Question

1) Assume that a swindler must disgorge her profits if she gets caught.

A) In order to make swindling unprofitable (expected value of swindling equals zero), how high must the probability of getting caught be?

B) If the probability of getting caught is 20%, swindling is profitable even if swindler disgorges all profits when caught. But if we add a fine for swindling, it would create more disincentive to swindle. What should the size of the fine be to produce the efficient amount of swindling (given the probability of getting caught is 20%)?

Answer 1

A) Let Prob of being caught = c and payoff = P1

Prob of not being caught = 1-c and payoff = P2.

Expected payoff = c*P1+(1-c)*P2.

To make swindling unprofitable Expected payoff = 0

c*P1+(1-c)*P2 = 0

cP1+ P2 -c*P2 = 0

c(P1-P2)+ P2 = 0

c(P2-P1) = P2

c = P2/(P2-P1).

This should be the prob of getting caught.

B)

Prob of getting caught = 0.2

Let fine be F.

Thus expected payoff = c*P1+(1-c)*P2-F

At c = 0.2;

Expected payoff = 0.2*P1+0.8*P2-F

To produce efficient amount of swindling Expected Payoff must be zero:

0.2P1+0.8P2 – F = 0

F = 0.2P1+ 0.8P2

This should be the fine for efficient level of swindling.