3.8 The dynamics of bathtubs
3.8 The dynamics of bathtubs
Key points
- Bathtub thinking skills to help you better understand accumulations.
- Stocks accumulate the net rate of change. The net rate of change of a stock is the sum of all its inflows less the sum of all its outflows.
- The net accumulation into a stock simply corresponds to the area between the inflow and the outflow curves.
- When the net flow is positive, the stock will increase.
- When the net flow is equal to zero, the stock remains unchanged.
- When the net flow is negative, the stock will decrease.
- At any point in time, the slope of the stock is equal to the net flow.
1. Watch the video
2. Do the exercise
Charting stocks. This exercise will help you practice your bathtub thinking skills. It has two parts.
- The population at the end of 2015 on Caiman Island was 10,000 people. The number of births is 100 people per year. The number of deaths is 60 people per year. What will the population be at the end of 2016? Assuming that flows are continuous, chart the flows and the stock over 1 year (2016).
- What will the population be at the end of 2019 (in 4 years) if births increase to 160 people/year for years 3 and 4? Assuming that flows are continuous, chart the flows and the stock over this four year period.
Hint: Don’t forget that (1) a stock accumulates the net flow and (2) the slope of the stock curve is equal to the rate of the flow at the same point in time.
A suggested worked solution is provided in the additional materials.
3. Study the class readings
Bathtub dynamics. This short text describes how stocks react to flows in seven different situations of change.
Additional materials
- Exercise – a suggested worked solution. This is a suggested worked solution for the additional exercise “Charting stocks”.
- Video sources and bibliography. The web sites, attributions and sources cited in the video “The dynamics of bathtubs”.
- The video transcript.