................................. 33
Solving game for given degree of moral hazard (p is given) ................................................ 34
Without info sharing ........................................................................................................................ 34
With info sharing about defaults ...................................................................................................... 36
With info sharing about types, or complete information sharing ........................................................ 38
ENort choice .................................................................................................................. 39
Extensions ..................................................................................................................... 44
Strategic Defense: Bouckaert and Degryse (2006) ............................................................................. 44
Liquidity Management: Castiglionesi, Li, and Ma (2020) .................................................................... 45
Empirics ........................................................................................................................ 45
1
,Guest lecture Cedric Huylebroek: BigTech in finance .............................................. 48
BigTech Business model ................................................................................................. 48
Drivers of BigTech in Finance .......................................................................................... 49
Pros and cons of BigTech in Finance ................................................................................ 49
Case Study: MyBank ....................................................................................................... 52
Case Study: BNPL ........................................................................................................... 53
Old policy trade oNs ....................................................................................................... 54
New policy trade oNs ...................................................................................................... 54
Future financial landscape ............................................................................................. 55
Guest lecture Cedric Huylebroek: Suptech ............................................................. 56
Traditional bank supervision ........................................................................................... 56
How can supervisory scrutiny a]ect banks? ..................................................................................... 57
SupTech ......................................................................................................................... 58
Real e]ects of Suptech ................................................................................................................... 59
Chapter 4: Lender-Borrower Relationships ............................................................. 60
Bank versus Arm’s length financing (paper by Rajan) ........................................................ 60
The project ..................................................................................................................................... 60
Financiers ...................................................................................................................................... 61
Di]erent scenario’s: ........................................................................................................................ 61
Creditor concentration: number of relationships ............................................................. 65
DGG – theoretical model ................................................................................................................. 66
Empirics ........................................................................................................................ 68
Indicators of bank-firm relationship strength .................................................................................... 68
Impact of bank-firm relationships on firms ....................................................................................... 68
Relationship banking and firms’ credit constraints ............................................................................ 69
Chapter 5: Individual bank runs and systemic risk ................................................... 72
Individual bank runs ....................................................................................................... 72
Diamond -Dybvig (1983) – model and variants .................................................................................. 72
Runs .............................................................................................................................................. 77
Regulatory intervention ................................................................................................................... 78
Systemic risk ................................................................................................................. 78
Banking competition and stability ................................................................................... 78
Empirics ........................................................................................................................ 79
Introduction ................................................................................................................................... 79
2
, Evidence ........................................................................................................................................ 80
Liquidity risk ................................................................................................................................... 82
Chapter 6: Banking regulation – micro and macro-prudential ................................... 84
Definition ....................................................................................................................... 84
Why macro-prudential regulation? .................................................................................. 85
Macro-prudential toolkit ................................................................................................. 86
Summary Guest Lecture Issam Halak ..................................................................... 87
Fragmented banking industry: “level playing field” (diagram) ............................................................ 87
Sub-optimal allocation of capital (large vs small country diagram) .................................................... 87
Motivations for financial integration / de-fragmentation .................................................................... 88
SIU: 4 work strands ......................................................................................................................... 88
Summary PWC Lecture .......................................................................................... 88
Output floor ................................................................................................................... 92
Impact Basel IV on banking industry ................................................................................ 92
3
, Chapter 1: Why do banks exist? Why are banks
special?
What do banks do & what is special about banks?
Bank = institution whose current operations consist of granting loans and receiving deposits
from the public
Essential activities
• Granting loans: giving credit to households and firms
• Receiving deposits: collecting money from public
Aspect 1: Current
• So not occasional operation à is their main activity
• In contrast to other firms that might give trade credit, allowing customer to pay later. (e.g.
