Let the unit price for the first time be x and the unit price for the second time be y.

A: (1000x+1000y)/2000 = (x+y)/2.

b: 1000 * 2/( 1000/x+ 1000/y)= 2xy/(x+y)

(x+y)/2-2xy/(x+y)=(x-y)^2/2(x+y)>； 0

Therefore, the unit price of A is always higher than that of B, and the purchase method of B is more cost-effective.