No. By state law, a home's Assessed Value is not half its purchased price, but half of its market value. Section 211.27(5) of Michigan Compiled Law states:
"Beginning December 31, 1994, the purchase price paid in a transfer of property is not the presumptive true cash value of the property transferred. In determining the true cash value of transferred property, an Assessing Officer shall assess that property using the same valuation method used to value all other property of that same classification in the assessing jurisdiction."
Also, please see the State Tax Commission's Bulletin Number 19, 1997 on "Illegal Practices of A: "Following Sales" and B: "Assessing over 50%" for more information.