Stock behavior by graphical integration

Graphical integration helps you find out how a stock will develop over time when you know the development of the flows. The method has three questions:
1. In what direction will the stock develop?
2. How much will the stock change?
3. What is the curvature of the stock development?

Using the above graph, you will learn to answer these questions. Assume that the stock is zero at time zero, and the outflow is 10 units per time unit all the time.

In the period from zero to 5 hours, the inflow is 10 units and the answers to the three questions are:
1. The inflow is equal to the outflow and the stock will not change.
2. The change is zero all the time, and the stock will remain at zero units.
3. A constant stock develops along a straight line.

In the period from 5 to 10 hours the inflow is 15 units and the three answers are:
1. The inflow is larger than the outflow and the stock will increase.
2. The net flow, that is the inflow minus the outflow, is equal to 5 units per hour. Since the net flow lasts for 5 hours, the total increase in the stock is five units per hour times 5 hours = 25 units. By time 10, the stock has increased from 0 to 25 units.
3. The net flow is constant. This means that the stock will increase at the same speed from hour to hour, it will increase linearly.

In the period from 10 to 15 hours the inflow decreases from 20 to 15 units per hour and the three answers are:
1. The net flow is positive in the entire period, the stock will increase. Do not be confused by the fact that the inflow is decreasing in this period.
2. The average net flow in the period is 5 units per hour, and the stock will increase by 25 units over the 5 hour period. This increase will add to the value of the stock at time 10. Hence, the value of the stock at time 15 will be 25+25 units = 50 units.
3. Just after time 10 the net flow is at its largest and the stock increases very fast. Just before time 15, the net flow is close to zero and the stock increases very slowly. Hence, the stock increases decreasingly towards its value at the end of the periodø

In the period from 15 to 20 hours the inflow decreases from 10 to zero units per hour, and the three answers are:
1. The net flow is negative and the stock will decrease.
2. The average net flow from 15 to 20 hours is minus 5 units per hour. The stock will decrease by 5 units per hour times 5 hours = 25 units. The stock was at 50 units at time 15 and will decrease to 25 units by time 20.
3. Just after time 15 the stock is decreasing very slowly. Just before time 20 it decreases at its fastest. The curvature is such that the stock decreases increasingly.

When you reason about the development of a stock in a model with feedback loops, it is difficult to know exactly how the flows will develop in the future. This means that graphical integration will not provide precise indications of the stock behavior. This is yet another reason why it is necessary to simulate behavior in a computer. Once you have simulated, you can see how the flows develop, and graphical integration helps you understand WHY stocks develop as the simulated behavior shows.