Your utility function is unreadable. Also, what is the point of substituting ... for letters in certain words? Are you cut-and-pasting from some assignment with special Dutch language characters?
Good luck
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 di¤er 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
1
2
h
while the bad Zwarte Pieten utility function is
Ub = w h
While the time spent in the cold by potential Zwarte Pieten does not
a¤ect their productivity it does a¤ect their well-being.
(a) Draw a diagram in (w; h) space and establish that the single-
crossing condition is satis…ed. In the same diagram indicate the
zero pro…t conditions for the Santa Claus committee. [20 marks]
Also, depict the zero pro…t condition for a …rm that hires an g-
type ZP and for a …rm that hires an b-type ZP, respectively. [Note:
These zero-pro…t conditions are represented by lines along which
the di¤erence between wage and productivity is equal to zero, i.e.
for which wg = 4000 and wb = 400.]
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