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If I received an amount equal to the income I would have gotten normally, then I have no preference over which option occurs. This still assumes that I have enough savings to live from, the offer is credible, there are no opportunity costs I’m losing, no effort is required on my part, etc.
This is the same question, unless I misunderstood. I do have a motivation to earn money, so practically I might want to increase the rate, but I have no preference between not loaning and a rate that will put me in the same place after repayment. With my assumptions, the rate would be zero, but it could increase to compensate - if there's an opportunity cost of X, I'd want to get X more on repayment, etc.
No, it does NOT assume that.
Basically you have a zero discount rate for money which you don't need at the moment. How about money which you can use and want to use today, what rate will persuade you to go without?