Suzette works in downtown L.A. as a? copy-shop manager, and she earns? $100 per day. She drives to? work, and parking is expensive at the nearby? lot: $19 per day. The company that owns the parking lot also owns many? others, and it is understaffed. Instead of putting an attendant at each? lot, it asks lot users to put the money in a special box on the premises along with their car license number. To check on? compliance, it sends an employee randomly to its different lots during the week. If a car is found parked in the lot whose owner? hasn't paid, a fine of? $36 is levied. The chance of being caught if the owner? doesn't pay is? 20% (i.e., the probability is? 0.20).
?Suzette's net income equals her pay of? $100 minus whatever parking costs she incurs? (fines or? payments). Letting z denote net income per? day, Suzette's utility as a function of z is given by z?1/2? (i.e., the square root of net? income).
?a) On a piece of? paper, graph? Suzette's utility function? (plot utility for z? = 16,? 25, 36,? 64, 100,? 121, etc.). Is she risk averse? (answer yes or? no)?
?b) Suzette's utility if she pays the parking fee is equal to ? Her expected utility if she? doesn't pay the fee is equal to ? ?(express as a value with one digit following the decimal? point). Remember? that, in a situation involving? risk, expected utility is equal to the probability of one outcome times its utility plus the probability of the other outcome times its utility. Should Suzette pay the parking fee? (yes or?no)?
?c) Suppose the fine were? $84 instead of? $36. ? Suzetter's expected utility if she? doesn't pay the fee is now equal to ? ?(express as a value with one digit following the decimal? point). Should Suzette pay the parking fee? (yes or? no)?
?d) Frank works as a salesman in a store near? Suzette's copy shop. He also earns? $100 per? day, and he parks in? Suzette's lot. ? Frank's utility? function, however, is 2z instead of the square root of z? (i.e., the utility of a given net income is 2 times the net? income). Graph? Frank's utility function. Is he risk averse? (yes or? no)?
?e) When the fine is? $36, Frank's utility if he pays the parking fee is equal to ? His expected utility if he? doesn't pay the fee is equal to ? (express as a value with one digit following the decimal? point). Should Frank pay the parking fee? (yes or? no)?
?f) When the fine is? $84, Frank's expected utility if he? doesn't pay the fee is equal to ? (express as a value with one digit following the decimal? point). Should Frank pay the parking fee? (yes or? no)?