Should schools and students pay sales tax (or VAT)?

http://www.boe.ca.gov/legdiv/legresearch.htm

It might seem odd for a state school or any government agency to pay taxes. Generally, they are exempt from income and property taxes, but likely pay sales tax (or VAT if outside the US) on purchases. Students of the state schools also pay sales tax on taxable items they purchase from the school bookstore or for their education (such as books).

Isn't this just a roundabout way for the state to be paying tax to itself?  Would it be more efficient to exempt purchases of state schools and agencies from sales tax?

What reminded me of this issue was an article about a bill (HB 4165) introduced in Singapore to create a VAT exemption for goods and services purchased from schools. ["Bill filed to exempt goods sold in schools from VAT," by Miranda, Business World Online, 5/23/14] The logic is also to keep school costs down. The bill sponsor suggests that when the school pays VAT, it must increase what it charges students.

California has had proposals to exempt textbooks and school supplies from sales tax. That is not easy to administer though because it is not clear that a book is a textbook (such as a novel) and some people buy textbooks or supplies that are not for school. See my 2/2/10 blog post. I note a few problems with such an exemption including complexity of defining the exemption and the reality that the seller might increase the cost of the items due to the exemption.

There are other ways to reduce costs for students, such by increasing government support through other spending cuts and efficiencies. But, that doesn't address the odd flow of funds when the state schools pay sales tax (such as a grade school buying textbooks), with the funds going to the state. Why not just exempt the direct purchase by the school.  I think the exemption for student purchases is the problematic one. For example, how does the seller know the buyer is buying the book or supply for school use?

What do you think?