The question is based on the government setting up a National Flood Insurance Programme (NFIP) to cover for floods. In the last two questions, it is stated that small claims want to be evaded. That is the NFIP doesn't want to deal with claims less than $5k. The last question asks which would be more suitable - excess (first part of $5k claim paid), deductible ($5k taken our from final claim) or franchise (pay out only if $5k). The first line of the answer states that a franchise is clearly inappropriate as it wouldn't reduce claims marginally above the threshold and has adverse incentive for people to inflate claims to reach the trigger points. Having an excess of $5k does not lead to inflate claims? I can't wrap my head around why one is more likely to change behaviour than the others. I cannot wrap my head around this. Which government program would expect customers to pay $5k in excess/deductible? I can imagine regulators at this if it were a private insurer (for unfairness).
A franchise will act as a trigger, so if there is a $10k claim and there was a franchise of $5k then the insurer will pay the full $10k and the insured will pay nothing, so there is a chance that people will inflate their claims. With an excess or deductible, the insured will have to pay the first $5k, so there is less incentive to inflate the claim.
