Estelle has an antique desk that she does not need, whereas Joel and his wife
have a new house with no furniture. Estelle and Joel would like to arrange a
trade, whereby Joel would get the desk at a price. In addition, the desk could
use restoration work, which would enhance its value to Joel. Specifically, the
desk is worth 0 to Estelle (its current owner), regardless of whether it is
restored. An unrestored desk is worth \(\$ 100\) to Joel, whereas a restored
desk is worth \(\$ 900\). Neither Joel nor Estelle has the skills to perform the
restoration. Jerry, a professional actor and woodworker, can perform the
restoration at a personal cost of \(\$ 500\). Jerry does not need a desk, so his
value of owning the restored or unrestored desk is 0 .
(a) Suppose Estelle, Jerry, and Joel can meet to negotiate a spot contract
specifying transfer of the desk, restoration, and transfer of money. Model
this as a three-player, joint-decision problem, and draw the appropriate
extensive form. Calculate the outcome by using the standard bargaining
solution, under the assumption that the players have equal bargaining weights
\(\left(\pi_{\mathrm{E}}=\pi_{\text {Jerry }}=\pi_{\text {Joel }}=1 /
3\right)\). Does the desk get traded? Is the desk restored? Is this the
efficient outcome?
(b) Suppose spot contracting as in part (a) is not possible. Instead, the
players interact in the following way. On Monday, Estelle and Jerry jointly
decide whether to have Jerry restore the desk (and at what price to Estelle).
If they choose to restore the desk, Jerry performs the work immediately. Then
on Wednesday, regardless of what happened on Monday, Estelle and Joel jointly
decide whether to trade the desk for
money. Model this game by drawing the extensive form. (Hint: The extensive
form only has joint-decision nodes.) Assume the parties have equal bargaining
weights at all joint-decision nodes. Determine the negotiation equilibrium.
Compare the outcome with that of part (a).
(c) Now suppose the players interact in a different order. On Monday, Estelle
and Joel jointly decide whether to trade the desk for money. Trade takes place
immediately. On Wednesday, if Joel owns the desk, then he and Jerry jointly
decide whether to have Jerry restore the desk (and at what price to Joel). If
they choose to restore the desk, Jerry performs the work immediately. Model
this game by drawing the extensive form. (Hint: Again, the extensive form only
has joint-decision nodes.) Assume the parties have equal bargaining weights at
all jointdecision nodes. Determine the negotiation equilibrium. Compare the
outcome with that of parts (a) and (b).
(d) Explain the nature of the hold-up problem in this example.