Team # 1916704 Page 3 of 19
Table 1: Variable Nomenclature of Model 1
Abbreviation Description Abbreviation Description
P
t
Nominal commodity price index µ Demand elasticity coefficient of intermediate
products
c
t
Actual consumption of the family A
t
full factors production rate
D
t
Balance of bank deposits held by the family γ Elastic coefficient of capital output
B
t
The size of the central bank’s digital currency
held by the family
χ Changes in the level of science and technology
E
t
The size of the physical currency of the central
bank held by the family
θ
t
Impact of technology
W
t
Nominal wage k
t
Firm−owned capital
n
t
Actual labor supply i
t
(z) Firm investment
R
D
t−1
Bank deposit interest rate R
L
t
Commercial bank loan interest rate
R
t−1
Central bank digital currency interest rate and
central bank real currency interest rate
B
′
t
Commercial bank loan to central bank
G
t
Firm profit dividend M
t
Deposit reserve
d
t
Actual bank deposit balance held by the fami-
ly
R
C
t−1
Deposit reserve ratio
b
t
The size of the actual central bank digital cur-
rency held by the family
R
T
t−1
Central bank loan interest rate
e
t
The size of the actual central bank ˛a´rs physical
currency held by the family
σ The cost of commercial banks in the process of
conducting loan business
g
t
Actual manufacturer profit dividend w
t
Commercial Bank Risk Management Capabil-
ity
w
t
Material currency δ Capital depreciation rate
u
t
Current utility function ρ
w
Commercial Bank Risk Management Capabil-
ity Smoothing Index
ϕ Negative utility of measurement work ρ
v
Family holding currency smoothing index
ϕ
d
Measuring the negative utility of using bank
deposits
ρ
r
1 Commercial Bank Credit Risk Premium S-
moothing Index
α
t
Proportion of bank deposits held by the family ρ
r
2 Commercial Bank Credit Risk Premium S-
moothing Index
v
t
Proportion of household holding currency ρ Inflation adjustment factor
ℓv
t
Proportion of digital currency held by the fam-
ily
r
1t
Commercial bank credit risk (with institution-
al guarantee)
q
t
The impact of the central bank’s digital curren-
cy
r
2t
Commercial bank credit risk (removal of insti-
tutional guarantee)
β Interval discount factor ϕ
P
Manufacturer price adjustment cost factor
z Manufacturer’s serial number ϕ
k
Firm capital adjustment cost factor
y
t
(z) Intermediate product r
10
Phase 0 commercial bank credit risk (with in-
stitutional guarantee)
y
t
Final product r
20
Phase 0 commercial bank credit risk (removal
system guarantee)
3.2 Variable Nomenclature
3.3 Model
Family First of all, combined with the actual situation, we assume that the family’s nominal budget
constraints.
P
t
c
t
+ D
t
+ B
t
+ E
t
= W
t
n
t
+ D
t−1
R
D
t−1
+ B
t−1
R
t−1
+ E
t−1
R
t−1
+ G
t
(1)
Turn it into an actual budget constraint, that is, divide both sides by P
t
.
c
t
+ d
t
+ b
t
+ e
t
= w
t
n
t
+ d
t−1
R
D
t−1
+ b
t−1
R
t−1
+ e
t−1
R
t−1
+ g
t
(2)
At the same time, we assume the current utility function of the family.
u
t
= log c
t
− ϕn
t
−
ϕ
d
2
(d
t
− d
t−1
)
2
(3)
Among them, the first item represents the utility of actual consumption to consumers. The parameter
ϕ measures the negative utility of the work, and the larger the value, the higher the negative effect.
The third item describes the negative effects of changes in actual bank deposits on households. Since
households use bank deposits to receive some restrictions and need to pay a certain "cost", the greater
the fluctuation of bank deposits, the greater the negative effect on the family.
To reflect the alternative advantages of central bank digital currency versus bank deposits, we intro-
duce a second constraint:
α
t
c
t
≤ d
t
(4)
α
t
= 1 − v
t
(5)
ℓv
t
= ρ
v
ℓv
t−1
+ (1 − ρ
v
)(α + (1 − ℓ)v
t−1
) + q
t
(6)
Here, v
t
indicates the proportion of households holding money, ℓv
t
indicates the proportion of house-
holds holding digital currency, and q
t
indicates the impact of central bank digital currency. It can be seen
that when q
t
is positive, an increase in q
t
will increase the amount of digital money held by households
and reduce the size of bank deposits.