UnsolvedExercises_Chapter14
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UNSOLVED EXERCISES
U2.
MicroStuff is a software company that sells two popular applications, WordStuff and ExcelStuff. It doesn’t cost anything for MicroStuff to make each additional copy of its applications. MicroStuff has three types of potential customers, represented by Ingrid, Javiera, and Kathy. There are 100
million potential customers of each type, whose valuations for each application are as follows:
(a)
If MicroStuff sets separate prices for WordStuff and ExcelStuff, what price should it set for each application to maximize its profit? How much profit does MicroStuff earn with these prices?
(b)
What does each type of customer (Ingrid, Javiera, Kathy) buy when MicroStuff sets separate profit-maximizing prices for WordStuff and ExcelStuff?
(c)
Instead of selling the applications separately, MicroStuff decides always to sell WordStuff and ExcelStuff together in a bundle, charging a single price for both. What single price for the bundle would maximize its profit? How much profit does MicroStuff make selling its software only in bundles? (If multiple prices maximize its profit, consider the highest price.)
(d)
What does each type of customer buy when MicroStuff sets a single profit-maximizing price for a bundle containing WordStuff and ExcelStuff? How does this answer compare with your answer in part (b)?
(e)
Which pricing scheme does each customer type prefer? Why?
(f)
If MicroStuff sold the applications both as a bundle and separately, which products (WordStuff, ExcelStuff, or the bundle) would it want to sell to each customer type? How can MicroStuff make sure that each customer type purchases exactly the product that it intends for them to purchase?
(g)
What prices—for WordStuff, ExcelStuff, and the bundle—would MicroStuff set to maximize its profit? How much profit does MicroStuff make selling the products at these three prices?
(h)
How do your answers to parts (a), (c), and (g) differ? Explain why.
U3.
Consider a managerial effort example similar to the one in Section 5. The value of a successful project is $420,000
; the probabilities of success are 0.5
with good supervision and 0.25
without. The manager’s expected payoff equals his expected income minus the cost of his effort. His current job pays $90,000
, and his cost for exerting the extra effort for good supervision on your project is $100,000
.
(a)
Show that inducing extra effort would require the firm to offer a compensation scheme with a negative base salary; that is, if the project fails, the manager pays the firm an amount stipulated in the scheme.
(b)
How might a negative base salary be implemented in reality?
(c)
Show that if a negative base salary is not feasible, then the firm does better to settle for low pay and no extra effort.
U4.
Cheapskates is a very minor-league professional hockey team. Its facilities are large enough to accommodate all of the 1,000
fans who might want to watch its home games. It can provide two kinds of seats—ordinary and luxury. There are also two types of fans: 60%
of the fans are blue-collar fans, and the rest are white-collar fans. The costs of providing each kind of seat and the fans’ willingness to pay for each kind of seat are given in the following table (measured in dollars):
Each fan will buy at most one seat, depending on the consumer surplus he would get (maximum willingness to pay minus the actual price paid) from each kind. If the surplus for both kinds is negative, then he won’t buy any. If at least one kind gives him a nonnegative surplus, then he will buy the kind that gives him the larger surplus. If the two kinds give him an equal nonnegative surplus, then the blue-collar fan will buy an ordinary seat, and the white-collar fan will buy a luxury seat.
The team owners provide and price their seating to maximize profit, measured in thousands of dollars per game. They set a price for each kind of seat, sell as many tickets as are demanded at these prices, and then provide the numbers of seats of each kind for which the tickets have sold.
(a)
First, suppose the team owners can identify the type of each individual fan who arrives at the ticket window (presumably by the color of his collar) and can offer him just one kind of seat at a stated price, on a take-it-or-leave-it basis. What is the owners’ maximum profit, 𝜋
∗
, under this system?
(b)
Now, suppose that the owners cannot identify the type of any individual fan, but they still know the proportion of blue-collar fans. Let the price of an ordinary seat be ?
and the price of a luxury seat be ?
. What are the incentive-compatibility constraints that will ensure that the blue-
collar fans buy the ordinary seats and the white-collar fans buy the luxury seats? Graph these constraints on an ?– ?
coordinate plane.
(c)
What are the participation constraints for the fans’ decisions on whether to buy tickets at all? Add these constraints to the graph in part (b).
(d)
Given the constraints you found in parts (b) and (c), what prices ?
and ?
maximize the owners’ profit, 𝜋
2
, under this price system? What is 𝜋
2
?
(e)
The owners are considering whether to set prices so that only the white-collar fans will buy tickets. What is their profit, 𝜋
𝑤
, if they decide to cater to only the white-collar fans?
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Related Questions
BPO Services is in the business of digitizing information from forms that are filled out by hand. In 2006, a big client gave BPO a distribution of the forms that it digitized in house last year, and BPO estimated how much it would cost to digitize each form.
Form Type
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A
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B
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.
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I. There are two contestants/opponents (who do not know each other and cannot communicate with each other during the game).
II. Each player is given $3 at the start of the game.
III. Independently and simultaneously, each player must choose whether they want to add $0, $1, $2 or $3 to their initial stake of $3. Doing so reduces their opponent’s award by $0, $2, $4, or $6, respectively.
