please help solving this

Question

Base on the understanding of Efficient market Hypothesis and Behavioral Finance two envelopes represent investment opportunities: What should the investor do ? choose envelope 1 or 2 ?

Case study You are offered the choice of two envelopes and are toldthatone contains twice as much money as the other. You make your choice, openenvelope one, and find that it contains $200. The referee asks if you would prefer envelope two. Since one envelope contains twice as much money as the other, but you do not know whether you have chosen the larger or the smaller, you know that the second envelope contains either $400 or $100, so you stand to gain $200 or lose $100 by switching from envelope one to envelope two. Do you switch? The source of the difficulty is that the problem is not sufficiently well defined. Here are some versions ofit which seem to give enough backgroundto enable you to make a decision. Version 1. The referee was given two sums ofmoney, one twice the size of the other, and tossed a coin to decide which one to put in each envelope. Version 2. The referee made a random drawing of a number on an interval (A,B). He then put that amount of moneyin one envelope andtwice as much in the other. Version 3. After you've opened the envelope the referee offers to toss a coin and depending on whether it comes heads ortails he will either double orhalve the amount of moneyyoureceive. Ifyou apply the criterion of maximising the expected value of a gamble, the answer to version 1 is that it doesn't matter what you do since the expectedvalue of each envelope is the same. The solution to Version 2 is that if the amount ofmoney you find in the first envelope is less than A+B) you should switch, andifitis more you should stick with your initial choice. Andif you find yourselfin version 3 you should accept the referee's offerto toss a coin. So which is the real problem, and the correct solution? You don't have enough infomation to know. So the answer to the question what should you do if faced with the two envelope problem is 'I don't know. Welcome to the world of radical uncertainty. Many theoretical economists will make all necessary additional assumptions in order to anive at a frigorous' answer. Many young MBAs in consulting firms will make up whatever numerical infomation is needed to predict the outcome of your choice. It is not clear what is leamt from either of these exercises. So what should the decision-maker do? Begin by asking what is going on here?' The trouble with the present case is that nothingis going on here. The problem is devoid of any context, which distinguishes it from any situationlikely to be faced in the real world. Often these kinds of problem are set in the laboratories of behavioural economists, who have normative models in their minds and who hopeto show thatindividuals fail to conform to their models of rationality. The shrewd participanthas the options of giving the answer the professor wants to hear-and helping him or her publish another paper describing the 'biases' displayed by supposedly rational' individuals; or of giving what the participant thinks is the right answer, or of giving the answer which the participant thinks the professor thinks is the right answer. It is a dilemma which clever students have faced since the time of the ancient Greeks. If someone was confronted with the two envelope problemin reallife, they would look for clues from the context. Who has organised the event andwhatmight be their motives? Does the referee seem friendly or hostile? Does he seem to know what is in each envelope? Is one envelope fatter than the other? They would drawon their wider knowledge of the world and the visual clues that have such animportant influenceonour actions. They would very sensibly ask whatis going on here? Version 1 resembles the philosophical problem often labeled as Burden's ass Athirsty and hungry donkey is placed equidistantbetween a trough of water andbale ofhayand dies of thirst and hunger because there is no rationalreason to choose one option rather thanthe other. What a decisionis may be less important thanmaking some decision. Elliott, patient of the neurophysiologist Antonio Darnasio, had sufferedbrain damage which destroyed his capacity for emotional response. As a result he would spend very large amounts of time debating trivial issues, such as the time of his next appointment. Ulysses Grant, the most successful of civil war generals and future US President, responded to the question are you sure you are right?': 'No, I am not, but in war anythingis better than indecision. We must decide. If I am wrong, we shall soon findit out and can do the other thing. But not to decide wastes both time andmoney, andmay ruin everything. Analogous issues are reported in modem electronics, where continuous variables must be translated into binary ones or vice versa and only microseconds are available for the choice. Almost everyone has experienced the committee which deliberates endlessly because there always might be a better option than the proposal under discussion. So version 2, in which the choice is whether to take up a fimm offer or to reject it in favour of an altemative that might or might not be betteris a common issue; one with which decision makers are very often faced What college to go to what house to buy, which potential partner to marry? A strategy which considers the range of possible outcomes andaccepts the offer which meets a predetermined thresholdis often a good way ofhandling these issues. In the real world, satisficing-looking for a solution that is good enough rather than the best possible-is generally superior to optimisation in conditions of radical uncertainty. The model developed here for version 2 is in the family of the threshold strategies developedby game theorists and the stopping rule, or secretary problem discussed in decision theory. Version 3 raises the question of when is it right to maximise the expected value of a gamble? If you are faced with repeated problems of similarkind-ifyou go to the casino to play roulette every night, then in the long run you will be better offif you perfom expected value calculations. However, people who perfomexpected value calculations are almost certainly not people who go to the casino very often Casinos and betting shops rely on the patronage of those who don't Many problems are essentially unique. When should the coronavirus lockdown be lifted? Ina one-off decision like that maximising expected value may or may notbe the right thing to do; it is certainly wise also to ask the question 'how would I feelifit went wrong? Minimising regret is a natural and often sensible approach. Maximising expected value seems appropriate if you are faced with a series of problems which are similar to each other, but what does 'similar' mean? The regret felt as a result of a badinvestment may be offset by the joy ofmaking a good one, but the regret at having chosenthe wrong college may not be offset by thejoy offinding the right partner-the two emotions are simply not additive. The value of economic models is to be found notin their ability to make specific predictions or recommendations because any such modelis likely to be at best a very rough approximationto the world of radical uncertainty, but in yielding insights which can be applied in a range of practical problems. And only a few economic models actually do. Models of the two envelope problem do yield such insights, but these are not the ones that are apparent at first sight. The two envelope problemis intriguing and illuminating, but