Practice Problems

$1.$

Logan has a car worth $$500.$ There is a $40\%$ chance that he gets into an accident which would cause enough damage to warrant $$300$ in repairs. Otherwise, nothing happens. Logan has utility preferences over consumption denoted by the function $U(c)=ln(c).$ Logan can also purchase insurance to minimize the loss at a rate of $$0\mathrm{.}50$ per dollar. How much should Logan spend on insurance to maximize his Utility $($in other words what is his $K^{**})?$

$\frac{}{1-}{C}_b+C_g=m+\frac{}{1-}(m-L)$