comment:
This is an IPAT-S script. IPAT-S is an open-source scripting language
for developing sustainability scenarios. It can be run using the free
IPAT-S software, available from:

	http://ipat-s.kb-creative.net/

For more information, please contact the author of IPAT-S,
Eric Kemp-Benedict (eric@kb-creative.net)
:comment

comment:
This sample IPAT-S script implements a simple trade balance model
for a small open economy. There is a goal for the income growth rate.
Also, a maximum savings rate is specified. The script then calculates
the maximum level of net exports consistent with the income growth goal,
subject to the cap on the savings rate. Finally, given government
expenditure as a proportion of GDP, the script calculates consumption
per capita.

The script uses a "textbook" version of the current account for
an open economy. It is based on a simplified balance of payments,
in which some transactions are set to zero.

Added to the basic national income accounts, the script implements
a simple model linking investment and growth. Rather than using a
standard growth model (e.g., using a neoclassical production function),
the script exploits a statistical regularity that can be seen in cross-
sectional and national time-series data on capital per worker, k,
and output per worker, x, where

       k = x ^ Kelast,

with Kelast about equal to 1.3. The "market optimism"
in this script is included in this equation. The national accounts 
and the capital accumulation equation are simply accounting identities,
but the assumption that capital per worker and output per worker
increase together does not always hold true. In some countries,
output has fallen dramatically while capital per worker remains
at relatively high levels.

The figures in the script are for a fictional country.

:comment

base year 2000
scenario years 2005 to 2030 by 5

comment:
K	capital
I	investment
X	output
P	population
S	domestic savings
L	labor force growth rate
income	income growth rate
p	population growth rate
:comment
summvar K I X P S
ratio L income p

##
## Scenario inputs
##
income = gr(<4.0%>)	# Income growth rate
L = gr(<3.0%>)		# Labor force growth rate
p = gr(<2.5%>)		# Population growth rate

# Max savings rate changes in a piecewise-linear fashion
# over time.
load _interpolate from 'IPATS_standard' as Interp
var maxSavRate		# Maximum saving rate
call Interp using maxSavRate year	\
		  2000	15%		\
		  2010	17%		\
		  2025	30%		\
		  2031	30%		\

var GovFrac
GovFrac = <10%>		# Government expenditure as % GDP

##
## Key parameters
##
number Kelast = 1.3	# K/worker = (X/worker) ^ Kelast
number deprec = 9%	# Capital depreciation rate

##
## Base-year data
##
X.0 = 480		# GDP, 1000 million $/year
K.0 = 360		# Capital stock, 1000 million $
P.0 = 80		# Population, million people

##
## Scenario calculations
##

# Population & GDP growth
:: 	>>p-> P >>income-> X

# Growth in capital stock
:: 	>> L * (X/L)^Kelast -> K

# Investment
comment:
 Rearrange
   dK/dt = -deprec * K + I
 to give
   dK/dt + deprec * K = I
:comment
:: 	rate(K) + deprec * K -> I

# Calculate a wage rate index, driven by average productivity growth
var wageRateIndex
wageRateIndex.0 = 100
:: 	>> X/L -> wageRateIndex

##
## Set up national accounts as an LP
##

comment:
  Note: An LP is not needed for this calculation. The solution to
  the LP is "S = maxS, EX - IM = maxS - I". However, by writing it
  as an LP it is easier to extend the script later with additional
  constraints and goals. It also has the advantage that the national
  accounts identity is explicit.
:comment

comment:
maxS	maximum level of savings, given max rate and total output
EX	exports
IM	imports
:comment
summvar maxS EX IM

# Set maximum level of savings, given max saving rate &
# total output, X
::	maxSavRate * X -> maxS

LP:
   solve for S EX IM
   max EX - IM

   # Basic identity for national accounts
   S - EX + IM = I

   # Constrain savings
   S <= maxS

:LP

##
## Report results
##
report wageRateIndex as "Wage Rate Index (2000=100)"
report 1000 * X/P as "Income ($/cap)"
report 1000 * (X * (1-GovFrac) - S)/P as "Consumption ($/cap)"
report 100 * S/X as "Savings Rate (% GDP)"
report 100 * I/X as "Investment (% GDP)"
report 100 * (S - I)/X as "Net Exports (% GDP)"