Quetion 2[20 marks in total ] Consider a model of one-period investment. There are m states on Date 1 and n securities available for trading. Short sales are allowed. Let aij be the unit price of Security j in State i on Date 1 , and pj be the unit price of Security j on Date 0 . Let A be the mn matrix whose (i,j) entry is aij and p be the 1n matrix whose (1,j) entry is pj. The market is said to satisfy the Law of One Price if for any x,yRn with Ax=Ay, we have px=py. The security j is called redudant if the j th column of A is a linear combination of the other columns of A. 1. [10 marks] (Medium) Assume that A is such that there is no redundant security in the market. Show that the Law of One Price holds no matter what p is. 2. [10 marks] (Straight forward) Consider the following concrete example with three states and four securities. Determine whether this market satisfies the Law of One Price. Ap=1.051.051.050.91.21.20.51.31.300.45;=(11.110.8). Quetion 2[20 marks in total ] Consider a model of one-period investment. There are m states on Date 1 and n securities available for trading. Short sales are allowed. Let aij be the unit price of Security j in State i on Date 1 , and pj be the unit price of Security j on Date 0 . Let A be the mn matrix whose (i,j) entry is aij and p be the 1n matrix whose (1,j) entry is pj. The market is said to satisfy the Law of One Price if for any x,yRn with Ax=Ay, we have px=py. The security j is called redudant if the j th column of A is a linear combination of the other columns of A. 1. [10 marks] (Medium) Assume that A is such that there is no redundant security in the market. Show that the Law of One Price holds no matter what p is. 2. [10 marks] (Straight forward) Consider the following concrete example with three states and four securities. Determine whether this market satisfies the Law of One Price. Ap=1.051.051.050.91.21.20.51.31.300.45;=(11.110.8)