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You can import Amazon products from Amazon to WordPress automatically using WordPress Automatic Plugin. It can import products by keyword, from a wishlist, from bestsellers page or specific products by ASIN.
For the plugin to automatically update the prices, you will need both steps
1- Visit the plugin settings page and enable the option to update the prices daily
2- Setup up an External cron job if you have not already set it up as explained in this tutorial
The corn job makes sure to trigger the processing your campaigns automatically and with every trigger, the plugin will pick an Amazon product and update its price
