Joint Promotions allow two guild members to help advertise each others' products (or at least that's how I imagine it). This benefits both by an increase in perks, which if you remember, helps increase the speed of which you sell your goods.
Starting a JP begins by selecting a shop, hitting the Joint Promotion (JP) button and selecting the people you want to buddy up with. One of the nice things to note is that your shop can only JP with two other shops! As such, offering to JP with one guild member costs 10 000 cash, offering to JP with two guild members costs 20 000 cash, and each subsequent one is free! Therefore, it is useful to just offer JPs with all the available shops on the list.
The average perk increase is 50%. Now if you pay with gold, this increases the perk to 80%. Is it worth it? Let's do some math.
Say your TR is 170 million. You roughly know your average perk works out to be around 800% (without JP). Normally you account for the different ARPD for different shops but because you'll be aiming to JP all your shops, you don't need to. Therefore, the estimate for how much JP affects your TR is given as (very roughly):
TR / TPerk * JPBonus/100 * No. of JP = 170 m / 900% multiplied by 50% x 2 = 9.5 x 2 = 18.9 million
If gold is used, this is (roughly) increased to:
TR / TPerk * JPBonus/100 = 170 m / 900% multiplied by 80% x 2 = 15.1 x 2 million = 30 million
For myself, at 50 shops, this 11 million increase in TR for 12 hours costs 300 gold. Not worth it in my opinion but that depends on how deep your pockets run and how close you are to the next level!