9. Moral Hazard Little Kona, a coffee shop in a town, recently hired Albert as a
ID: 1113117 • Letter: 9
Question
9. Moral Hazard
Little Kona, a coffee shop in a town, recently hired Albert as a manager. His effort level cannot be observed. The profit of the restaurant (before paying Albert) is as given in the following table.
Bad economy (Prob. = 0.4)
Good economy (Prob. = 0.6)
Low effort (a = 0)
$40,000
$60,000
High effort (a = 1)
$70,000
$90,000
Suppose Little Kona offers Albert 10% of its profits. Assume that Albert’s utility is given by U = w – C(a), where w = income and C(a) is cost of effort. Assume that C(0) = 0 and C(1) = $5,000.
What level of effort will Albert choose? _____________
Does this profit-sharing contract solve the principal agent problem? ____________
Explain. _______________________________________________________________________
________________________________________________________________________.
Show your working here:
Suppose Little Kona offers fixed compensation X to Albert if revenue equals $60,000 or more, and zero compensation otherwise. What is the minimum value of X that Little Kona must offer (to Albert) in order to induce high effort (a =1). _____________________.
What profit does Little Kona earn if sets compensation equal to X? _______________.
Show your working here:
Bad economy (Prob. = 0.4)
Good economy (Prob. = 0.6)
Low effort (a = 0)
$40,000
$60,000
High effort (a = 1)
$70,000
$90,000
Explanation / Answer
E(u)=.4(4000) + .6(6000)
=1600+3600
=5200$
Albert’s expected payoff when he makes effort
Cost of effort is 5000$
E(u)=.4(7000-5000) +.6(9000-5000)
=.4(2000) +.6(4000)
=800+2400
=3200$
So Albert will choose to make low effort as his expected utility is higher when he makes low effort.
The profit sharing contract doesn’t solve the principle agent problem as Albert is motivated to act in his own best interests which are contrary to Little Kona’s interests.
The minimum value of x should make Albert’s payoff when he makes effort equal to or more than the payoff that he makes when he makes low effort.
.4(x-5000) + .6(x-5000) =5200
.4x-2000+.6x-3000=5200
X=10200
The minimum value of x is 10200$
When x is 10200$ Little Kona’s profit is
.4(70000-10200) +.6(90000-10200)
=71800
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