Page 57 - IJPS-11-1
P. 57
International Journal of
Population Studies Macroeconomic factors and housing dynamics
accidentally dead, and the government spending is equal to wealth of people who cannot survive are collected by the
the revenue from leasing land. government and will be distributed in the next period as
The aggregate level government budget constraint can government transfer.
be expressed as: Every household makes decisions to maximize their
lifetime utility:
G + t B + t Tr = t p L + l t Wτ (X)
t
V ( , , s h j = ) max ( { uc , h ) πβ+ V h , s , j + 1 )}
'
( t +
where B is the aggregate social benefit, Tr refers to the t t { , t+ t ch 1 , t s + 1 } t t j 1 t + 1
t
t
accumulated government transfers at time t, and Wτ (XVI)
t
refers to the total payroll tax collected from all working- Which subjects to
age populations.
c + s + ph − h h )
According to our assumption, each retiree gets an equal t t + 1 t ( t t − 1
+
h
I j w
share of B , and denoted by b which is: ≤ s t (1 r+ t ) ( ) (1 τ − t ) δ − h ph t − 1
t
t
t
( ,h
∑ j Jr= 1 ∏ ( i j= π Pw + I j b + tr − t tc h t t − 1 ) (XV)
( ) t
j
) τ
b = j= i= 1 it t (XI) h
t
i J =
j Jr+ ∑ = 1 ∏ ( i Jr+ = 1 it j ) s t + 1 ≥ − (1 λ− ) ph t (XVI)
jJ =
π
P
t
h
In this equation, the numerator is the expression of tc h ,h τ h ph t − 1 , h t − 1 ≠ h t
t
B . The denominator captures the number of all retirees. ( t − 1 t ) = 0, h t − 1 = h t (XVII)
t
Government transfer is uniformly distributed among
all living households in the next period. Therefore, the c,h ≥ 0 (XVIII)
expression is:
Equation XV is the budget constraint for a household
jJ ∏ ij (1 π − i ) (1 r+ s j + (1 δ − ) ph h j 1 and equations XVI and XVI are borrowing constraints.
tr ∑ [ t + 1 ) t + 1 h t + 1 t + ) # When a household attempts to buy a house, they are eligible
to borrow money using the house as collateral, up to a
(XII) maximum of (1−λ) of the house’s value. In this case, λ is the
downpayment ratio, where 0 ≤ λ ≤ 1 Borrowing behavior
where the s t +1 refers to the financial asset of the age j is denoted as a negative s . For simplicity, we assume that
j
t
group and 1 ph j 1 stands for the rest of the market the interest rate for borrowing and saving is the same. The
h
h
t
1 t
value of housing assets. I(j) here is an index function, which equals to 1 when j >
Jr, and to 0, otherwise. The housing market is not perfectly
For the government spending, we have: liquid; if the household wants to move to a new house, the
G =p L t (XIII) transaction cost tc (h ,h ) occurs which is proportional τ
l
h
t-1
1
t
The revenue from land sales is used to support to the market value of the house. Since the government does
government spending. not collect the property tax, the transaction cost mainly
consists of the agents’ commission fee.
2.5. The household’s problem 2.6. Equilibrium conditions
In each period, the event proceeds as follows. At the A stationary equilibrium consists of value functions and
beginning of each period, households receive or make cohort-specific decision rules {c, hs} for each household,
interest and principal payments from the previous period’s production plans {Y ,Y,K,N,L} for representative firms,
c
h
savings or borrowings. They then supply labor to firms to and a set of endogenous prices {r,p ,w,tr}, such that each of
h
earn wage income, and government transfers are deposited the following holds.
into their accounts simultaneously. For retirees, this is also • Households optimize. Given the price set, the
when social benefits are paid. Then with all this income, household’s problem value function is solved, subject
agents decide whether to move to a new house. If they to constraints.
choose to move, they sell their old house and purchase a
new one at current house prices. The expenditure on non- • The firm’s profit is maximized.
durable consumption is made. Then agents determine
1
how much to save or borrow in financial assets. Finally, w ( Z ) 1 1 (XIX)
c 1
uncertainty about early death is revealed. Both forms of t t r
t
Volume 11 Issue 1 (2025) 51 https://doi.org/10.36922/ijps.3645
