Consider the two options in the following table, both of which have random outcomes:
Option 1 |
Option 2 |
||
Probability of Outcome |
Possible Outcomes ($) |
Probability of Outcome |
Possible Outcomes ($) |
1/16 |
150 |
1/5 |
120 |
4/16 |
300 |
1/5 |
255 |
6/16 |
750 |
1/5 |
1,500 |
4/16 |
300 |
1/5 |
255 |
1/16 |
150 |
1/5 |
120 |
a. Determine the expected value of each option.
Expected value of Option 1: $[removed]
Expected value of Option 2: $[removed]
b. Determine the variance and standard deviation of each option.
Instruction: Round your answers for standard deviation to 2 decimal places.
Variance of Option 1: [removed]
Standard deviation of Option 1: [removed]
Variance of Option 2: [removed]
Standard deviation of Option 2: [removed]
c. Which option is most risky?
rev: 06_10_2013_QC_3
Problem 12-02
For each of the following scenarios, determine whether the decision maker is risk neutral, risk averse, or risk loving. |
a. |
A manager prefers a 20 percent chance of receiving $1,400 and an 80 percent chance of receiving $500 to receiving $680 for sure. |
[removed] |
Risk averse. |
[removed] |
Risk neutral. |
[removed] |
Risk loving. |
b. |
A shareholder prefers receiving $920 with certainty to an 80 percent chance of receiving $1,100 and a 20 percent chance of receiving $200. |
[removed] |
Risk loving. |
[removed] |
Risk averse. |
[removed] |
Risk neutral. |
c. |
A consumer is indifferent between receiving $1,360 for sure and a lottery that pays $2,000 with a 60 percent probability and $400 with a 40 percent probability. |
[removed] |
Risk loving. |
[removed] |
Risk neutral. |
[removed] |
Risk averse. |
Problem 12-03
Your store sells an item desired by a consumer. The consumer is using an optimal search strategy; the accompanying graph shows the consumer’s expected benefits and costs of searching for a lower price. |
a. |
What is the consumer’s reservation price? |
$[removed]
b. |
If your price is $3 and the consumer visits your store, will she purchase the item or continue to search? |
[removed] |
She will continue to search. |
[removed] |
She will purchase the item. |
c. |
Suppose the consumer’s cost of each search rises to $16. What is the highest price you can charge and still sell the item to the consumer if she visits your store? |
$[removed]
d. |
Suppose the consumer’s cost of each search falls to $2. If the consumer finds a store charging $3, will she purchase at that price or continue to search? |
[removed] |
She will purchase the item. |
[removed] |
She will continue to search. |
Problem 12-14 (Algo)
BK Books is an online book retailer that also has 10,000 “bricks and mortar” outlets worldwide. You are a risk-neutral manager within the Corporate Finance Division and are in dire need of a new financial analyst. You only interview students from the top MBA programs in your area. Thanks to your screening mechanisms and contacts, the students you interview ultimately differ only with respect to the wage that they are willing to accept. About 20 percent of acceptable candidates are willing to accept a salary of $50,000, while 80 percent demand a salary of $80,000. There are two phases to the interview process that every interviewee must go through. Phase 1 is the initial one-hour on-campus interview. All candidates interviewed in Phase 1 are also invited to Phase 2 of the interview, which consists of a five-hour office visit. In all, you spend six hours interviewing each candidate and value this time at $850. In addition, it costs a total of $4,400 in travel expenses to interview each candidate. |
You are very impressed with the first interviewee completing both phases of BK Books’s interviewing process, and she has indicated that her reservation salary is $80,000. Should you make her an offer at that salary or continue the interviewing process? |
[removed] |
Continue the interviewing process. |
[removed] |
You should be indifferent between these two options. |
[removed] |
Make her an offer. |
Problem 12-05 (Algo)
A risk-neutral consumer is deciding whether to purchase a homogeneous product from one of two firms. One firm produces an unreliable product and the other a reliable product. At the time of the sale, the consumer is unable to distinguish between the two firms’ products. From the consumer’s perspective, there is an equal chance that a given firm’s product is reliable or unreliable. The maximum amount this consumer will pay for an unreliable product is $0, while she will pay $170 for a reliable product. |
a. |
Given this uncertainty, what is the most this consumer will pay to purchase one unit of this product? |
$[removed]
b. |
How much will this consumer be willing to pay for the product if the firm offering the reliable product includes a warranty that will protect the consumer? |
$[removed]
Problem 12-18 (Algo)
