3. (16) Principal-agent problem This question relates to the form of employment

Question

3. (16) Principal-agent problem 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 moral hazard. A. 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 = y1/2, 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) (3) Calculate her expected income, expected utility, certainty-equivalnet income, and risk premium under the franchise contract. c) (1) Would she prefer receiving 50% of the commission income or paying the annual franchise fee and receiving the entire commission? B. We now take into account that Susan can decide how hard she will work. If she 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 = 0.9y1/2. 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 = 1.1y1/2. d) (4) Under the commission contract, would she or would she not choose to work hard? Show the calculations. e) (3) Under the franchise contract, would she or would she not choose to work hard? Show the calculations. f) (1) Would she prefer the commission contract or the franchise contract?

Explanation / Answer

a) EI Expected Income = 0.5*0.06*3000000+ 1333333*0.5*0.06 = 90000*0.5 + 40000*0.5 = $65000

Expected utility = 0.5U(90000) + 0.5U(40000) = 150 + 100 = 250

CR Certaininty equivalent Income = U^2 = 250^2 = $62500

Risk Premium = 65000-62500 = $2500

b) EI Expected Income = (0.06*3000000+ 1333333*0.06)*0.5 - 60000 = 90000 + 40000 - 60000 = $70000

Expected utility = 0.5U(180000) + 0.5U(80000) - U(60000) = 108.6

CR Certaininty equivalent Income = U^2 = 108.6^2 = $11795

Risk Premium = 70000-11795 = $58205

c) So she should not go with franchise option though expected earning is high but risk premium is very high and utility has decreased.

d) If she works hard

EI Expected Income = 0.5*0.06*3000000+ 1333333*0.5*0.06 = 90000*0.75 + 40000*0.25 = $77500

Expected utility = 0.75U(90000)*0.9 + 0.25U(40000)*0.9 = 247.5

CR Certaininty equivalent Income = U^2/0.81 = 247.5^2/0.81 = $75625

Risk Premium = 77500-575625 = $1875

If not work hard

EI Expected Income = 0.5*0.06*3000000+ 1333333*0.5*0.06 = 90000*0.25 + 40000*0.75 = $52500

Expected utility = 0.75U(90000)*1.1 + 0.25U(40000)*1.1 = 247.5

CR Certaininty equivalent Income = U^2/1.21 = 247.5^2/1.21 = $50625

Risk Premium = 52500-505625 = $1875

So as expected utility and risk premium is same so it is equal if she work hard or not.

Related Questions

Navigate

• Browse (All)
• Browse 3
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.