5. Consider a setting like the mug experiment described in class. An agent has current wealth in and may have II] or 1 mugs. Let in stand for the number of mugs. An allocation is a (m, 11)) pair. For instance, (1,15) means I have a 1 mug and $15, while (0, 20) means 0 mugs and $20. Suppose that the agent's utility for allocations is given by a(m, as) = u1(m) + u2(w) where u(m) 6 ifmzl 1 _ o ifm=0 for 6 > 0 and 152(10): w. (a) Suppose the agent does not own a mug. Compute Willingness-toPay (WTP). That is, WTP solves: u(1,m WTP) = u[0,w). That is, this is the highest price a person would be willing to pay to acquire a mug. (b) Suppose the agent does own a mug. Compute Willingness-toAccept (WTA). That is, WTA solves: u(1, m} = u(0, w + WTA). That is, this is the lowest price a person would be willing to accept to give up a mug. (c) Calculate WTA - WTP. Explain what this means in a few sentences. Hint: This is a standard utility maximizing agent. Now consider again the same setup as above: an agent has current wealth to and may have m E {0,1} mugs. An allocation is a (m,w) pair. Now, suppose that the agent is loss averse with utility for allocations given by n(m, w | r] = m (m | n) + w (w | m) where v (m|r) 6(mr1) ifm>r1 1 1 z\\ (6(1'1 m)) if m 5 r1 and wrg ifw>r2 v w r = M I?) {Mrgw) iwarg for 6 > 0, A 2 1. The reference point r = {r1,r2) is given by the agent's current situation (the status quo). {(1) Suppose the agent does not own a mug. Compute WTP. (e) Suppose the agent does own a mug. Compute WTA. (1") Calculate WTA - WTP as a function of A. When is it positive? How does it change as A increases