Jaclyne is a collector who derives utility from Sculptures (S) and Antiques (A), which sell for Ps and Pa respectively. Due to the pandemic, Jaclyne is trying to economize, but she decides that she must still purchase enough of these to give her a level of U0 utils of utility. Given that we can represent Jaclyne's preferences with the utility function U=A^1/2S^2/3.

Suppose the government requisitions many sculptures to put in vaccine factories in order to increase employee happiness and productivity. Consequently, the price of Sculptures rises a little. Find a mathematical expression for the magnitude of Jaclyne's substitution effect in terms of her sculpture demand in response to this price change.