supplier credit, BNPL)
Aspect 2: Loans and deposits
• = fragility of banks
• On the debit side: all deposits liquidity may be taken at the same time (“bank run”)
• On the credit side: all lines of credit might be demanded at the same time
Aspect 3: Public
Taking deposits from public affects broader economy à justification for regulation
• Bank provides unique services
o Liquidity: people can access their money when needed
o Means of payment: banks enable transactions and payments
• Small depositors lack expertise to evaluate banks
Functions and role of banks
1. Liquidity and payment services
• Money exists to reduce transaction costs
o No money à need to barter (=trading goods for goods)
o Bartering is inefficient because you need to identify a willing counterparty
• Money keeps it usefulness overtime (you expect to use again)
• Money has positive value because it backed by government and thus can be used
for payment
• Function of money
o Means of payment (buying things)
o Store of value (you can save for future use)
4
, o Unit of account (common measure to put a value on goods/services)
• Providing payment services not profitable but necessary for granting loans and
having deposits + info obtained through checking account is valuable for
monitoring firms
o New threat from stablecoin, fintech, open banking…
2. Managing financial risks – transforming risk
Risk
Liquidity risk Interest rate risk Credit risk Financial market
Risk
= deposits can = loans are usually fixed-rate = borrowers
be withdrawn at <-> deposits rates change may default on
any but banks daily --> possible profit loans Propietary trading risk
margin shrinking. Although = banks themselves trade
transformed this also so are prone to market
in LT loans and quite limited because moving unexpectedly
can't converted depository beta is low so
this into cash deposit IR don't move much
Originate and hold to
with market rates Originate and distribute
= now they sell of the loans
to investors and collect
fees instead of holding till
maturity --> reducs long
term risk exposure
3. Alleviating asymmetric information problems
• Ex – ante asymmetric information
o One person has more info than the other
ð Result: adverse selection
ð Solution: banks screen borrowers or use contracts to reduce this
• Interim asymmetric information
o After getting loan borrower might change the distribution of payoffs or
project risk
• Ex - post asymmetric information
o Borrowers knows cash flow but bank does not so he can hide cash (cash-
flow diversion)
4. Banks and economic growth
• Bank oriented economies in 80s experienced high economic growth à suggesting
that strong banking sector benefits economic development
ð Relationship strong bank sector + economic growth weakened
over time. From 90s onward financial markets (stocks and bonds)
became more important
• Beck, Degryse & Kneer (2014) studied optimal size of financial sector relative to
GDP
ð Core function of banks (handing out credit) is good for growth
5
, ð Auxiliary services (asset management, trading, investment
banking) makes growth more volatile
• Crowding out effect of human capital
o Talented people are attracted to finance bcs of high salaries and prestinge
instead to sectors that drive real economic growth
Who borrows from banks?
Basics of credit rationing: fixed investment model
Can lenders recoup their investment?
Setup
• Lender/investor
• Entrepreneur/borrower with cash A
• Project cost I à A<I
• Borrower borrows I-A
Moral hazard problem
Probability of success Private benefit
Behaves PH 0
Misbehaves PL B
B is the private benefit the entrepreneur gets if misbehaves
Verifiable outcome
• Project succeeds with probability p and return R
• Project fails with probability 1-p and returns nothing
Assumptions
• Borrowers and investors are risk neutral
• Rate of return expected by investors is zero (due to risk neutrality)
• Lenders are in competitive market so profit is zero
𝑝! 𝑅" = 𝐼 − 𝐴
ð Because lenders make zero expected profit the expected repayment under success
probability pH must equal their initial loan
• Interest rate derivation
𝑹𝒍 = (𝟏 + 𝒊)(𝑰 − 𝑨)
→ 𝒑𝑯 (𝟏 + 𝒊)(𝑰 − 𝑨) = 𝑰 − 𝑨(inserting equation above)
𝟏 𝟏
→𝟏+𝒊=𝒑 →𝒊=𝒑 −𝟏
𝑯 𝑯
6
, This implies that if pH = 1 (so no risk) that i = 0 and if pH<1 then i >0 so lender charge a
default premium
• When project succeeds total return is R = Rb + Rl
• When project fails both get 0 so R= 0
• Project is only viable if there is no moral hazard
NPV if the borrower behaves 𝑝! 𝑅 − 𝐼 > 0
NPV if the borrower does not behave 𝑝' 𝑅 − 𝐼 + 𝐵 > 0
ð so no loan that gives incentives to misbehaves will be granted
• Total expected payoff (lender + borrower) if the borrower shirks
𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑝𝑟𝑜𝑓𝑖𝑡 𝑜𝑓 𝑙𝑒𝑛𝑑𝑒𝑟 𝑖𝑓 𝑏𝑜𝑟𝑟𝑜𝑤𝑒𝑟 𝑠ℎ𝑖𝑟𝑘𝑠 = 𝑝' 𝑅" − (𝐼 − 𝐴)
𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑝𝑟𝑜𝑓𝑖𝑡 𝑜𝑓 𝑏𝑜𝑟𝑟𝑜𝑤𝑒𝑟 𝑖𝑓 𝑠ℎ𝑒 𝑠ℎ𝑖𝑟𝑘𝑠 = 𝑝' 𝑅( + 𝐵 − 𝐴
→ 𝑝' 𝑅" − (𝐼 − 𝐴) + 𝑝' 𝑅( + 𝐵 − 𝐴 < 0
So when there are incentives to misbehave the project should not be financed
Lenders’ credit analysis
Incentive compatibility constraint
à the borrower must prefer to behave (and perform well) rather than misbehaving and taking the
private benefit B
So for this we need the following:
𝑬𝒙𝒑𝒆𝒄𝒕𝒆𝒅 𝒑𝒓𝒐𝒇𝒊𝒕 𝒕𝒐 𝒃𝒐𝒓𝒓𝒐𝒘𝒆𝒓 𝒊𝒇 𝒃𝒆𝒉𝒂𝒗𝒆𝒔
> 𝒆𝒙𝒑𝒆𝒄𝒕𝒆𝒅 𝒑𝒓𝒐𝒇𝒊𝒕 𝒕𝒐 𝒃𝒐𝒓𝒓𝒐𝒘𝒆𝒓 𝒊𝒇 𝒎𝒊𝒔𝒃𝒆𝒉𝒂𝒗𝒆
→ 𝒑𝑯 𝑹𝒃 > 𝒑𝑳 𝑹𝒃 + 𝑩
→ ∆𝒑𝑹𝒃 > 𝑩
𝑩
→ 𝑹𝒃 ≥ ∆𝒑
-
ð Result: the borrower needs to keep at least 𝑅( = ∆. otherwise she will misbehave.
This is the minimum reward necessary to align incentives
When linking this to borrower and lender payoff
