Introduction
These scenarios will give you practice applying concepts from the readings to models of real-world situations.
Activity Instructions
Read the following scenarios and complete the corresponding questions. Please remember to answer in complete and grammatically correct sentences. I am looking for your thought process in the answers to the questions, so be complete in your answers and use the opportunity to clearly demonstrate your newly acquired knowledge.
Scenario 1 (length: as needed)
Suppose the hotel in the lecture example raised its price from $30 to $30.50. With the new price, the hotel expects 96 guests to arrive 5% of the time, 97 guests 10% of the time, 98 guests 20% of the time, 99 guests 30% of the time, 100 guests 25% of the time and 101 guests 10% of the time. The variable costs per occupied room and overbooking costs are the same as in the lecture.
Calculate the expected revenue, expected variable costs and expected costs from overbooking.
Using marginal analysis, should the hotel raise its price? Explain your answer.
Scenario 2 (length: as needed)
You are considering auctioning a Leonardo Da Vinci original sketch. You entice four bidders to come to your auction. The bidders' 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?
How would your answers change to the above questions if the valuations of the sketch are $3.0, $2.7, $2.0 and $1.5?
Scenario 3 (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.