Here is the attachment file of the homework. I am competely lost and I was wandering if i can get help!!1
February 17, 2015
due: February 24, 2015
Law and Economics
Problem Set 3
The probem set is out of 50 points.
This question relates to the form of employment contract between a real estate agent and
her real estate agency (like Coldwell-Banker or Century 21).
The agency provides the
agent with a desk, secretarial and paralegal services, and its reputation for honest dealing.
Susan is a real estate agent.
Since she is a single mother, she is concerned with
the uncertainty associated with her volume of sales. The brokerage contract between the
seller (of a home that has been put on the market for sale) and the real estate agent
specifies a commission of 6% (payable upon sale).
The listing agency presents Susan
with two options.
She can split her commission earnings 50-50 with the agency or pay an
annual franchise fee of $60,000 to the agency and receive the entire commission.
The question has two parts.
In part A, there is no moral hazard.
In part B, there is
Her expected sales are $3,000,000 with a probability of 0.5 and $1,333,333 with a
probability of 0.5.
Her utility function is u = y
, where y is her employment income.
a) (4) Calculate her expected income, expected utility, certainty-equivalent income, and
risk premium under the 50% of commission earnings contract.
b) (2) Would she prefer receiving 50% of the commission income or paying the annual
franchise fee and receiving the entire commission? Show the calculations.
We now take into account that Susan can decide how hard she will work.
works hard, her expected sales are $3,000,000 with a probability of 0.75 and $1,333,333
with a probability of 0.25, and her utility function is u = 0.9y
. If she does not put in the
extra effort, her expected sales are $3,000,000 with a probability of 0.25 and $1,333,333
with a probability of 0.75, and her utility function is u = 1.1y
c) (4) Under the commission contract, would she or would she not choose to work hard?
Show the calculations.