I need some help in this problem

Q 1: what will that investor choose according to Efficient market Hypothesis?

The Two Envelope Paradox: The Infinite Case PAUL CASTELL & DIDERIK BATENS Jackson, Menzies and Oppy conclude their paper (above) with the follow- ing comment: 'Our diagnosis of where the reasoning in the original case goes astray depended on the fact that the subject knows that the amount of money is bounded top and bottom. This assumption could be dispensed with in fantastical cases... It would still be wrong to prefer one envelope over the other. However, we cannot offer the same diagnosis of the error in the expected value calculation to the opposite conclusion... we can reasonably insist that "the standard method for probabilistic and expected value reasoning ought not to be applied in such cases.' It seems to us that it is precisely in these fantastical' cases that the Two Envelope Paradox is a serious conceptual challenge. We show that the paradox can indeed be tackled in the infinite case using 'standard methods'. 1. To recap: Mary is a Bayesian who is allowed to pick one of two enve- lopes, A and B.2 The only information given to her is that each envelope contains a cheque in dollars and that the figure on one cheque is the double of the figure on the other. Mary picks envelope A at random, say by tossing a coin. Before opening either envelope Mary is given the opportunity to swap A for B. Should she do so? She is also given the opportunity to swap after opening one of the envelopes. Should she do so? Before opening she reasons that supposing A contains $x, then B contains either $2x or $x/2. She judges each equally likely, so the expected value of B is 1/2.$2x + 1/2.$x/2 = $1.25x. Thus it seems that she has reason to swap (whichever envelope she chooses). We shall not rehearse the case in which the possible values of the cheques form a finite set. Here it is easy to show that the expected gain by swap- ping, before Mary knows the amount in A, is zero (see Kraitchik, p. 253). This is not in the least paradoxical. Before opening her envelope, Mary neither has a reason to swap nor a reason not to swap, but opening enve- lope A sometimes gives her (probabilistic or deductive) reason to swap and sometimes gives her (deductive) reason not to swap. The infinite case that we investigate next is far more interesting. Here it The finite case was already treated perfectly well by M. Kraitchik in La Mathema- tique des Jeux (Bruxelles: Imprimerie Stevens Frres, 1930), p. 253: 'Le paradoxe des cravates'. 2 We suppose that Mary accepts Bayes's rule and the principle of maximum expected utility, and that her utilities are proportional to monetary units. ANALYSIS 54.1, January 1994, pp. 46-49. Paul Castell & Diderik Batens The Two Envelope Paradox: The Infinite Case PAUL CASTELL & DIDERIK BATENS Jackson, Menzies and Oppy conclude their paper (above) with the follow- ing comment: 'Our diagnosis of where the reasoning in the original case goes astray depended on the fact that the subject knows that the amount of money is bounded top and bottom. This assumption could be dispensed with in fantastical cases... It would still be wrong to prefer one envelope over the other. However, we cannot offer the same diagnosis of the error in the expected value calculation to the opposite conclusion... we can reasonably insist that "the standard method for probabilistic and expected value reasoning ought not to be applied in such cases.' It seems to us that it is precisely in these fantastical' cases that the Two Envelope Paradox is a serious conceptual challenge. We show that the paradox can indeed be tackled in the infinite case using 'standard methods'. 1. To recap: Mary is a Bayesian who is allowed to pick one of two enve- lopes, A and B.2 The only information given to her is that each envelope contains a cheque in dollars and that the figure on one cheque is the double of the figure on the other. Mary picks envelope A at random, say by tossing a coin. Before opening either envelope Mary is given the opportunity to swap A for B. Should she do so? She is also given the opportunity to swap after opening one of the envelopes. Should she do so? Before opening she reasons that supposing A contains $x, then B contains either $2x or $x/2. She judges each equally likely, so the expected value of B is 1/2.$2x + 1/2.$x/2 = $1.25x. Thus it seems that she has reason to swap (whichever envelope she chooses). We shall not rehearse the case in which the possible values of the cheques form a finite set. Here it is easy to show that the expected gain by swap- ping, before Mary knows the amount in A, is zero (see Kraitchik, p. 253). This is not in the least paradoxical. Before opening her envelope, Mary neither has a reason to swap nor a reason not to swap, but opening enve- lope A sometimes gives her (probabilistic or deductive) reason to swap and sometimes gives her (deductive) reason not to swap. The infinite case that we investigate next is far more interesting. Here it The finite case was already treated perfectly well by M. Kraitchik in La Mathema- tique des Jeux (Bruxelles: Imprimerie Stevens Frres, 1930), p. 253: 'Le paradoxe des cravates'. 2 We suppose that Mary accepts Bayes's rule and the principle of maximum expected utility, and that her utilities are proportional to monetary units. ANALYSIS 54.1, January 1994, pp. 46-49. Paul Castell & Diderik Batens