𝑻𝒐𝒕𝒂𝒍 𝒓𝒆𝒕𝒖𝒓𝒏 𝑹 = 𝑹𝒃 + 𝑹𝒍
𝑰𝒏𝒔𝒆𝒓𝒕𝒊𝒏𝒈 𝒊𝒏𝒄𝒆𝒏𝒕𝒊𝒗𝒆 𝒄𝒐𝒎𝒑𝒂𝒕𝒊𝒃𝒊𝒍𝒊𝒕𝒚 𝒄𝒐𝒏𝒔𝒕𝒓𝒂𝒊𝒏𝒕 𝒈𝒊𝒗𝒆𝒔:
𝑩
→ 𝑹𝒍 ≤ 𝑹 −
∆𝒑
7
,Table of Contents
Chapter 1: Why do banks exist? Why are banks special? ........................................... 4
What do banks do & what is special about banks?.............................................................. 4
Bank ................................................................................................................................................ 4
Functions and role of banks............................................................................................................... 4
Who borrows from banks? ................................................................................................ 6
Basics of credit rationing: fixed investment model .............................................................................. 6
Lenders’ credit analysis ..................................................................................................................... 7
Debt overhang ................................................................................................................................ 10
Investor activism: active role of banks/other financial intermediaries............................... 12
Introduction ................................................................................................................................... 12
Basics of investor activism .............................................................................................................. 13
Advising ......................................................................................................................................... 15
Empirics ......................................................................................................................................... 17
Chapter 2: Asymmetric Information – problems and solutions ................................. 20
Equilibrium credit rationing ............................................................................................ 20
Definition ....................................................................................................................................... 20
Credit rationing due to adverse selection ......................................................................................... 21
Collateral ....................................................................................................................... 23
Ex-ante theories: Screening versus Rationing ................................................................................... 23
Ex-post theories regarding collateral: solving ex-post frictions ........................................................... 25
Empirics ........................................................................................................................ 25
Berger, Frame and Ioannidou (2011) ................................................................................................. 25
Collateral and Credit (Degryse, De Jonghe, Laeven and Zhao (2025)) ................................................. 27
Chapter 3: Information sharing in banking markets ................................................. 29
Information sharing ........................................................................................................ 29
Model 1: information sharing Padillo & Pagano RFS 1997 .................................................................. 29
Extension of model 1: Padilla and Pagana (2000) .............................................................................. 33
Solving game for given degree of moral hazard (p is given) ................................................ 34
Without info sharing ........................................................................................................................ 34
With info sharing about defaults ...................................................................................................... 36
With info sharing about types, or complete information sharing ........................................................ 38
ENort choice .................................................................................................................. 39
Extensions ..................................................................................................................... 44
Strategic Defense: Bouckaert and Degryse (2006) ............................................................................. 44
Liquidity Management: Castiglionesi, Li, and Ma (2020) .................................................................... 45
Empirics ........................................................................................................................ 45
1
,Guest lecture Cedric Huylebroek: BigTech in finance .............................................. 48
BigTech Business model ................................................................................................. 48
Drivers of BigTech in Finance .......................................................................................... 49
Pros and cons of BigTech in Finance ................................................................................ 49
Case Study: MyBank ....................................................................................................... 52
Case Study: BNPL ........................................................................................................... 53
