a trader i has following utility function: ui(x1, x2) = x 1 x 1 2 ,

where xi refers to the quantity of asset with price pi , and i = 1, 2 in this case.

Suppose the total money of this trader to be completely used for trading is M, and during the whole trading process the price of asset remains constant.

Determine the optimal quantity xi for each asset that this trader can buy when she wants to maximize her utility function.

Describe in words about her preferences correponding to = 0, = 1, and = 0.5.