$10.00 Please help me sovle this problem
- From Economics: Game-Theory
- Closed, but you can still post tutorials
- Due on Nov. 05, 2009
- Asked on Nov 02, 2009 at 6:32:59PM
Q:An absentee land owner has a farm and
hires a worker to work it. The output of the farm as a function of the worker’s
effort, e, is e½ (that is, the square root of e). The land owner can not directly
observe the worker’s effort, but she does get to write a contract ahead of time,
specifying the share a of output that the worker gets to keep. The worker learns
a, and then chooses his effort level e. Effort is costly to the worker. Given a and
e, the land owner’s utility is uL(a,e) = (1 – a)e½
(that is, the share of the output
the land owner keeps), and the worker’s utility (which could, in principle, be
negative) is uW(a,e) = ae½ – e (that is, her share of output minus her effort).
Assume that both a and e are no smaller than 0 and no larger than 1.
a. Given an a, what level of effort will a worker choose in a Subgame
Perfect Nash Equilibrium?
b. Use backward induction and your answer in (a) to find the level of a the
land owner will set and the effort level e that the worker will choose in the
Subgame Perfect Nash Equilibrium.
c. Suppose that a benevolent social planner wants to maximize the sum of
the two players’ utilities but that this social planner cannot specify a, the
land owner still gets to do this. Instead, the social planner only gets to set
e. What e will the social planner choose? Is the choice affected by the
choice of a?
d. Suppose that a benevolent social planner wants to maximize the sum of
the two players’ utilities but that this social planner cannot specify e, the
worker still gets to choose this. Instead, the social planner only gets to set
a. What a will the social planner choose?
