I would have it changed to meet your contract. To the argument that you can't get R15 in 2x4 framing, see here. I've only had unfaced fg installed, so staples would be superflous.

The International Energy Conservation Code recommends minimum wall insulation of R13 in Zone 4 and R20 in Zone 5. (Missouri spans both zones, so the requirement differs depending on your location.)

There is no pushing back and there is no hassle; it is simply a matter of following a contractural agreement.

The insulation is stuck to the paper so it won't sag after the drywall is installed regardless of how its stapled. The staples keep the paper flat on the studs but not always successfully. A paper facing is a royal pain to fuss with and makes it more difficult to fill all voids well and IMO that is more important than an addition R-2. Every added inch of insulation saves a little less than the one before it so a 15% increase in thickness will not be a 15% increase in thermal efficiency. But the GC owes it to you so he should not be surprised if you point out the deficinecy. Removing stapled insulation is an even bigger pain so he might offer you an attractive credit.

I never specify paper faced insulation; its not only a nuisance to install, its not a good vapor retarder. I recommend unfazed insulation and a sheet of 4 mil polyethylene.

Provided the R-13 insulation complies with your local building code requirements, I would look for your builder to implement an alternative which offsets the difference in energy efficiency. This could range from upgrading the air sealing of your home to upgrading to a more efficient hot water heater, furnace or air conditioner.

Does the contract state that the insulation material be R15 or the total wall value? Add in the inside and outside coverings and you may be up to R15.

R values are certified by approved testing methods. To specify a wall assembly R value in a contract that was calculated by the designer and open to interpretation by the contractor would be unenforcible. You could argue about the R value of still air on the wall surface or the heat transfer through the studs. But I've seen worse things specified in a contract.

"The first floor is 2x6 framing and has R19 installed. The second floor is 2x4 framing and has R13. Our contract stated R15 insulation. "

Was your contract reviewed by a lawyer? If so then ask his or her opinion of what the word insulation means in context of your contract. Be prepared for a fight with the builder and his general contractor. My simple interpretation is this is a breach of contract and you have the right have it corrected to your satisfaction.

I'm still a bit skeptical of the R-15 rating for the same material and thickness that is rated at R-13. Apparently its just more compressed but if air is a better insulator than the material, at some point compression should not increase the R-value. Is the R-15 insulation right at the inflection point? But, its written on the package so it must be right. Right?

I just checked out some information from Owens Corning. R-15 fiberglass is about twice the density in lbs/s.f. as R-13 fiberglass. What it gives up in less air is more than made up for by less convection movement of the air.

I'll bet the GC is going to tell you the wrong insulation was delivered.

CRH's idea about upgrading other energy conservation features is a good one.