What governs how fast grandmas make cookies?

They were making 10 each time, now it's 14. What governs the rate?

In 1.0 and later, it's largely through doubling upgrades.

The base rate is 0.5 CpS, or 0.8 after you buy Forwards from grandma. This increases by 0.02 for each grandma after buying One mind, an additional 0.02 for each grandma after buying Communal brainsweep, and 0.05 for each portal after buying Elder Pact.

The rest of the grandma upgrades make grandmas 2^18 = 262,144 times as efficient.

• Six upgrades that double the rate are unlocked after having hired specific numbers of grandmas: 1, 5, 10, 50, 100, and 200.
• The nine grandma costumes are unlocked for having at least 15 of each building (Farm through Prism). These are also doubling upgrades.
• Buying seven grandma costumes unlocks Bingo center (quadruple); waiting after that unlocks Ritual rolling pins (double).
• During Christmas, the "festive hat" upgrade chain will eventually unlock Naughty list (double).

Once you enter the Grandmapocalypse by buying One mind, part of the grandmas' production actually becomes quadratic (O(n^2)) because the base rate for each grandma includes something multiplied by the number of grandmas, and that in turn is multiplied by the number of grandmas. With more than 40 grandmas, the majority of your production is from quadratic effects.

As with every other source of cookie production, this is multiplied by your cookie production multiplier (mostly flavored cookies and heavenly chips), egg multiplier (Easter-related), covenant multiplier (95% if in effect), frenzy multiplier (usually 100%, occasionally 700%, 50%, or 66600%), and wrinkler multiplier (100% to 600%).

Sources: "Grandma", "Upgrade", and "CpS" pages on Cookie Clicker Wiki

This is the relevant code for the Grandmas in Cookie Clicker Classic:

var grandmaGain=Math.ceil(4+(Factories?1:0)+(Mines?2:0)+(Shipments?3:0)+(Labs?4:0)+(Portals?(Pledge?5+Portals*0.5:5):0)+(Times?6:0));
cps+=Grandmas*grandmaGain/5;

That confirms Sconibulus' idea that it might be related to the amount of available items. That said:

• There is a base of 4 cookies.
• If you have a Factory, it adds another 1 cookie.
• If you have a Mine, it adds another 2 cookies.
• If you have a Shipment, it adds another 3 cookies.
• If you have an Alchemy Lab, it adds another 4 cookies.
• If you have a Portal, the formula gets a bit complicated (See below).
• If you have a Time machine, it adds another 6 cookies.

The Portal itself adds 5 cookies. If you have a Pledge on top of that, you gain an additional .5 per portal.

The Grandmas produce the applicable sum of cookies every five seconds.

The formula changed completely in 1.0.