Savings

The box in the middle of the model, labeled Savings, represents a level (or stock) in the model. The Savings level amounts to the accumulation of production (at the production rate) less the accumulated consumption (at the consumption rate). Savings, like any level, gets stated in terms of a fixed unit of measure. In the case of this model I have used the unit "economic units."

Feedback

In any economic system Savings have an influence on production. In the simplest agrarian economies, the saving of grain allows for farmers to expend more energy cultivating more ground. In a slightly more advanced economy, saving grain allows the farmer to buy a plow, which together with his additional effort will increase production.

To make the model reflect the information of additional Savings we have added a feedback from Savings to the production rate. This will allow the model, with the addition of another variable that we will discuss in the next tab (above), to calculate changes in the production rate as a result of changes in the amount of Savings.

Reinforcing Loop

You'll notice, inside the loop formed by the feedback from Savings to production rate, a graphic, which looks like a snowball rolling downhill and labeled "Reinforcing." This graphic indicates that this is a reinforcing loop. That means that the production rate moves in the same direction as changes in Savings levels, i.e. when the Savings level increases so does production rate and when the Savings level decreases production rate also decreases.

Variables Determining Savings Levels

(initial level of (Savings)) + (accumulated (production rate) less accumulated (consumption rate))

initial level of (Savings)

The initial value for Savings equals 10,000 economic units. (I have included the initial Savings in the formula to save space on the screen.)

accumulated (production rate)

The accumulation of all production from the beginning of the simulation, at the production rate to the current time.

accumulated (consumption rate)

The accumulation of all consumption from the beginning of the simulation, at the consumption rate to the current time.

 

Production Rate

The arrow on the left-hand side, labeled production rate, represents the rate at which this system produces economic goods. In a model like this we represent rates in terms of the number of units per specific periods of time. In the case of this model the production rate is in terms of economic units per year.

Feedback

(I will explain the feedback from production rate to consumption rate in the Consumption Rate tab.)

Variables Determining Production Rate

base production rate + max((Savings X fractional production improvement), production rate limit)

base production rate

The base production rate variable tells the model what number to use as the base for the production rate calculation for all periods. The purpose of this variable will become more apparent as we move to more sophisticated models.

The base production rate equals 600 economic units per year. (I have changed the base production rate to 600 economic units per year in this and all succeeding models so that the beginning production rate value will always equal 1,000 economic units per year.):

(base production rate of 600 economic units per year plus (Savings times fractional production improvement of .04).)

fractional production improvement

This variable tells the production rate flow regulator what increases in production occur as a result of increases in the Savings level.

Using the feedback from Savings the model now calculates the production rate using the formula above.

The production rate increases as Savings grow, or will decline if Savings declines. We have set the fractional production improvement at 4% (or 0.04) per annum.

production rate limit

The variable that has no border, titled "production rate limit," keeps production rate from falling below zero in the case that Savings drops below zero.

I will discuss the fact that Savings can drop below zero under the simulation tab.

Consumption rate

The arrow on the right-hand side, labeled consumption rate, represents the rate at which the system consumes economic goods. Like the production rate, the consumption rate is stated in terms of economic units per year.

Feedback

The feedback from production rate to consumption rate transmits information about the production rate for use in the calculation below.

Variables Determining Consumption Rate

production rate X fractional consumption rate

production rate

Described in previous tab—Production Rate.

fractional consumption rate

The fractional consumption rate consists of a fraction that, when multiplied by the production rate, gives the value for the consumption rate.

To keep the values the same as the previous model I have set the initial value for the fractional consumption rate at .98 (or 98%), which yields the same value as the 980 economic units in the previous model.

In plain language this fraction means that the system consumes 98% of what it produces.

In the next tab (above)—Simulation—I will describe how you can change the fractional consumption rate to run different simulations.

Simulation

You will now see, with the changes that we have added to the model, a significantly different result in the performance of the plotted variables. (Fractional production improvement = 4% and initial fractional consumption rate = 98%)

In this simulation (based on the initial parameters) you will see that, in addition to Savings increasing over time, both the production rate and the consumption rate increase over time.

You can change the fractional consumption rate and rerun the simulation. You can, however, only change the fractional consumption rate because we want to show the effect that different consumption rates and Savings levels have on the production rate.

You can run several simulations using different fractional consumption rates. We suggest you run several simulations at less than 1.0 and at least one simulation using a fractional consumption rate in excess of 1.0 (over 100%). You will notice that when the fractional consumption rate exceeds 100% all of the variables, including production rates and consumption rates, will decline over time.

If, when running simulations, you enter a value at or near the limit of 1.2, you will see that consumption and production level off toward the end of the simulation. This occurs because of the limitation placed on the model by the production rate limit. I have placed no limits on Savings because I want you to see the long-term effects of dis-saving (i.e. consumption in excess of production).

Time

The duration of the simulation consists of 50 years.

Reading the Chart

The following tips might help you read and interpret the chart generated by the simulation.

Scales

On this chart the values for Savings are represented by the scale on the left-hand side of the chart. The values for the production rate and the consumption rate are both indicated by the scale on the right-hand side of the chart. Note: the range of these scales will change with different variables.

Plots

The names of the variables appear at the top of the chart. You can tell which line represents which variable by holding your mouse over the name of the variable, which will cause the line to thicken.

production rate

In this model the production rate (based on default values) rises steadily from 1,000 economic units per year (600 economic units per year plus 4% times 10,000 economic units of initial Savings) for each of the 50 years in the simulation (to roughly 1,040 economic units per year.)

consumption rate

The consumption rate in this model (based on default values) rises steadily from 980 economic units per year (production rate of 1,000 economic units per year .98) for each of the 50 years in the simulation (to roughly 1,019 economic units per year (1040 times .98).)

(This model allows you to change the consumption rate using the slider on the right to change the base consumption rate, which I will describe below.)

Savings

The amount of Savings increases over time from the initial amount of 10,000 economic units, which we plugged into the model, to a value at the end of 50 years to approximately 11,000 economic units (using the unitless fractional consumption rate of .98.)

Conclusion

At this point, although very simple, we have a model that fairly represents the interaction of the elements of an economy at various levels of abstraction. This model applies to a single economic good, a group of economic goods, or an entire economy.

This model shows the relationship between production, consumption, and savings. It shows how reduced consumption in the short run leads to greater savings that lead to greater production and consumption in the long run. It also shows how dis-saving – i.e. consumption rate greater than 100% of the production rate – causes both production and consumption to fall in the long-run.

You should remain cautious about making assumptions that go beyond those given in this model. In using the model to represent higher and higher levels of abstraction, more and more detail about the interactions of elements in an economy become clouded. If you have any doubts, you should review the earlier comments about the distinctions between aggregation and levels of abstraction.

From this model we will start to add some constraints and additional assumptions in order to demonstrate the effects of different fractional rates of consumption on an economy .