Question $5$

An individual is facing a random loss, $x,$ that is uniformly distributed on

$(0,200).$ The individual can buy partial insurance cover against this loss

under which the individual would pay $Y=$min$(x,100),$ so that the

individual would pay the loss in full if the loss was less than $100,$ and

would pay $100$ otherwise.

The individual makes decisions using the utility function $u(x)=\frac{x^2}{5}$

Is the individual prepared to pay $80$ for this partial insurance cover if

the individual's wealth is $300?$