Assume that a consumer's preferences over goods A and B may be expressed by the utility function $u(A,B)=(AB{)}^{0\mathrm{.}5}.$ Assume the consumer has $100$ monetary units. Assume also that A costs $1$ monetary unit, while $B$ costs $2$ monetary units. What is the impact of the substitution effect as the price of B rises to $3$ monetary units? Detail your answer. Do not even think of using chatGPT.