Old policy trade oNs ....................................................................................................... 54
New policy trade oNs ...................................................................................................... 54
Future financial landscape ............................................................................................. 55
Guest lecture Cedric Huylebroek: Suptech ............................................................. 56
Traditional bank supervision ........................................................................................... 56
How can supervisory scrutiny a]ect banks? ..................................................................................... 57
SupTech ......................................................................................................................... 58
Real e]ects of Suptech ................................................................................................................... 59
Chapter 4: Lender-Borrower Relationships ............................................................. 60
Bank versus Arm’s length financing (paper by Rajan) ........................................................ 60
The project ..................................................................................................................................... 60
Financiers ...................................................................................................................................... 61
Di]erent scenario’s: ........................................................................................................................ 61
Creditor concentration: number of relationships ............................................................. 65
DGG – theoretical model ................................................................................................................. 66
Empirics ........................................................................................................................ 68
Indicators of bank-firm relationship strength .................................................................................... 68
Impact of bank-firm relationships on firms ....................................................................................... 68
Relationship banking and firms’ credit constraints ............................................................................ 69
Chapter 5: Individual bank runs and systemic risk ................................................... 72
Individual bank runs ....................................................................................................... 72
Diamond -Dybvig (1983) – model and variants .................................................................................. 72
Runs .............................................................................................................................................. 77
Regulatory intervention ................................................................................................................... 78
Systemic risk ................................................................................................................. 78
Banking competition and stability ................................................................................... 78
Empirics ........................................................................................................................ 79
Introduction ................................................................................................................................... 79
2
, Evidence ........................................................................................................................................ 80
Liquidity risk ................................................................................................................................... 82
Chapter 6: Banking regulation – micro and macro-prudential ................................... 84
Definition ....................................................................................................................... 84
Why macro-prudential regulation? .................................................................................. 85
Macro-prudential toolkit ................................................................................................. 86
Summary Guest Lecture Issam Halak ..................................................................... 87
Fragmented banking industry: “level playing field” (diagram) ............................................................ 87
Sub-optimal allocation of capital (large vs small country diagram) .................................................... 87
Motivations for financial integration / de-fragmentation .................................................................... 88
SIU: 4 work strands ......................................................................................................................... 88
Summary PWC Lecture .......................................................................................... 88
Output floor ................................................................................................................... 92
Impact Basel IV on banking industry ................................................................................ 92
3
, Chapter 1: Why do banks exist? Why are banks
special?
