Not all goods are perfectly elastic. Take a look at the research surrounding the minimum wage.
If we were to increase the minimum wage by $0.50 (~6.7%) we'd only have about a 1% increase in food prices (http://www.ers.usda.gov/media/306735/aib74703_1_.pdf). Also take a look at the study regarding fast food prices by Card and Krueger.
Increasing the minimum wage in general does not cause a net rise in unemployment (http://www.deakin.edu.au/buslaw/aef/workingpapers/papers/200...).
The people who would receive the BI are the in the lowest income brackets. The bottom three income quintiles on average spend more in a year than they earn. This mean redistributing money to the lower income quintiles effectively results in more money being put back into the economy.
You can see this by studying the economic effect of various subsidies. Food stamps have the highest return on the dollar, with $1.73 in economic activity generated for every dollar spent on food stamps. And subsidies to the higher tax brackets like the Bush tax cuts have a negative return. http://frac.org/initiatives/american-recovery-and-reinvestme...