Problem set 2

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Problem set 2
Problem set 2
Exercise 1
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• By Thomas and Lars
• PS Choose the environment, choose many pages per
  sheet.

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1. The putting out system
Problem set 2
Exercise 1
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(a) Show that in equilibrium e q ½
Problem set 2
Exercise 1
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Because of the decision making structure the
putter-out maximizes surplus given the home
workers optimal response function.
Problem set 2
Exercise 1
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Home workers maximation problem
Problem set 2
Exercise 1
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The first order condition
Problem set 2
Exercise 1
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• This is also the optimal response function

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The putter outs maximation problem
Problem set 2
Exercise 1
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First order condition
Problem set 2
Exercise 1
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(b) Draw iso-profit and iso-utility curves,
illustrate the equilibrium.
Problem set 2
Exercise 1
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Problem set 2
Exercise 1
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Problem set 2
Exercise 1
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(c) Explain the intuition behind U-shaped
iso-utility curves.
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Problem set 2
Exercise 1
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• If income and effort are separated in the utility
  function, then we would have normal shaped
  iso-utility curves with prefered direction to the
  north-west.
• But when the home worker increases his effort
  marginally, he effects his income as well. Thus,
  we do not have a single negative effect on his
  utility through this increase in effort, but also
  a positive effect through the income increase.

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(d) For which values of q is a
pareto-improvement possible, if e is set to 1?
Problem set 2
Exercise 1
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Problem set 2
Exercise 1
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Problem set 2
Exercise 1
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When e is set to 1 we have that
Problem set 2
Exercise 1
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Pareto improvements are possible when
Problem set 2
Exercise 1
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Problem set 2
Exercise 1
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e) Why isnt such (e,q)-combinations incentive
compatible?
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The nature of the game makes any other values
impossible.
Problem set 2
Exercise 1
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• We assume complete and perfect information in
  this one-shot game, given standard rationality
  assumptions.
• The home worker maximizes his utility, and then
  the putter out maximizes his surplus given the
  workers optimal response. Thus, none of the
  players have an incentive to change his optimal
  strategy.

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Problem set 2
Exercise 1
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• If we had changed the nature of the game, by for
  example cooperation, then we could have achieved
  pareto improvements which were incentive
  compatible.

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2. Contingent renewal
Problem set 2
Exercise 2
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The probability for contingent renewal
p A ae,
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Problem set 2
Exercise 2
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(a) Derive the optimal effort of the worker as
a function of w. (b) Show that e aR /
(1r-p), where R r (u (w,e) / r Vu) is the
unemployment rent.
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Problem set 2
Exercise 2
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Problem set 2
Exercise 2
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Problem set 2
Exercise 2
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Problem set 2
Exercise 2
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where
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Problem set 2
Exercise 2
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(c) Show that de /dw a / (1r-p)
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Problem set 2
Exercise 2
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d) Compare the equilibrium with the
equilibrium in the putting-out system.
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Comparing the two cases
Problem set 2
Exercise 2
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• The overall structure in these two cases has much
  in common, and that is why we have these
  similarities.
• The employer/putter out can not monitor the
  worker completely, and in simular cases with
  monitoring you achive pareto optimality.
• The worker decides his own effort in both cases,
  and he is in a way superior when choosing his
  strategy. If the employer/putter out could have
  dictated him to choose a higher effort, we would
  have achived a pareto optimal situation.

Laget av Thomas Aanensen og Lars Solberg
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