Pelican Point Financial Group’s clientele consists of two types of investors. The first type of investor makes many transactions in a given year and has a net worth of over $2.5 million. These investors seek unlimited access to investment consultants and are willing to pay up to $35,000 annually for no-fee-based transactions, or alternatively, $50 per trade. The other type of investor also has a net worth of over $2.5 million but makes few transactions each year and therefore is willing to pay $100 per trade. |
As the manager of Pelican Point Financial Group, you are unable to determine whether any given individual is a high- or low-volume transaction investor. To deal with this issue, you design a self-selection mechanism that permits you to identify each type of investor. You offer two types of plans for customers with more than $2.5 million in assets: one plan has an annual maintenance fee but offers a large number of “free” transactions (call this the “Free Trade” Account); the other plan has no annual maintenance fee but charges for each transaction (call this the “Free Service” Account). Determine the specifics for each plan as listed below: |
“Free Trade” Account:
Annual maintenance fee |
$[removed] |
Number of “free” transactions |
[removed] |
Price for each transaction in excess of the number of “free” transactions |
$[removed] |
“Free Service” Account:
Price per transaction |
$[removed] |
rev: 06_11_2013_QC_3145
Problem 12-15 (Essay, Autogradable)
Congress enacted the Health Insurance Portability and Accountability Act (HIPAA) to potentially help millions of employees gain access to group health insurance. The key provision of HIPAA requires insurance companies and health insurance plans administered by employers who self-insure to provide all employees access to health insurance regardless of previous medical conditions. This provision is known as “guaranteed issue” and is a controversial topic in the insurance industry. |
If everyone is free to drop coverage, what type of problem may arise due to “guaranteed issue”? |
[removed] |
Free recall. |
[removed] |
Moral hazard. |
[removed] |
Winner’s curse. |
[removed] |
Adverse selection. |
Problem 12-07 (Algo)
You are one of five risk-neutral bidders participating in an independent private values auction. Each bidder perceives that all other bidders’ valuations for the item are evenly distributed between $20,000 and $50,000. For each of the following auction types, determine your optimal bidding strategy if you value the item at $35,000. |
a. First-price, sealed-bid auction.
[removed] |
Bid $35,000. |
[removed] |
Bid $20,000. |
[removed] |
Bid $32,000. |
[removed] |
Bid $50,000. |
b. Dutch auction.
[removed] |
Let the auctioneer continue to lower the price until it reaches $32,000, and then yell “Mine!”. |
[removed] |
Let the auctioneer continue to lower the price until it reaches $50,000, and then yell “Mine!”. |
[removed] |
Let the auctioneer continue to lower the price until it reaches $35,000, and then yell “Mine!”. |
[removed] |
Let the auctioneer continue to lower the price until it reaches $20,000, and then yell “Mine!”. |
c. Second-price, sealed-bid auction.
[removed] |
Bid $32,000. |
[removed] |
Bid $50,000. |
[removed] |
Bid $35,000. |
[removed] |
Bid $20,000. |
d. English auction.
[removed] |
Remain active until the price exceeds $50,000, and then drop out. |
[removed] |
Remain active until the price exceeds $32,000, and then drop out. |
[removed] |
Remain active until the price exceeds $35,000, and then drop out. |
[removed] |
Remain active until the price exceeds $20,000, and then drop out. |
Problem 12-04
You are the manager of a firm that sells a “commodity” in a market that resembles perfect competition, and your cost function is C(Q) = 2Q + 3Q^{2}. Unfortunately, due to production lags, you must make your output decision prior to knowing for certain the price that will prevail in the market. You believe that there is a 70 percent chance the market price will be $200 and a 30 percent chance it will be $600. |
a. |
Calculate the expected market price. |
$[removed]
b. |
What output should you produce in order to maximize expected profits? |
[removed] units
c. |
What are your expected profits? |
$[removed]
Problem 12-12
As the manager of Smith Construction, you need to make a decision on the number of homes to build in a new residential area where you are the only builder. Unfortunately, you must build the homes before you learn how strong demand is for homes in this large neighborhood. There is a 60 percent chance of low demand and a 40 percent chance of high demand. The corresponding (inverse) demand functions for these two scenarios are P = 300,000 – 400Q and P = 500,000 – 275Q, respectively. Your cost function is C(Q) = 140,000 + 240,000Q. |
How many new homes should you build, and what profits can you expect?
Number of homes you should build: |
[removed] homes |
Profits you can expect: |
$[removed] |
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