The choice of a lawyer as a special case of self-insurance-cum-protection

We consider decision about the choice of a lawyer as a particular case of self-insurance-cum-protection when the lawyer's cost is repaid  in case of victory.   The problem was introduced by Sevi and Yafil (2005) in the context of self-protection, which requires assumption that the size of  loss does not depend on effort (level of the expenditure on lawyer). In this paper we drop that assumption and our model includes possibility that both loss and  probability of  incuring a loss depend on effort.  We compare effort in our case with the standard one and prove that repayment is good incentive to invest more in modified SICP. We also show  that unlike the standard cases of SP and SICP, the level of effort is monotone in risk aversion. We prove that in our model DARA implies that lawyer's service is a normal good, which is intuitive. We show that for certain type of increase in risk aversion, the reimbursement effect is stronger then the risk aversion effect. For other changes in risk aversion there is a probability threshold that if the probability of a loss is below that level, then risk-aversion effect prevails. For higher initial probabilities, reimbursement effect is stronger.