Scenario 1 (length: as needed)
You are considering auctioning a Leonardo Da Vinci original sketch. You entice four bidders to come to your auction. The biddersâ€™ valuations of the sketch in decreasing order are $3.0, $2.2, $2.0, and $1.5 (in millions).
- If you used a second-price sealed bid auction, who would win and what would the winning price be?
- If you used a first-price sealed bid auction and the optimal strategy for the participants was to shade their bid by 20% and the participants used this strategy, who would win and what would the winning price be?
- Which auction should you choose to maximize your profit?
Answer the above questions if the valuations of the sketch are $3.0, $2.7, $2.0 and $1.5.
Scenario 2 (length: 0.5 page)
In the auction described above, suppose that you could entice additional bidders to attend your auction. However, none of the new bidders would have a valuation greater than $3.0 million. Despite that fact, you expect the amount that the winning bidder must pay to increase regardless of the type of auction you use (first- or second-price sealed bid). For each auction, explain why you would expect the auction price to increase. If you want, you may assume the valuations of the original four participants are $3.0, $2.2, $2.0 and $1.5 million.
Scenario 3 (length: 0.5 page)
Some recent Super Bowl advertisements have spent very little time mentioning anything about their product–or even the name of the company. In particular, the two-minute long Ram Trucks “Farmer” commercial had only a few brief and almost unidentifiable views of their product until the last ten seconds of the commercial. Further, the name of the company was only mentioned in the last five seconds of that commercial. Explain why this commercial demonstrated the concept of signaling described in the textbook. In other words, why should consumers be convinced that a Ram truck is of high quality because of the airing of that commercial?
Scenario 4 (length: as needed)
Suppose there are two types of people who need health insurance; high-risk and low-risk consumers. High-risk consumers have a relatively high probability of needing expensive medical care and on average incur $2,000 of medical expenses per year. The high-risk consumers would be willing to pay up to $2,500 for insurance that covers all their medical bills. Low-risk consumers would be willing to pay up to $1,500 for full-coverage insurance and on average would incur on average $1,200 in medical bills. Assume 1/3 of all consumers are high-risk and the remaining 2/3 of consumers are low-risk. Consumers know whether they are high-risk or low-risk. The insurance company knows 2/3 of all consumers are low-risk but cannot identify which consumers are low-risk.
- If all consumers bought insurance, what price must the insurance company charge to break even in expectation? That is, what price must the insurance company charge so that the expected payments equals the premium?
- Which consumers would purchase insurance at that price?
- Are there wealth-creating transactions that are not consummated because of the information asymmetry?
Scenario 5 (length: 0.5 â€“ 1 page)
A struggling company currently has a net worth of $700,000. It owes $500,000 from debt financing (assume these are loans from the bank if you wish). The value of the company to the owners is the difference between the net worth and the amount owed to the debt holders. What is the current value of the firm to the owners?
Now assume that a project is presented to the owners that results in a loss of the entire worth of the company with a probability of 50% and results in a gain of $500,000 with probability 50% (resulting in a net worth of $1,200,000). Show that this in expectation decreases the firmâ€™s value, and explain why, in spite of that, the owners of the company would want to undertake the project.