a general lesson- aggregate outcomes do not always resemble individual outcomes Lets start with a discrete commodity, of which only one unit can be consumed Normalize this to be commodity 1 Proposition Suppose that the preference relation >on X={x1∈{0,1},(x2xL)∈R1},is rational, continuous and locally non-satiated on the commodities other than commodity 1, and if x*={x∈Bo:x≥ y for all y∈Bo}, Where B0={x∈x:x1=0and∑2px≤v andA general lesson– aggregate outcomes do not always resemble individual outcomes. Let’s start with a discrete commodity, of which only one unit can be consumed. Normalize this to be commodity 1. Proposition: Suppose that the preference relation  on X  x1  0, 1,x2,... xL    L1  , is rational, continuous and locally non-satiated on the commodities other than commodity 1, and if x  x  B0 : x  y for all y  B0 , where B0  x  X : x1  0 and i2 L pixi  w , and