$($a$)$ In the 'good' state her wealth is w$1=50,000-0\mathrm{.}05$q$=$ the value of the car net of the total cost of the insurance she chooses to buy. In case the car gets stolen, her income will be equal to the amount of coverage she purchased net of the cost: w$2=$q$-0\mathrm{.}05$q$.$ Her objective is to choose q that will maximize her expected utility: maxEU$=0\mathrm{.}99$ln$(50,000-0\mathrm{.}05$q$)+0\mathrm{.}01$ln$($q$-0\mathrm{.}05$q$)($b$)$ Find the F$.$O$.$C$.$ And q$=10,000*10,000*0\mathrm{.}05=500$ dollars. Given the premium that the insurance company is charging Albina will choose to only purchase partial insurance, meaning that she 'redistributed' some of her wealth from the good state to the bad state, but she is still bearing some risk by herself.