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Simply so, can regular paint be used as primer?

Paint shouldn't be used as a primer. Primers are specifically made for adhesion and sealing. Self priming and paint & primer in one is a load of crap. Years ago we called adding primer to paint for colors that didn't cover a "split coat" which served as our first coat but it does nothing for priming.

Also, is Primer more expensive than paint? Primer is cheaper than paint, so it helps you coat the surface and take care of issues using a cheaper material than top coat paint. Also, once priming is complete you can expect less time and fewer coats of top coat paint to complete the project.

In this way, is it better to use primer or two coats of paint?

Priming is best. If you have to do two coats of paint to cover the old color, why not use a good primer or primer/sealer and one coat of a good paint? Most people will say otherwise, but primer will stick to old paint a lot better than new paint will. Use one coat of primer and one coat of paint.

Does primer cover better than paint?

This will not only protect your furniture from paint drips and splatters, but also all of the dust from sanding. Tinted primer does a better job of covering the existing paint color than plain primer, so your finish coat will be more vibrant and may require fewer coats.