If the economy was based on bitcoin, how would someone go about getting a loan? In today's society, people often take out loans from banks. In an economy that was run on bitcoins, how would someone go about getting a loan? I do not understand how this would work with Bitcoin's deflationary model. It seems a loan would be creating a short on bitcoins which could be very harmful with the value of bitcoins increasing.
Loans are possible in a deflationary environment.  Currently bitcoins is too volatile (which has nothing to do with deflation) to make lending viable.  For the purpose of answering the question I will assume that in the future volatility is either low or easily hedges.

The interest in a loan comes from 4 components:


Opportunity Cost.  Instead of giving you a loan I could do something else productive with the money.  If I could get a 10% ROI on my money by installing a new air-conditioner that will factor into the interest I change.  It would be a loss to loan money to you at less than 10% (after adjusting for the other risks) as I would "earn" more by taking the 10% ROI.
Inflation risk.  If money is worth 5% less in one year I will want to be paid 5% more even on a no risk no profit loan.  Thus inflation contributes to the overall interest charged.  Deflation would subtract from the overall interest charged.
Default risk.  If you don't pay me I lose money.  In the long run I need to collect interest equivalent to % of amount loaned that is lost due to defaults.  If I project I will lose on average 10% of amount loaned and charge 11% interest then I would break even.  Note: real world calculations are more complex because one may collect some revenue even from loans that default and may receive collateral, or sell defaulted loan for some recovery.  Still default risk needs to be included in the price of the loan.
Delayed Consumption.  By giving you a loan (even if priced to exactly break even) I am delaying my ability to use my money today.  I can't use it until repaid thus I will charge a premium for the time I lose waiting for repayment (sometimes called time value).  Thus even if all other costs/risks are 0% there will be some interest charged otherwise I might as well just keep the money in a can.


Interest is the "cost" of money.  Of the four components that contribute to that cost only one of them is related to inflation/deflation.  If in the long term all other factor were equal (which is unlikely), the USD had 3% inflation rate, and BTC had a 2% deflation rate one would be expect interest rates in BTC to be ~5% lower.