IV. Each player knows that their payoff at the end of the game is based on…
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I. There are two contestants/opponents (who do not know each other and cannot communicate with each other during the game).
II. Each player is given $3 at the start of the game.
III. Independently and simultaneously, each player must choose whether they want to add $0, $1, $2 or $3 to their initial stake of $3. Doing so reduces their opponent’s award by $0, $2, $4, or $6, respectively.
IV. Each player knows that their payoff at the end of the game is based on…
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lead you to believe that if you commit to a price of $300,000, there is a 0.5 chance you will be able to sell the machine. If you commit to a price of
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sell the machine. These probabilities are summarized in the following table.
For each posted price, enter the expected value of attempting to sell the machine at that price. (Hint: Be sure to take into account the value of the
machine to your company in the event that you are not be able to sell the machine.)
Posted Price
Expected Value
($)
Probability of Sale
($)
$500,000
0.1
$
$400,000
0.2
$…
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Select correct one
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A victim need not be physically injured or
harmed for a battery to occur so long as
offensive contact is involved.
True or False
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Related Questions
- BPO Services is in the business of digitizing information from forms that are filled out by hand. In 2006, a big client gave BPO a distribution of the forms that it digitized in house last year, and BPO estimated how much it would cost to digitize each form. Form Type Mix of Forms Form Cost A 0.5 $3.00 B 0.5 $1.00 The expected cost of digitizing a form is . Suppose the client and BPO agree to a deal, whereby the client pays BPO to digitize forms. The price of each form processed is equal to the expected cost of the form that you calculated in the previous part of the problem. Suppose that after the agreement, the client sends only forms of type A. The expected digitization cost per form of the forms sent by the client is . This leads to an expected loss of per form for BPO. (Hint: Do not round your answers. Enter the loss as a positive number.)arrow_forwardYou have been assigned to create a new TV game show, and you have an interesting idea that you call, “I WANT TO BE A MILLIONAIRE.” The basics are: 1) two contestants; 2) the show begins with each contestant being given $1 million (!); and then 3) they begin playing a game that can increase or decrease that $1 million. You worry that the initial outlay of $2 million will stun your producers, so you decide to prepare them with a simpler version of your game that you call: “I WANT $3.” There are four steps in this simpler game: There are two contestants/opponents (who do not know each other and cannot communicate with each other during the game). Each player is given $3 at the start of the game. Independently and simultaneously, each player must choose whether they want to add $0, $1, $2 or $3 to their initial stake of $3. Doing so reduces their opponent’s award by $0, $2, $4, or $6, respectively. Each player knows that their payoff at the end of the game is based on their initial $3,…arrow_forwardCameron sells premium steak at the local market. He has a lot of customers due to the promising taste and texture of his steak. One kilogram of his premium steak costs $80.50. However, it would only cost $68.50 per kilogram if a customer buys 3 kilograms and $58.50 per kilogram if a customer buys 5 kilograms. Cameron can supply 100 kilograms of premium steak in a day, but his supply only lasts for an hour and a half. Which of the following statements is true? With this pricing scheme, Cameron is extracting all the consumer surplus. Cameron is basing his pricing scheme on the maximum amount a customer is willing to pay for his premium steak. Cameron is using third degree price discrimination by charging different prices for different "blocks" of kilograms for his premium steak. Cameron receives a larger revenue and profts with this pricing scheme compared to charging a single lower price for larger quantities. None of the above are true.arrow_forward
- Seven years ago, you started a cross-town delivery service. You have two types of deliveryservices. You have a small parcel service for anything that is flat and measures less than 11x17. You have a package service using a 100 lb capacity bike trailer for anything weighting up to 10lbs. Initially, you charged the same price for each service, but since the beginning of the Covid19 pandemic you have seen an increased in the demand for your package service. The demand for the package services seems to be more inelastic than the demand for parcels. You are now wondering if you should charge different prices for the parcel and package service or should you segment the market and charge two different prices? Complete the tables below and determine the best price strategy: price the services differently in each segment; or continue the one price policy? The Packages Market Price Packages TR MR TC MC…arrow_forwardSeven years ago, you started a cross-town delivery service. You have two types of deliveryservices. You have a small parcel service for anything that is flat and measures less than 11x17. You have a package service using a 100 lb capacity bike trailer for anything weighting up to 10lbs. Initially, you charged the same price for each service, but since the beginning of the Covid19 pandemic you have seen an increased in the demand for your package service. The demand for the package services seems to be more inelastic than the demand for parcels. You are now wondering if you should charge different prices for the parcel and package service or should you segment the market and charge two different prices? Complete the tables below and determine the best price strategy: price the services differently in each segment; or continue the one price policy? Combined Parcels & PackagesPrice Parcels and Packages TR MR TC MC MR-MC…arrow_forwardSeven years ago, you started a cross-town delivery service. You have two types of deliveryservices. You have a small parcel service for anything that is flat and measures less than 11x17. You have a package service using a 100 lb capacity bike trailer for anything weighting up to 10lbs. Initially, you charged the same price for each service, but since the beginning of the Covid19 pandemic you have seen an increased in the demand for your package service. The demand for the package services seems to be more inelastic than the demand for parcels. You are now wondering if you should charge different prices for the parcel and package service or should you segment the market and charge two different prices? Complete the tables below and determine the best price strategy: price the services differently in each segment; or continue the one price policy? The Parcels Market Price Parcels TR MR TC MC MR-MC…arrow_forward
