In a bank-based economy, how do banks determine how to split the economic pie with the businesses? In an economy with a bank-based financial system (little or no stock market activity allowed), I think I've got this much down:

The banks lend to businesses, who then make products and services. The businesses pay their suppliers according to the market rate. In other words, the businesses share their piece of the pie with suppliers according to how valuable they think the supplier is to them. 

However, I'm not quite sure how the banks determine how much the businesses should get for their efforts. I am assuming that the banks don't compete among themselves to sell loans to the businesses. The dividing of the pie between the banks and businesses in this case seems rather arbitrary. I know the banks simply expect an interest on their loan money, but it seems like the fixing of the interest rate seems arbitrary. Is it based on perceived risk of the industry in which the business operates? How would this risk be calculated for emerging industries, where there is little or no information?
I would say that if you assume away competition among banks, then the interest rate would be equal to the rate of profit in the industry or firm considered. If there is only one bank in a position of monopoly as a supplier of loans, then it will set the highest possible rate of interest, and that is the rate of profit : firms can not pay higher interest without bankruptcy. Then of course you can argue that there is a decreasing marginal efficiency of "capital", therefore the rate of profit would depend on how much money firms borrow from our single bank, and things would be more complicated. But I think it might still be a good approximation for practical cases. And if there is no available experience on a new industry, then our bank has to guess about the future rate of profit.

If you assume perfect competition among banks, then the question is about the lowest possible interest rate, and that would depend on risk of default : banks have to gain some profits on most loans to compensate for the defaults. Again if you don't know about risk you have to estimate it.