Egg-Laying Hens
An exercise in using a utility tree to choose among three chicken breeds (brown, white, red) based on profit and survival probabilities, demonstrating that the highest-profit option may not be the best investment due to risk.
THE IDEA
Problem: Egg-Laying Hens
You are planning to raise egg-laying hens for sale to egg farmers and are analyzing which of three breeds—brown, white, or red—would be most profitable. One hundred brown hens will earn you $200 profit, a hundred white $300, a hundred red $400. Unfortunately, chicks are highly vulnerable to a current viral epidemic. The Department of Agriculture informs you that brown chicks have an 80 percent chance of surviving the virus, white chicks 50 percent, and red chicks 30 percent.
Considering the profit and the virus, which chicken is your best investment? Work the problem on a sheet of paper using a utility tree.
Solution hint: The completed tree shows that brown chicks are the preferred option, but by a narrow margin. This makes sense from a profit-probability perspective, similar to the “Japanese Goods” problem.
When to use it
Choosing between investment options with different expected returns and risk levels.
Selecting a supplier based on cost and reliability (e.g., percentage of on-time deliveries).
Deciding on a marketing campaign that has different probabilities of success and potential revenue.
Evaluating different crop varieties given varying yields and resistance to disease.
FROM THEORY TO EVERYDAY LIFE
In practice
Egg-Laying Hens Problem
Three breeds: brown ($200 profit, 80% survival), white ($300, 50%), red ($400, 30%). Expected values: brown = $160, white = $150, red = $120. Brown is the best investment, despite having the lowest profit, due to higher survival probability.
A MOMENT TO REFLECT
Put it to work.
How would your decision change if the survival probabilities shifted (e.g., brown 70%, white 60%, red 40%)?
What other factors (e.g., feed costs, market demand) could be added to the utility tree to make the analysis more realistic?
Why is it important to explicitly calculate expected values rather than just comparing profits?
CONTINUE THE CONVERSATION
Source texts
- The Thinkers Toolkit by Morgan D Jones