Assignment-
1. The price of flat screen TVs has fallen dramatically since 2001. For example, a 42" retailed for $7999 in 2001; a comparable SONY can be had for about $250 today. At the same time the volume of sales has risen from a trickle to a torrent.
(a) Can shifts in demand for TVs explain these data? What would cause such demand shifts?
(b) How about shifts in supply? What would have caused these shifts?
(c) Do you think changes in both supply and demand have occurred? What do you think the most reasonable explanation for these data? Feel free to include any information you like to buttress your case; do not get hung up on the specifics of flat screen technology, e.g. plasma versus LED.
2. One of the most widely-prescribed pharmaceutical products is methylphenidate, a prescription drug (patented by Ciba, now Novartis, in 1954) marketed under the name Ritalin. Ritalin is a stimulant used in the treatment of "Attention Deficit Disorder" (A.D.D.). A.D.D. is a common and somewhat controversial problem, most prevalent in children between the ages of six and twelve; A.D.D. used to be called "hyperactivity."
Children having A.D.D. experience varying degrees of difficulty in concentrating. Concentration appears to be improved by stimulating blood flow to the frontal lobes of the brain. Clinically, Ritalin stimulates blood flow and seems to be effective in reducing the symptoms of A.D.D. for many children, although the mechanism through which this occurs is unclear.
"Central Audition Disorder" (C.A.D.) is another common childhood disorder. C.A.D. is a deficiency in the hearing software; i.e. it is not a physical problem with the hearing apparatus, but rather some sort of information processing problem. Many of the symptoms of C.A.D. are similar to those of A.D.D. In fact, medical researchers wonder whether A.D.D. and C.A.D. are different, or just the same problem showing up in different ways. If A.D.D. and C.A.D. are the same or closely-related disorders, then Ritalin might prove to be an effective treatment for C.A.D. Does methylphenidate alleviate the symptoms of C.A.D.?
The data include information on 64 children, all of whom had been diagnosed as suffering from C.A.D. The children were given a battery of auditory tests; the data below are from a "binaural resynthesis" test (minimum possible score, 0; maximum, 100; scores in increments of five). Next, half the children (treatment group) were given Ritalin - about .5 mg./kg. of body weight - half received a placebo (control group), and all were retested. Neither the doctors nor the subjects knew who received Ritalin (a "double blind experimental design").
The Excel file Ritalin.xlxs contains data on
- Improvement - Second test score minus first;
- Treatment - a variable equal to one for the treatment group and zero for the control;
Novartis has various options. One is simply to go ahead and market Ritalin as a treatment for C.A.D. Alternatively, they could conduct a large, but expensive, set of clinical trials that would provide much better information on how Ritalin influences C.A.D., then decide on whether to go to market. They can also do nothing further. If the product goes to market, the controversial nature of Ritalin makes an expensive and embarrassing lawsuit a possibility; whether this occurs will depend a lot on how the drug ultimately performs. The decision problem may be described as:
- Choose whether to do a clinical trial, the cost of which is $1 (million). For our purposes you may assume that what you would like to know is which of three possibilities is most descriptive, and that the clinical trial will reveal this perfectly. The three relevant possibilities (described more fully below): "low," "medium" and "high". These correspond to the situations that generate the different legal outcomes set out below.
- Next, decide whether to market the product. The total cost of the marketing effort will be $1.5 million. If there is no clinical trial, you proceed directly to this step.
- If the product is marketed, experience will reveal the true impact of the drug, and determine whether you get sued. There are three cases to worry about. First, the medication might have a small or negative impact ("low"). This will generate $1 million in profit from sales, but lead to a lawsuit which will be litigated and lost, resulting in damages of $5 million and legal expenses of $1 million. Second, the impact might be positive but not very large. This "medium" outcome will also generate a lawsuit, but it will be won, avoiding the damages but still causing the legal fees to be incurred. It will also yield profit from sales equal to $10 million. Finally the product may have a large beneficial effect. If this happens there will be no suit and profits from sales will be $20 million.
(a) Describe Novartis' decision using a decision tree.
(b) Given the data, what decision do you recommend? Explain. (I do not expect an elaborate statistical analysis of the data; however, you may analyze it in any manner you see fit.)
3. Your firm has assembled a three person team to commercialize an idea R&D has discovered. One employee (R) is from R&D, another is a marketing manager (M), and the other is from operations (O). How well the team functions is a matter of choice. R can always choose to put his feet up and think about research, an activity he values at 5 (whatever units you like). M and O do not do well in isolation, and each attaches zero value to having to keep herself occupied. But M and O can always discuss their hobbies, careers, etc., an activity they collectively value at 10. R does not play well with others. Chatting one on one with either M or O is an activity R and M, or R and O, collectively value at 5. The firm knows R, M and O have alternatives to pursuing the commercialization project seriously, but is unsure exactly how the players value them, and is contemplating providing the players value V (specific values given below) to share among them in whatever way they like provided the project is completed.
(a) Describe this situation as a three-player coalitional game, i.e., what are the individual rationality and coalitional rationality conditions?
(b) How will value be appropriated by the players if V = 15?
(c) How about if V = 20?
4. Consider the classic Hotelling (1929) model: Two vendors, A and B, sell the same kind of ice cream. Working for the same franchiser, they charge the same (fixed) price. But each can choose where to locate on the beach. The customers, sunbathers, are spread evenly along the beach. Sunbathers also are averse to walking, so they purchase their ice cream from the closest vendor.
(a) Assuming all bathers purchase ice cream, describe the vendor problem as a two-player game in which player's strategy choices are locations. (It is easiest to start with a picture, as below, in which the line represents the beach, vendors are located and x and y; and payoffs are proportional to the number of bathers who purchase from each vendor.)
(b) What are the Nash equilibrium location choices? Explain carefully.
(c) Assuming all bathers enjoy ice cream equally, who are the overall most satisfied bathers? The least? Why?
(d) Can you think of other kinds of business situations that Hotelling's idea illuminates?
(e) How about presidential politics?
i. Why do candidates shift to the center after winning their party's nomination?
ii. Who will be least happy with the position eventually chosen by their party's candidate?
iii. These unhappy voters often threaten not to vote. How seriously should this threat be taken?
5. Retailers of shoes display their shoes in a very particular way: (i) They display just one shoe, and (ii) The shoes on display are either all right shoes or all left shoes; nearly every chain shows only right shoes.
(a) Consider a simple model of the shoe business, in which retailers A and B can simultaneously choose a shoe display policy, which, for simplicity, is either "left" or "right".
i. Produce a normal form game (payoffs can be generic, i.e., + and -, or "high" and "low".) Explain the business argument leading to the pattern of payoffs you choose.
ii. Find all the Nash equilibria of the game.
iii. Does your model explain the above-described behavior of retailers, or does it suggest this behavior is surprising?
(b) The question of how players arrive at equilibrium strategies is a natural one about which game theory has relatively little to say. Suppose you are a new shoe retailer in a market where the existing firms show only right shoes.
i. What would you observe in your business if your policy is to display left shoes?
ii. Would any of these observations lead you to consider switching the policy to right shoes?
iii. Suppose you are new to the shoe business and are setting your firm's shoe display policy with no clue what others policy is. Based on what you observe in your business as rime passes (i.e., no direct exploring of what other firms do), are there forces that will lead you eventually to adopt the same policy as others?
(c) In your local shoe market, all firms follow the right shoe display policy. Suppose a huge national retailer, e.g., Walmart, enters your market. Suppose Walmart has a nationwide left shoe display policy. With reference to (a)(ii), what do you predict will happen right away? Over time?
Attachment:- Ritalin.rar