King Bishop owns a pawn shop in a rough neighborhood. The value of his inventory is $1000. With probability 0.1, his pawn shop will be burglarized, reducing the value of his inventory to $200. King can purchase insurance against theft at a price of $0.20 per dollar of coverage. This means that each dollar of insurance coverage purchased reduces King's wealth in the "good state" (i.e., if no burglary occurs), Wg, by $0.20 but increases King's wealth in the "bad state" (i.e, if burglary occurs), Wb, by $0.80 = $(10.20). King's preferences over certain wealth are described by the utility function, U(W)=1000W. Which is the correct expression for King's MRS function, which describes -- for each contingent wealth bundle, (Wg,Wb) -- how much additional wealth King requires in the "bad state" to be willing to give up $1 of wealth in the "good state"?

a) MRS= (9Wb^1/2)/(Wg^1/2)

b) MRS= (9Wb^2)/(Wg^2)