I doubt you would see much benefit from a barrier in MN. From my research only the far southern states get much benefit but even then they need to focus on air sealing and having high levels of insulation.
The priorities in a home should be air sealing the attic floor and then insulation. Since you have to get under the insulation to air seal the air sealing has to come first.
You also need to understand insulation and radiant heat. Insulation is not a radiant barrier, a barrier reflects radiant heat, but insulation will stop radiant heat at the right depth. Fiberglass is a very open insulation with lots of air spaces and radiant heat will travel deeper into the insulation. With foams and cellulose the radiant heat is captured closer to the top of the insulation giving better protection from the heat.
ORNL had a savings calculator for radiant barriers on their website. If you played with it you saw that under insulated homes gained the most benefit from a barrier. As the level of insulation was increased the benefit decreased. So the more insulation you had the less benefit you received the from barrier and the less cost effective it became. With a well insulated home there was a 1-2% savings on AC, not the entire heating AND cooling costs.
In my area a couple of companies are selling the barrier at $1 to $1.50 a square foot laid out on the attic floor. ORNL says that dust degrades the effectiveness of the barrier in 1 to 10 years when laid on the Attic floor. Where as dust will have no effect on air sealing and insulation.
You should also learn about differences in insulation and how they perform in different installations. As we know fiberglass is very air porous and does not perform close to its full potential when there are air currents washing over it. Its like stepping outside on a cold windy day and feeling the air blow right through that sweater that was keeping you warm in the house. A wind breaker over it does a lot to keep you warmer on the windy day. Cellulose does a much better job of trapping and holding the air when left uncovered and performs better in the attic. The settling that occurs actually helps trap the heat and is not a bad thing. Cellulose over the top of fiberglass is almost like a windbreaker over a sweater.
If you heating degree days are close to or exceed you cooling degree days then you are better off spending you money on other energy saving projects. Since barriers lose their effectiveness due to dust when laid in the attic floor I do not think that is a worth wile way to install it in any location.
If you reflect back to the interior of the home it will reduce the loss-rate by some amount, if you have a datasheet it's usually there how to compute heat-transfer per hour, most have the spectral breakout.
What's missing in modern architecture is thermal-mass storage as part of the daily cycle, some adobe homes stay cool all summer w/o air-conditioning, this can be engineered.
A good wall system has the weather barrier, insulation, thermal-mass, interior finish.
Existing systems are missing the thermal-mass, calculated by thickness and transmittivity to hold heat-cold long enough to reduce energy inputs, easy to sim nowadays.
My practical solution so far is extra sheetrock for existing homes, insulation doesn't stop heat-transfer, just slows it down, thermal-mass doesn't stop it either but slows it way down to where the temperature differential is never very close to the interior, hence comfort zone is preserved.
My recyled product concept for this is recycled sheetrock with additives to increase it's use this way, and, built in pairs of heat-transfer units that recirculate the ceiling heat back to the floor, last round of thermal expansion looks as if it can be passive.
For new construction my spec is a common cement wall with in most cases a foam insert, standard window & wiring, I add in thermal fluid transfer, and adjust how thick the cement & insulation is to adjust, room-by-room the comfort-zone rating per 30F difference per hour down to not much.