- Firm A is planning to rollout a new nationwide wireless telephone service next month. Its potential customers are either light users or regular users and these exist in equal proportion in the population. The firm must decide between offering a plan with 300 minutes, 600 minutes, or offering both plans. Each of these options costs the firm $10 to provide, and consumers’ willingness to pay is given below: (Image Attached) Each potential customer calculates the net payoff (benefit minus price) that he would get from each of the plans and buys the plan that gives the highest net payoff, so long as the payoff is nonnegative. Assume that if both plans give an equal, non-negative payoff the customer buys the 600 minute plan. a) What prices should the firm set if it wants to offer both plans, such that light users purchase the 300 minute plan and regular users purchase the 600 minute plan? b) How much higher is a regular user’s payoff under the scenario in part (a) above than if the firm…arrow_forwardAssume you have your car broken down just before the weekend. You value your weekend trip as much as v and if you have to stay home you get the zero utility. There are two dealerships in your town. At the beginning of the day they simultaneously choose a price for repair. Dealers know that when you come to one of them and observe the price, you can always call to another dealer to make an inquiry about his price. The call is costless. The other dealer, however, can be occupied for this day. Assume, this happens with probability a which is a common knowledge (but the dealers do not know whether the other dealer is occupied or not). Assume zero repair cost for the dealer and find a symmetric equilibrium of the game.arrow_forwardA risk-neutral firm produces chemical products, and its objective is to maximize expected profit. There is a risk that there will be an accident during the production process, and dangerous chemical products will be released into the ocean, polluting the water. To reduce the risk of an accident, the firm can choose Low or High investment in safety. Low Investment in Safety_ Cost for firm= $0 Probability of an Accident = 80% Probability of No Accident =20% High Investment in Safety Cost for firm= $150 Probability of an Accident = 20% Probability of No Accident = 80% The Government wants to reduce the risk of an accident, but the Government cannot observe the fir m's investment in safety. Therefore there is a moral hazard problem. However, the Government can observe whether an accident occurred or not. So the government decides to create a fine (penalty): if an accident occurs, the firm must pay a fine F to the Government. If an accident does not occurs, then the firm does not have to…arrow_forward
- After graduating, you start work as a management consultant. You are paid $210 per hour. One morning before work, you decide to buy a new car. You know the exact model you want, and you know that in your area the price ranges from $39,000 to $41,000, with the average price you can expect to pay being $40,000. You can choose among hundreds of dealers, but you don't know which dealer will give you the best price. Time is literally money, since every hour you spend searching is an hour you don't get paid. Each visit to a dealer takes an hour. Your expected marginal benefit of another search is the difference between the current dealer's offer and the average price. The first dealer you go to asks $40,500 for the car. Should you accept the price or keep searching? (Keep in mind that each visit to a dealer takes an hour.) Keep searching. Accept the price. Suppose you kept searching, and the next dealer you go to asks $40,150. Do you think you should accept this price or keep searching? O…arrow_forwardA computer reseller needs to decide how many laptops to order next month. The lowest end laptop costs $220 and the retailer can sell these for $300. However, the laptop manufacturer already announced that they are coming out with a new model in a couple of months. Any laptops that will not be sold by the end of next month will have to be heavily discounted at half-price. The reseller also needs to consider that every time he fails to fulfill a laptop order, he stands to lose $25 for every unit. Based on the past months’ sales, the reseller estimates the demand probabilities for sales (S) as follows: P(0 units) = 0.3; P(1 units) = 0.4; P(2 units) = 0.2; P(3 units) =0.1. The reseller thinks it’s a good idea to conduct a survey on whether or not his customers are going to buy laptops and how many. The survey results will either be Yes (Y), No (N) or Don’t Know (DK). The probability estimates of the results based on the demand for number of units are: P(Y|S = 0 units) = 0.1 P(Y|S = 1…arrow_forwardA computer reseller needs to decide how many laptops to order next month. The lowest end laptop costs $220 and the retailer can sell these for $300. However, the laptop manufacturer already announced that they are coming out with a new model in a couple of months. Any laptops that will not be sold by the end of next month will have to be heavily discounted at half-price. The reseller also needs to consider that every time he fails to fulfill a laptop order, he stands to lose $25 for every unit. Based on the past months’ sales, the reseller estimates the demand probabilities for sales (S) as follows: P(0 units) = 0.3; P(1 units) = 0.4; P(2 units) = 0.2; P(3 units) =0.1. The reseller thinks it’s a good idea to conduct a survey on whether or not his customers are going to buy laptops and how many. The survey results will either be Yes (Y), No (N) or Don’t Know (DK). The probability estimates of the results based on the demand for number of units are: P(Y|S = 0 units) = 0.1 P(Y|S = 1…arrow_forward
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