No. Going by the same logic, bracers of armor +4 should cost 1,000 gp, and we all know that's not the case. An item that grants a permanent shield effect shouldn't cost less than 16,000 gp (which is the price of a pair of bracers of armor +4, and also the cost of adding a +4 enhancement bonus to a shield). I agree with Thanee's 3,000 gp (x1.5) cost for magic missile protection, so 20,500 gp isn't unreasonable.
HOWEVER, it should be noted that at high levels, a brooch of shielding doesn't last very long (5d4+5 = avg. 17.5, which means the brooch can absorb an average of only 5.7 magic missile spells cast by a 9th level caster. Additionally, while the ring (or whatever) of permanent shield does take up a slot, it's not as inconvenient as an actual shield (doesn't require a free hand, doesn't weigh anything, can't be disarmed, etc.). For good measure, I'd multiply the item price by another 1.5 and round it down to 30,000 gp.