an individual has a state sub-utility function given by:u (I) = ?1/?e^??Iwhere I denotes the income of that individual and ? > 0. Let 1 ? ? denote the probabilitythat the individual is not caught for reckless driving and ? denote the probability she is not

3. Define the deterrence effect of a flat fine as the percentage decrease in utility it causes: DEF (I) = du (LF) dF. JU (LF)I F=0 Note that we evaluate the deterrence result at F = 0 to measure the effect that the introduction of a fine, where none existed before, has on the degree of risk the driver faces. Verify that DEF (1) is given by: DEF (I) = -* dF. (Note: We will carry out all calculations in the exercise using differentials. To cal- culate the reduction in expected utility caused by the fine, use the differential. To convert to a percent change, divide by the absolute value of expected utility. Finally. evaluate the expression you obtain at the appropriate fine, either F = 0 or 7 = 0.) 4. Does the deterrence effect DEF () depend on the individual's income level I? If so, how? Does the deterrence effect depend on the individual's absolute risk aversion? If so, how? 5. Now, suppose that the individual has to pay a fine proportional to her income: F =TI, where r is the rate at which the driver is fined. If the driver is caught speeding, then her income in that state will be: Ic = (1-7) I and, consequently, the lottery she faces is given by: Lp = [1, (1 - 7) 1; 1 - #, "]. Compute the individual's expected utility U (Lp) and her certainty equivalent