What do banks do & what is special about banks?
Bank = institution whose current operations consist of granting loans and receiving deposits
from the public
Essential activities
• Granting loans: giving credit to households and firms
• Receiving deposits: collecting money from public
Aspect 1: Current
• So not occasional operation à is their main activity
• In contrast to other firms that might give trade credit, allowing customer to pay later. (e.g.
supplier credit, BNPL)
Aspect 2: Loans and deposits
• = fragility of banks
• On the debit side: all deposits liquidity may be taken at the same time (“bank run”)
• On the credit side: all lines of credit might be demanded at the same time
Aspect 3: Public
Taking deposits from public affects broader economy à justification for regulation
• Bank provides unique services
o Liquidity: people can access their money when needed
o Means of payment: banks enable transactions and payments
• Small depositors lack expertise to evaluate banks
Functions and role of banks
1. Liquidity and payment services
• Money exists to reduce transaction costs
o No money à need to barter (=trading goods for goods)
o Bartering is inefficient because you need to identify a willing counterparty
• Money keeps it usefulness overtime (you expect to use again)
• Money has positive value because it backed by government and thus can be used
for payment
• Function of money
o Means of payment (buying things)
o Store of value (you can save for future use)
4
, o Unit of account (common measure to put a value on goods/services)
• Providing payment services not profitable but necessary for granting loans and
having deposits + info obtained through checking account is valuable for
monitoring firms
o New threat from stablecoin, fintech, open banking…
2. Managing financial risks – transforming risk
Risk
Liquidity risk Interest rate risk Credit risk Financial market
Risk
= deposits can = loans are usually fixed-rate = borrowers
be withdrawn at <-> deposits rates change may default on
any but banks daily --> possible profit loans Propietary trading risk
margin shrinking. Although = banks themselves trade
transformed this also so are prone to market
in LT loans and quite limited because moving unexpectedly
can't converted depository beta is low so
this into cash deposit IR don't move much
Originate and hold to
with market rates Originate and distribute
= now they sell of the loans
to investors and collect
fees instead of holding till
maturity --> reducs long
term risk exposure
3. Alleviating asymmetric information problems
• Ex – ante asymmetric information
o One person has more info than the other
ð Result: adverse selection
ð Solution: banks screen borrowers or use contracts to reduce this
• Interim asymmetric information
o After getting loan borrower might change the distribution of payoffs or
project risk
• Ex - post asymmetric information
o Borrowers knows cash flow but bank does not so he can hide cash (cash-
flow diversion)
4. Banks and economic growth
• Bank oriented economies in 80s experienced high economic growth à suggesting
that strong banking sector benefits economic development
ð Relationship strong bank sector + economic growth weakened
over time. From 90s onward financial markets (stocks and bonds)
became more important
• Beck, Degryse & Kneer (2014) studied optimal size of financial sector relative to
GDP
ð Core function of banks (handing out credit) is good for growth
5
, ð Auxiliary services (asset management, trading, investment
banking) makes growth more volatile
• Crowding out effect of human capital
o Talented people are attracted to finance bcs of high salaries and prestinge
instead to sectors that drive real economic growth
Who borrows from banks?
Basics of credit rationing: fixed investment model
Can lenders recoup their investment?
