A drop in an interest rate is like giving free money to a person who has borrowed in the past. It is somewhat of taking excess resource from the savers and giving it to the spenders. The savers and spenders must be in balance to utilize all the resource in an economy efficiently. but I can only charge interest if there is competition to get at my excess resource.
Going back to the farmer - machine model, I am going to borrow 5 bushels of wheat/year for 2 years if only I can sell the machine to the farmers for atleast 10 bushels - the machine takes 2 years to build and costs 10 bushels to build. If I need to pay interest on the borrowing, I need to sell it higher than 10 bushels. The 10 farmers are going to pay 10 bushels or higher only if the machine can increase their production by 5 bushels/year or more, assuming a 2-year machine life. This circle will keep going at higher interest rate as long as the machines are being improved to increase productivity. Once the productivity stops, the interest rate would go down to zero. At zero interest rates, things could break down as there would become a deadlock between farmers and machinists, leading to a downward trend in productivity.
How does population increase feature in this - say economy adds 1 extra worker per year. There is need to feed the extra worker but the extra worker can also work. GDP will be measured by how many bushels are being exchanged every year. Does the extra worker's increase in goods exchange translate to better living conditions than in the past - could lead to downward standard of living or upward depending on the skill base the person brings. the economy will benefit if the extra person is helpful in increasing the productivity.
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