Question

1. You have been hired to advise the Ministry of Primary Industries on its policy directed at deterring illegal fishing. Thieves make money Wout of illegal fishing. The existing probability of apprehending a fisheries thief is p < 0.5. If caught they are fined F and their wealth is (W-F). The Ministry is proposing to deter illegal fishing by eitherdoubling the fine (F)for illegal fishing (holding probability constant) ordoubling the probability (p)of catching the fish thieves (holding the fine constant). As an economist, you are well aware of the relevance of an individual’s attitude to risk and suggest analysing the problem in terms of a risk adverse and a risk loving thief.

1. If fish thieves are risk averse, what policy (doubling the fine or doubling the probability of catching the thief) will do better in deterring illegal fishing?
2. If fish thieves are risk loving, what policy (doubling the fine or doubling the probability of catching the thief) will do better in deterring illegal fishing?

Hint: use a graph to answer each question.(hints to the problem are given below)

First, set the problem up.

Expected wealth = E(W) = W₀– pF; if we double pthen E(W) = W₀– 2pF

If we double Fthen E(W) = W₀– p2F. Thus E(W)is the same. The best deterrent is the option that results in the lowest expected utility.

1. Doubling the fine has the biggest impacton the risk averse thief’s EU
2. Downside risk is not as significant for the risk loving thief. For this person, the best deterrent is to double the chance of being caught. These thieves like to take risks.

Answer 1

Let us examine the situation.

Let U(x) be the utility function of the theives, where x = wealth of theives

1) If we double the fine, then expected utlity E(U) = U(W)* Probability of not being caught + U(W-2F) * Probability of being caught

E(U) = U(W)*(1-p) + U(W-2F)*p = E1

2) If we double the probabilty, then expected utility

E(U) = U(W)*(1-2p) + U(W-F)*2p = E2

For a risk averse person, marginal utility is positive but diminishing.

Hence for a risk averse person, E1 < E2, hence doubling the fine is the best policy for a risk averse thief.

For a risk loving person, marginal utility is positive and increasing

Hence for a risk loving person, E2 < E1, hence doubling the probability if the best policy for a risk loving thief.

We can use utility function of U(x) = x0.5 for a risk averse person and U(x) = x2 for a risk loving person and compare values of E1 and E2 and we can confirm that we get the best result.