Setup
• Lender/investor
• Entrepreneur/borrower with cash A
• Project cost I à A<I
• Borrower borrows I-A
Moral hazard problem
Probability of success Private benefit
Behaves PH 0
Misbehaves PL B
B is the private benefit the entrepreneur gets if misbehaves
Verifiable outcome
• Project succeeds with probability p and return R
• Project fails with probability 1-p and returns nothing
Assumptions
• Borrowers and investors are risk neutral
• Rate of return expected by investors is zero (due to risk neutrality)
• Lenders are in competitive market so profit is zero
𝑝! 𝑅" = 𝐼 − 𝐴
ð Because lenders make zero expected profit the expected repayment under success
probability pH must equal their initial loan
• Interest rate derivation
𝑹𝒍 = (𝟏 + 𝒊)(𝑰 − 𝑨)
→ 𝒑𝑯 (𝟏 + 𝒊)(𝑰 − 𝑨) = 𝑰 − 𝑨(inserting equation above)
𝟏 𝟏
→𝟏+𝒊=𝒑 →𝒊=𝒑 −𝟏
𝑯 𝑯
6
, This implies that if pH = 1 (so no risk) that i = 0 and if pH<1 then i >0 so lender charge a
default premium
• When project succeeds total return is R = Rb + Rl
• When project fails both get 0 so R= 0
• Project is only viable if there is no moral hazard
NPV if the borrower behaves 𝑝! 𝑅 − 𝐼 > 0
NPV if the borrower does not behave 𝑝' 𝑅 − 𝐼 + 𝐵 > 0
ð so no loan that gives incentives to misbehaves will be granted
• Total expected payoff (lender + borrower) if the borrower shirks
𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑝𝑟𝑜𝑓𝑖𝑡 𝑜𝑓 𝑙𝑒𝑛𝑑𝑒𝑟 𝑖𝑓 𝑏𝑜𝑟𝑟𝑜𝑤𝑒𝑟 𝑠ℎ𝑖𝑟𝑘𝑠 = 𝑝' 𝑅" − (𝐼 − 𝐴)
𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑝𝑟𝑜𝑓𝑖𝑡 𝑜𝑓 𝑏𝑜𝑟𝑟𝑜𝑤𝑒𝑟 𝑖𝑓 𝑠ℎ𝑒 𝑠ℎ𝑖𝑟𝑘𝑠 = 𝑝' 𝑅( + 𝐵 − 𝐴
→ 𝑝' 𝑅" − (𝐼 − 𝐴) + 𝑝' 𝑅( + 𝐵 − 𝐴 < 0
So when there are incentives to misbehave the project should not be financed
Lenders’ credit analysis
Incentive compatibility constraint
à the borrower must prefer to behave (and perform well) rather than misbehaving and taking the
private benefit B
So for this we need the following:
𝑬𝒙𝒑𝒆𝒄𝒕𝒆𝒅 𝒑𝒓𝒐𝒇𝒊𝒕 𝒕𝒐 𝒃𝒐𝒓𝒓𝒐𝒘𝒆𝒓 𝒊𝒇 𝒃𝒆𝒉𝒂𝒗𝒆𝒔
> 𝒆𝒙𝒑𝒆𝒄𝒕𝒆𝒅 𝒑𝒓𝒐𝒇𝒊𝒕 𝒕𝒐 𝒃𝒐𝒓𝒓𝒐𝒘𝒆𝒓 𝒊𝒇 𝒎𝒊𝒔𝒃𝒆𝒉𝒂𝒗𝒆
→ 𝒑𝑯 𝑹𝒃 > 𝒑𝑳 𝑹𝒃 + 𝑩
→ ∆𝒑𝑹𝒃 > 𝑩
𝑩
→ 𝑹𝒃 ≥ ∆𝒑
-
ð Result: the borrower needs to keep at least 𝑅( = ∆. otherwise she will misbehave.
This is the minimum reward necessary to align incentives
When linking this to borrower and lender payoff
𝑻𝒐𝒕𝒂𝒍 𝒓𝒆𝒕𝒖𝒓𝒏 𝑹 = 𝑹𝒃 + 𝑹𝒍
𝑰𝒏𝒔𝒆𝒓𝒕𝒊𝒏𝒈 𝒊𝒏𝒄𝒆𝒏𝒕𝒊𝒗𝒆 𝒄𝒐𝒎𝒑𝒂𝒕𝒊𝒃𝒊𝒍𝒊𝒕𝒚 𝒄𝒐𝒏𝒔𝒕𝒓𝒂𝒊𝒏𝒕 𝒈𝒊𝒗𝒆𝒔:
𝑩
→ 𝑹𝒍 ≤ 𝑹 −
∆𝒑
7
