I currently have Iphoto v. 9.1.4. There is an update v. 9.4.3 that I am unable to install. I keep getting a message, "you have updates available for other accounts. To update this application, sign into the account you used to purchase it."

It means you are not signed into the same Apple ID that you were when you purchased iPhoto. Sign out and sign in with your other Apple ID.

This happens also sometimes when you are logged in with the correct ID or when you are not logged in.

Sign Out.

Then on the Featured page, at the right, click on "Account", you will be asked to sign in, sign in with your ID and hit the "view account" button, hit one of the possibilities like "manage...", you are transferred to that page, in that page on the menu bar click the "Updates" icon, you will be transferred there.

The iLife apps have been shipping as part of the bundled software with new Macs for a number of years. Your Mac shipped new from the factory with Snow Leopard, either 10.6.1 or 10.6.2. The iLife apps on your Mac are not the Mac App Store (MAS) versions. Your iLife apps are the boxed software versions that came on the bundled install DVDs. Your apps update through the Software Update facility in the Apple menu.

The OP has iPhoto 9, which was only ever available in the App Store. The versions that came on discs were iPhoto 8 and earlier.

So they purchased it from the App Store at some point, and supposedly is signed into the same account despite error messages to the contrary. Perhaps try in a test user to see if the issue persists?

EDIT: Actually I partially take that back, Apple briefly sold iLife '11 on a disc before discontinuing it. However is that was the case then the update available on the Apple Support website would work, and the OP stated they already tried that.

From my research, I believe that you are mistaken. iPhoto v. 9 is part of iLife '11 which was issued first by Apple in OCT of 2010 as boxed software on DVD and is still available from both Amazon and Ebay in the single user and Family Pack modes. The MAS beta was not introduced until 6 JAN 2011 as part of Snow Leopard 10.6.6. The MAS version of iLife '11 did not become available until that time. So the OP may or may not have the MAS version.

EDIT -

However is that was the case then the update available on the Apple Support website would work, and the OP stated they already tried that.

I don't see where the OP has said any such thing.

I am operating on process of elimination and personal experience.

The OP's profile indicates they have a Late 2009 iMac, which would have shipped with iLife '09 as bundled software DVDs. They now have iPhoto 9.1.4, which is part of iLife '11, which they have not yet specified how they acquired.

In their post before your first post they stated "If I download the update I do get a message that says that I must go through the app store."

In my experience if someone who has the App Store versions installed tries to update using the download from the Apple Support site (this one: http://support.apple.com/kb/DL1650), it tells them they must update through the App Store. This suggests to me that it was purchased from the App Store.

I recognize that my reasoning for this assumption was not clear in my original posts.

Please try each of the following steps you haven't already taken, until the issue is resolved. After each step, relaunch the App Store and try again.

1. Follow the instructions in this Apple Support article.

2. If any App Store purchases were made under a different Apple ID, or if the bundled iLife applications were accepted under a different ID, sign in to the App Store with that ID to update.

3. Alternatively, delete the probem applications and re-download them with the ID you're using now. If you haven't already purchased them with that ID, you'll have to do that first, because purchases can't be transferred from one account to another.

4. Select the Purchased tab in the App Store window. If you see an item in the list marked "You have 3 apps to accept," click Accept.

5. Triple-click anywhere in the line below on this page to select it:

/Library/Caches/com.apple.appstore/adoption.plist

Right-click or control-click the highlighted line and select

Services ▹ Reveal

from the contextual menu. A Finder window may open with a file selected. If it does, delete the selected file. You may be prompted for your login password.

Then repeat step 4.

6. Select

Store ▹ View My Account

from the App Store menu bar, then select View hidden purchases. If you're trying to update any hidden purchases, unhide them.

7. Launch iTunes and select

Store ▹ Authorize This Computer

from the menu bar.

8. If you've moved any App Store apps out of the Applications folder, or into a subfolder, put them back. Never move or copy those applications. If you have backup copies of the apps on another volume, unmount it and try to update again.

9. Contact Account and Billing Support.