Please answer the following questions on the mathematical proof of endowment eff

Please answer the following questions on the mathematical proof of endowment effect experiement and loss aversion. a. Describe the endowment effect experiment and provide an intuitive argument for how loss aversion can help explain these results. If any addtional information is need to answer the question please let me know.
(1 pt) b. Show mathematically how loss aversion can help explain the result of the endowment effect experiment. We will break this down into several steps. First, some assumptions and notation: Suppose the value of a certain bundle of cash (c) and mugs (m) given a reference point in cash (rc) and a reference point in mugs (rm) is v(c, m|rc, rm) = c + m + µ(c − rc) + µ(m − rm), where µ(z) = ( z z ≥ 0 zλ z < 0. i. Suppose an agent is endowed with a mug (worth m = $2 to them) and no cash, so c =$0, and assume that the reference point for each good is the subject’s endowment of that good. Solve for the value of keeping the mug and thus not getting any cash. (1 pt) ii. Suppose the same agent with the same endowment (and thus the same reference points) is considering trading their mug for c = $3. Solve for value of trading the 1 mug for the money (i.e. the value when m = $0 and c = $3 given the same reference point as before). (1 pt) iii. Suppose the agent decides to keep the mug only if the value in i) is larger than the value in ii). Under what conditions on λ can the agent support keeping the mug? (1 pt) iv. Will the agent always trade their mug for cash if they are offered more money (c) than the mug is worth to them (m)? Explain using your answer in part iii). (1 pt)

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