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Population growth in a holding cost model
The need to purchase new fixed assets as population rises can be seen very clearly
under a new capital approach. However, under a holding cost approach, this need
appears on the revenue/financing side.
To illustrate this, consider the following simple example, where States initially own all
their assets (debt free), and States with population growth must either lease or purchase
the additional assets they need to provide services to their expanded population:

three States, each with 1 million population in year 1 - State A has no population
growth, but States B and C have 1.05 million population in year 2;

each State requires 1 school per 5,000 persons (the proportion of each State’s
population that is school-aged is equal);

in year 1, each State owns the 200 schools that it requires (debt free);

in year 2, State B leases from the private sector the additional schools that it
requires, whereas State C borrows to purchase the additional schools;

the value of a school is $3 million;

for simplicity, we will assume zero inflation, and ignore depreciation; and

the real interest rate is 4% (under zero inflation, this is also the nominal interest rate).
The fiscal situation is presented in the following table.
Expense
Revenue/Financing
Combined
Owns 200 schools
$24m holding revenue ($24pc)
Nil
Owns 200 schools
$24m holding revenue ($24pc)
Nil
Year 1 – all States - population 1 million
Uses 200 schools (x $3m x 4%)
$24m holding cost ($24pc)
Year 2 – State A - population 1 million
Uses 200 schools (x $3m x 4%)
$24m holding cost ($24pc)
Year 2 – State B - population 1.05 million
Uses 210 schools (x $3m x 4%)
$24m holding cost ($22.86pc)
plus $1.2m lease cost ($1.14pc)
equals $25.2m total cost ($24pc)
Owns 200 schools
$24m holding revenue ($22.86pc)
Deficit
$1.2m
($1.14pc)
Owns 210 schools
$25.2m holding revenue ($24pc)
Deficit
$1.2m
($1.14pc)
Year 2 – State C - population 1.05 million
Uses 210 schools (x $3m x 4%)
$25.2m holding cost ($24pc)
Debt of $30m (x 4%)
$1.2m interest cost ($1.14pc)
$24m net revenue ($22.86pc)
All States face a constant expense of $24 per capita, regardless of population growth.
However, States with population growth experience a fall in their per capita net
investment returns to $22.86 per capita in year 2, putting these States at a fiscal
disadvantage compared to State A. This is regardless of the decision to buy or lease
new schools.