not because it gives an answer to the question 'what should you do if confronted by two envelopes? paint Case study You are offered the choice of two envelopes and are toldthatone contains twice as much money as the other. You make your choice, openenvelope one, and find that it contains $200. The referee asks if you would prefer envelope two. Since one envelope contains twice as much money as the other, but you do not know whether you have chosen the larger or the smaller, you know that the second envelope contains either $400 or $100, so you stand to gain $200 or lose $100 by switching from envelope one to envelope two. Do you switch? The source of the difficulty is that the problem is not sufficiently well defined. Here are some versions ofit which seem to give enough backgroundto enable you to make a decision. Version 1. The referee was given two sums ofmoney, one twice the size of the other, and tossed a coin to decide which one to put in each envelope. Version 2. The referee made a random drawing of a number on an interval (A,B). He then put that amount of moneyin one envelope andtwice as much in the other. Version 3. After you've opened the envelope the referee offers to toss a coin and depending on whether it comes heads ortails he will either double orhalve the amount of moneyyoureceive. Ifyou apply the criterion of maximising the expected value of a gamble, the answer to version 1 is that it doesn't matter what you do since the expectedvalue of each envelope is the same. The solution to Version 2 is that if the amount ofmoney you find in the first envelope is less than A+B) you should switch, andifitis more you should stick with your initial choice. Andif you find yourselfin version 3 you should accept the referee's offerto toss a coin. So which is the real problem, and the correct solution? You don't have enough infomation to know. So the answer to the question what should you do if faced with the two envelope problem is 'I don't know. Welcome to the world of radical uncertainty. Many theoretical economists will make all necessary additional assumptions in order to anive at a frigorous' answer. Many young MBAs in consulting firms will make up whatever numerical infomation is needed to predict the outcome of your choice. It is not clear what is leamt from either of these exercises. So what should the decision-maker do? Begin by asking what is going on here?' The trouble with the present case is that nothingis going on here. The problem is devoid of any context, which distinguishes it from any situationlikely to be faced in the real world. Often these kinds of problem are set in the laboratories of behavioural economists, who have normative models in their minds and who hopeto show thatindividuals fail to conform to their models of rationality. The shrewd participanthas the options of giving the answer the professor wants to hear-and helping him or her publish another paper describing the 'biases' displayed by supposedly rational' individuals; or of giving what the participant thinks is the right answer, or of giving the answer which the participant thinks the professor thinks is the right answer. It is a dilemma which clever students have faced since the time of the ancient Greeks. If someone was confronted with the two envelope problemin reallife, they would look for clues from the context. Who has organised the event andwhatmight be their motives? Does the referee seem friendly or hostile? Does he seem to know what is in each envelope? Is one envelope fatter than the other? They would drawon their wider knowledge of the world and the visual clues that have such animportant influenceonour actions. They would very sensibly ask whatis going on here? Version 1 resembles the philosophical problem often labeled as Burden's ass Athirsty and hungry donkey is placed equidistantbetween a trough of water andbale ofhayand dies of thirst and hunger because there is no rationalreason to choose one option rather thanthe other. What a decisionis may be less important thanmaking some decision. Elliott, patient of the neurophysiologist Antonio Darnasio, had sufferedbrain damage which destroyed his capacity for emotional response. As a result he would spend very large amounts of time debating trivial issues, such as the time of his next appointment. Ulysses Grant, the most successful of civil war generals and future US President, responded to the question are you sure you are right?': 'No, I am not, but in war anythingis better than indecision. We must decide. If I am wrong, we shall soon findit out and can do the other thing. But not to decide wastes both time andmoney, andmay ruin everything. Analogous issues are reported in modem electronics, where continuous variables must be translated into binary ones or vice versa and only microseconds are available for the choice. Almost everyone has experienced the committee which deliberates endlessly because there always might be a better option than the proposal under discussion. So version 2, in which the choice is whether to take up a fimm offer or to reject it in favour of an altemative that might or might not be betteris a common issue; one with which decision makers are very often faced What college to go to what house to buy, which potential partner to marry? A strategy which considers the range of possible outcomes andaccepts the offer which meets a predetermined thresholdis often a good way ofhandling these issues. In the real world, satisficing-looking for a solution that is good enough rather than the best possible-is generally superior to optimisation in conditions of radical uncertainty. The model developed here for version 2 is in the family of the threshold strategies developedby game theorists and the stopping rule, or secretary problem discussed in decision theory. Version 3 raises the question of when is it right to maximise the expected value of a gamble? If you are faced with repeated problems of similarkind-ifyou go to the casino to play roulette every night, then in the long run you will be better offif you perfom expected value calculations. However, people who perfomexpected value calculations are almost certainly not people who go to the casino very often Casinos and betting shops rely on the patronage of those who don't Many problems are essentially unique. When should the coronavirus lockdown be lifted? Ina one-off decision like that maximising expected value may or may notbe the right thing to do; it is certainly wise also to ask the question 'how would I feelifit went wrong? Minimising regret is a natural and often sensible approach. Maximising expected value seems appropriate if you are faced with a series of problems which are similar to each other, but what does 'similar' mean? The regret felt as a result of a badinvestment may be offset by the joy ofmaking a good one, but the regret at having chosenthe wrong college may not be offset by thejoy offinding the right partner-the two emotions are simply not additive. The value of economic models is to be found notin their ability to make specific predictions or recommendations because any such modelis likely to be at best a very rough approximationto the world of radical uncertainty, but in yielding insights which can be applied in a range of practical problems. And only a few economic models actually do. Models of the two envelope problem do yield such insights, but these are not the ones that are apparent at first sight. The two envelope problemis intriguing and illuminating, but not because it gives an answer to the question 'what should you do if confronted by two envelopes? paint