Stone-Geary 偏好效用函数

The Stone-Geary function is often used tomodel problems involving subsistence levels of consumption.  In these cases, a certain minimal level ofsome good has to be consumed, irrespective of its price or the consumer’sincome.  
The Stone-Geary uses the natural logfunction to model utility.  The sum ofall the proportions of the goods consumed must equal 1.  In the problem below, the subsistence levelsof A and B are α and β.  The term I is income, and pk {k=a,b} arethe prices of A and B.