A *model* is a hypothetical and simplified description of the real
world. It defines a set of 21 variables representing
the events, states and the most important equations which we assume exist among
the entities.

The *Global
Future Model* describes
how we assume the variables are linked to each along a time
axis. Two types of variable are distinguished: 1. *stock* variables referring to variable values at a point on the time axis (e.g. population
at end of a year), and 2.* flow* variable (e.g. number of births and deaths during a year) referring to variable
values between 2 points of time on the axis.

Each variable value must therefore be identified by both name and time reference.
We refer to a time period as a *year*. The
model is called *dynamic* because some variable values can be related
to other variable values with different time references (e.g. population
value at the end of this year is determined by the population value at the
end of the previous year plus the births minus the deaths within the population
this year).

The *Global Future Model* relates the
variable to each other by *definition* and *structural* equations.
A definition equation expresses how variable values are associated
by arithmetic operators (as the population
at the end of this year in the last example of the previous paragraph). A structural
equation is more complex specified by a function
(e.g. linear, product, exponential function) with one or more *parameters* characterizing
the equation (e.g. the birth and the death rates in a population change equation).
The parameter values must either be estimated
(e.g. the birth rate) or autonomously set (e.g. a policy parameter referring
to investment allocation). Both stock variables start
values and parameter values can be changed in the run menu.

The first equation we introduce in the model to be used for reflecting possible
possible global future scenarios is the definition of the stock variable global *population* represented
by the variable id **Pop(t)** where the index * t* points to the end
of the year to which the variable relates. We define the value of this variable
as already indicated above. Since we are considering global entities, we don't
have to worry about migration.

** Pop(t) = Pop(t-1) + Births(t) - Deaths(t) **

The variables in this equation are expressed in** million persons (Mp). **

The next variable is the production *capital*. **Cap(t)** changes
from the end of one year to the end of next by the *investment* symbolized
by **Inv(t)** minus by the *depreciation* **Depr(t)
**of capital :

** Cap(t) = Cap(t-1) + Inv(t) - Depr(t) **

The model distinguishes between two sets of energy resources, the *non-renewable*, **NRes(t)**,
and the *renewable*, **RRes(t)**, resources.
The **NRes(t)** summarizes
the known non-renewable energy resources left at the end of year **t**:

** NRes(t) = NRes(t-1)-NUsed(t) **

where **NUsed(t)** is the amount of non-renewable resources used during
the year **t**. New non-renewable energy resources
identified are ignored in the model.

The variable** RRes(t)** indicates the amount of existing renewable energy
resources at the end of year **t**:

** RRes(t) = RRes(t-1) + RDev(t)**

The increase of new renewable resources **RDev(t)** is the amount of new
renewable resource capacity developed during the year **t**.
In the model, all renewable resources applied during the year are assumed
to be ready for reuse at the end of each year. Depreciated renewable resources
are ignored in the model.

The last resource included in the model is arable *land*. **Land(t)** expresses
the value of arable land at the end of year** t** valued in
**2014 USD.** The annual change to this resource is the* investment
in cultivating* new
land, **Cult(t)** minus the value of *decayed
land*, **Decay(t)**,
during the year **t**:

** Land(t) = Land(t-1) + Cult(t) - Decay(t) **

The *climate* is a major factor for the
global population. The cumulating man-made *greenhouse
gas *concentration in the atmosphere is assumed to be a dominant
factor of changing climate. The stock variable, **Gas(t), **is
an indicator representing the result of cumulated emission of CO2 at** t
**and measured in** ppm **(particles per million)**.** The
value difference between the beginning and end of a year is the flow variables annual emission ** Em
(t)** also expressed in **ppm**:

** Gas(t) = Gas(t-1) + Em(t) **

The greenhouse gases are assumed to be irreversible in the short run.

The next definition equation expresses a balance restriction, i.e. that
the different uses of annual products, including *consumption*** Consume(t). ** must
add up to the production:

** GWP(t) - Inv(t) - RDev(t) - Cult(t) - Consume(t)
= 0**

The *energy* used from the two
sources introduced above is assumed to equal the energy
required by the production. The model assumes that all available renewable
energy resources at the start of a year are utilized. Non-renewable
resources are used to fill the energy gap if **Energy(t)-RRes(t-1)>0**:

** Energy(t)- NUsed(t) - RRes(t-1) = 0**

All variable values, except for the population, greenhouse gas and gas emission, are expressed in 2014 Million USD value.

