Posted by James on Sunday, January 3, 2010 at 7:20am.
. As tradition has it, Santa Claus is coming on the 5th of December from
Spain to the Netherlands to bring gifts to Dutch children. Help is
needed to distribute the gifts for which the Santa Claus committee is
hiring helpers, so-called Zwarte Pieten.
There are two types of Zwarte Pieten; good ones who can deliver 4000
gifts in this night, while the bad ones can only manage 400 gifts. Zwarte
Pieten will be paid by their productivity.
While the Dutch Santa Claus committee is not able to observe the
productivity of Zwarte Pieten before the 5th of December, they have to
settle pay beforehand.
The good Zwarte Pieten differ from the bad ones in their cold weather
endurance, which they can use to signal their type by standing in the
cold. The good Zwarte Pieten have a utility function over wages, w,
and hours spend in the cold h
Ug = w - .5h
while the bad Zwarte Pieten utility function is
Ub = w - h
While the time spent in the cold by potential Zwarte Pieten does not
affect their productivity it does affect their well-being.
(a) Draw a diagram in (w; h) space and establish that the single-
crossing condition is satisfi
ed. In the same diagram indicate the
fit conditions for the Santa Claus committee. [20 marks]
Also, depict the zero pro
fit conditions for a fi
rm that hires a g-
type ZP and for a
rm that hires an b-type ZP, respectively. [Note:
t conditions are represented by lines along which
the difference between wage and productivity is equal to zero, i.e.
for which wg = 4000 and wb = 400.]
(b) If the committee could identify the good from the bad Zwarte
Pieten, would any candidate spend any time in the cold?
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