A community faces two environmental hazards: flood and landslide. The annual probability of a flood is 0.12 with an average damage cost of ₦2.5 million; the annual probability of a landslide is 0.05 with an average damage cost of ₦4 million. The government can invest in mitigation measures as follows:

- Flood mitigation: each ₦0.5 million spent reduces the flood probability by 0.02, linearly, down to a minimum probability of 0.04.
- Landslide mitigation: each ₦0.8 million spent reduces the landslide damage cost by ₦0.5 million, linearly, down to a minimum damage of ₦1 million.

With a total mitigation budget of ₦2 million, how should the funds be allocated between the two hazards (in whole units of the respective measures) to minimise the expected annual loss (probability × damage), and what is the minimum expected loss (in million naira)?

Question

A community faces two environmental hazards: flood and landslide. The annual probability of a flood is 0.12 with an average damage cost of ₦2.5 million; the annual probability of a landslide is 0.05 with an average damage cost of ₦4 million. The government can invest in mitigation measures as follows:

- Flood mitigation: each ₦0.5 million spent reduces the flood probability by 0.02, linearly, down to a minimum probability of 0.04.
- Landslide mitigation: each ₦0.8 million spent reduces the landslide damage cost by ₦0.5 million, linearly, down to a minimum damage of ₦1 million.

With a total mitigation budget of ₦2 million, how should the funds be allocated between the two hazards (in whole units of the respective measures) to minimise the expected annual loss (probability × damage), and what is the minimum expected loss (in million naira)?

Accepted Answer

Allocate the full ₦2 million to flood mitigation (four units). Minimum expected annual loss = ₦0.30 million.

Neco Model Questions Vol1 2017 Geography Question 27

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