The *births* and *deaths* mechanisms
in the global population are described by *births*, **Births(t)**,and *deaths,
***Deaths(t) **,
respectively. These two flow variable are assumed to be determined by functions,** f1()** and

** Births(t) = f1(Pop(t-1)) **

and

** Deaths(t) = f2(Pop(t-1)) **

The *Gross World Product*,** GWP(t)**,
is an important flow variable representing the value of all
*products *and *services * available for
the world population during the year. It corresponds in principle to the sum
of the **GDP** of all countries/societies in the world. The value
of **GWP(t)** is assumed to be a function
** fb()** of the

** GWP(t) = fb( Pop(t-1), (Cap(t-1))**

The energy resources required for **GWP(t)** are
expressed by the function ** fe()** of

** Energy(t)= fe(GWP(t)**)

Investment, **Inv(t)**, in the
world production capital, **Cap(t)**,
is an assumed political determined percent **p1** of the **GWP(t)** ( This
entity excludes investment,** RDev(t)**,
in renewable energy resources, **RRes(t)**, and investment, **Cult(t)**),
in arable land,** Land(t)**, which are treated separately)**:**

** Inv(t) = p1*GWP(t) **

The value of annual capital depreciation, **Depr(t), **is
assumed to be a
function** d() **of

** Depr(t) = d(Cap(t-1)**)

Cultivating new and maintaining old land areas
for harvesting food requires also its share in percent, **p2** of **GWP(t)**:

** Cult(t) =p2*GWP(t)**

A part of the land area **Land(t-1)** also decays during
the year symbolized by the function ** d3()**:

** Decay(t) = d3(Land(t-1)** )

The percent of **GWP(t)** spent on developing new
renewable energy resources is represented by the
policy parameter **p3**:

** RDev(t)=p3*GWP(t)**

The use of non-renewable resources, **NUsed(t)**,
during the year is determined by energy requirements **Energy(t)** and
the available renewable resources
**RRes(t-1)** at the start of the year. If required **Energy(t)<=
RRest(-1)**, the value of** NUsed(t)** becomes **0**.
By means of the parameter **p4** the development of new reneable
energy resources can in this situation be reset to a percentage, **p4**, of previous
year's
**RDev(t-1)**:

**RDev(t)**=**p4*RDev(t-1)**

to avoid unwanted cycling.

The use of non-renewable energy resources,** NUsed(t),** generates
the annual greenhouse
gas emission,** Em(t) **symbolized
by the function** a3(): **

** Em(t) = a3(NUsed(t))
**

The changes in climate are indicated by changing global
temperature, **Temp(t)**, which is determined by the cumulative
green house gas variable,** Gas(t-1)**,
represented in the model by the function* a4()*:

** Temp(t)= a4(Gas(t-1))**

The temperature is expressed
relative to the mean world surface temperature for the period **1961-1990**.

**Food(t)** is determined by the available
cultivated **Land(t-1)** . The function ** a5()** represents
the agriculture production :

** Food(t) = a5(Land(t-l))
**

The well-being of the global human population is indicated by the variable **Welfare(t)** determined
by a function ** w()** of the variables

** Welfare(t) = w(Food(t)/Pop(t-1), Consume(t))/Pop(t-1),
Temp(t))**

Note that the the last function is an arbitrary preference function which is, in the real world, implicitly determined by political decisions.

To obtain a computable model, initial values for the stock values and estimates for the functions are needed. A number of international organizations compile relevant statistics. Unfortunately, neither are statistics for all variables available nor are those available accurate because of the complexity of the implied measurement. For this model, data from a number of international organizations are used:

**CIA (US Central Intelligence Agency), FAO (UN
Food and Agriculture Organization), IPCC (UN Intergovernmental Panel on
Climate Change), UNSTAT (UN Statistical Division), **and the ** World
Bank**.

Stock variables at the end of year
0, i.e.** 2014**, are frequently extrapolations from
statistics for earlier years. Data for some variables, e.g. **Capital(t)** ,
are not available on a world basis and are rough estimates. Data for remaining
non-renewable energy resouces, **NRes(t)**, are being revised frequently
because of new resources found. These and similar data uncertainties are not
as critical as they may appear if flow variable values for their annual changes
are available.

Default values used are adjusted such that the model computations will provide results approximately corresponding to forecasts or recommendations from different UN organizations.

To learn more about how the model can be used, you are invited to inspect
the **Experiments**.

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