Quote from: jtimon on July 14, 2011, 10:36:39 AM

I think I've get it. The increase in saving doesn't comes from a reduction in consumption but from a reduction in spending (while maintaining consumption). That makes sense.

Exactly. I think its helpful to assume a fix amount of money in the system. So when more goods have been produced, your money is worth more. imho the additional money value should equal the growth of production (velocity of money assumed constant and demand-price-curves for all goods have equal slopes; else, the additional purchase power depends on the composition of your consumer basket).
The bonus on purchase power can now be distributed to additional savings and spendings. So you could maintain your former consumption and save the left over money. or you could partly or fully consume the additional purchase power. However, lets say, 10% more produced goods in the long run somehow implies, that 10% more goods are being bought. As an aggregate, this leaves the savings/spendings quota unaffected.
Example: You earn 1000$, save 200, consume 8 goods for 100 each. Now production grows 25% -> money stays the same -> prices are p0*0.75
On average, Joe now buys 10 goods for 75 each = 750 and saves 250 (=200*(1+growth))

This assumes of course an average rate of stock-holding or at least this holds longterm.

Quote from: jtimon on July 14, 2011, 10:36:39 AM

I'm still confused about the relation between growth and interest rates. Doesn't seem obvious because there's a few factors.

I will try a story and formalize a little bit: ATTENTION!!! took me an hour to write Cheesy

t0: The tribe, 10 people, produces 100 fish by fishing with a fishing rod, everybody catches and eats 10 fish, no inequality, interest is 0.

One guy is very clever and claims he can build a fishingnet to catch 40 fish but needs one fishingperiod time to knot it, so he proposes: Everybode give me one fish, so we all have 9 and after that I can catch 40 fish every period. The others agree, but they want some profit from sparing their fish: two additional fish in t1. everybody hungers with his 9 fish, the net is built. Interest is 100%.

t1: The tribe, 10 people, produce 90+40=130 fish with 9 fishing rods and 1 fishing net. "cleverguy" catches 40 but has to give 9*2=18 Fishes and is left over with 22, the rest has 12 fishes each. There was 30% growth, there is some interest and now there is inequality.

t2: cleverguy has 40 fish for himself (debt paid), he can eat 20 of his 40 fishes and give 20 to another tribemember "workerguy" to allow him to stop fishing and build another net. He will happily agree because of the 10 bonus fish. Now there is more inequality because workerguy earns double. Also there is some interest.

t3: Production is 120 fish (economy shrunk for the investment), cleverguy hat 40 fish and a net to sell, since he can only use one net at once. 8 Members have 10 fish each, workerguy has 20 fishes and might buy cleverguys net or build his own net (by the way this assumes, fish is still eatable after one period of time). Lets say workerguy buys the net for a bit more than 10 fish. Cleverguy now has a bit more than 50 fish and pays two workers to knot a net. More inequality, some interest.

t4: Production is around 140 fish, workerguy now also has 40 fish and cleverguy hast 2 nets. now cleverguy and workerguy compete for workers. btw there is more fish than the tribe can eat, so cleverguy and workerguy can pay some tribemembers to massage their feet.

t5: There are several nets, prices for nets fall, no need to produce 400 fish

t6: there are 4 fishers with nets, everybody eats 16 fish and gets fat and healthy, the other 6 dont need to fish but serve the tribes needs (foot massages). notice: at the end of this process, everybody will have the same purchase power for fish and massages, because its pretty easy to enter the fishingindustry with another net in case fish gets to expensive for the benefit of the fishers. So "wages" of fishers and massagers converge!! -> Equality is back.

Now to sum that up. In the beginning there was no inequality. At the time, where the new technology arrived, inequality started to rise, it started to fall again when the growth rate maxed and at the point of maximum exploitation of the new technology equality came back. (This assumes however that there are no other goods like weapons and mercenaries to buy for cleverguy...)

Now back to your statement:

Quote from: jtimon on July 14, 2011, 10:36:39 AM

At the same time growth increases the offer and the demand for money.

I think it is not "at the same time" but FIRST it increases demand for money. AFTER the highest growth-rate within that "kontrdiev-cycle" is passed, the newly available ressources/money (supply) outweigh the demand (=your "offer" if I got it right). At the end of the cycle there is even a lot of supply, so interest falls (in my extreme case above it falls to zero) and wages converge.

Ok, sounds a bit artificial but consider this on a larger scale with 100 or 1000 people, where it is a lot easier that due to some entrepreneur, a "money/fish-market" emerges.
In reality there are of course other factors like regulation, central bank/inflation and there always is some rate of innovation unequal to zero so it is hard to see a clean reverse u-shape curve my theory describes. But: The other factors do not interfer with my causal relationship but all the effects sum up. So other factors held constant, it should be possible to make this empirical relation visible.