Final Exam SOLUTIONS. 1. (10 points) (This question is based on the Comcast article on the class website.)

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1 MBA814 Spring 214 Mike Conlin EXAM A Final Exam SOLUTIONS 1. (1 points) (This question is based on the Comcast article on the class website.) Comcast has instituted a new pricing scheme which raises the price to almost all consumers. As part of the scheme, Comcast has decided to provide a price reduction for that month to those customers who are willing to call Comcast and complain about the new pricing scheme for half an hour. Suppose there are two types of customers: Type A s who are willing to pay a maximum of $8 per month for Comcast and Type B s who are willing to pay a maximum of $6 per month for Comcast. The opportunity cost associated with Type A s time is $2 per hour while the opportunity cost associated with Type B s time is $1 per hour. Assume there are 5 Type A individuals and 2 Type B individuals and that Comcast cannot differentiate between them on the call (but may be able to distinguish them by who is willing to complain for a half hour). Comcast incurs a constant marginal cost of $5 for each customer and Comcast s fixed costs are $1,. Type A Type B Willing to pay 8 6 Opportunity Cost for half an hour 1 5 Number 5 2 a) In order to maximize profits, what price should Comcast charge (P C ) and what discount (D C ) should Comcast provide to those customers who complain for half an hour? Show Calculations. P c =65 and D C =1. That way, Type B pays the maximum they are willing to pay and Type A does not have incentive to obtain the discount by waiting in line (because the discount is not greater than Type A s opportunity cost). Therefore, profits equal 5(65-5)+2(55-5)-1=3 b) Now suppose Comcast is revisiting its new pricing scheme and is now deciding not only on price (P C ) and discount (D C ) but also on how long a customer needs to complain in order to obtain the discount. In order to maximize profits, how long should Comcast require a customer to complain and what price and discount should they choose? Show Calculations. P C P C -D C Profits 1 hour wait 7 5 5(7-5)+2(5-5)-1=315 2 hour wait 8 4 5(8-5)+2(4-5)-1=345 3 hour wait 8 3 5(8-5)+2(3-5)-1=325 So the maximum profits of $345 are when the delay is 2 hours, P c =8 and D C =4.

2 2. (8 points) My kids are going to the Beauty and the Beast Musical at the Wharton Center. Suppose the musical plays the entire week with one show a day. The demand for this musical varies depending on whether it is a weekday (Monday, Tuesday, Wednesday, Thursday and Friday) or a weekend day (Saturday and Sunday). The demand is the same on all weekdays and this demand is depicted on the graph below as D wd. D we on the graph below denotes the demand on each weekend day (so that the demand on Saturday is the same as on Sunday) Dwd Dwe MR wd MR we Suppose the Wharton Center sets one price for a weekday show (P wd ) and one price for a weekend show (P we ). Suppose the marginal cost of a person attending the musical is constant at $1. What are the Wharton Center s weekly profits if the capacity of the Wharton Center is 1,6? Assume that the weekly fixed costs are $1,. Show your calculations and use above graph. Profits= 2(6-1)16+5(45-1)14-1=35,

3 3. (14 points) (This question is based on the bailout articles on the class website.) Suppose it is 28 and American International Group (AIG) executives are deciding whether to make a very risky investment. They can either choose to make this risky investment or choose not make this risky investment. If they choose not to make the risky investment, AIG s expected 28 payoff is $14B ($14 Billion) and the United States government s 28 payoff is. If they make this risky investment and the economy takes a dive, they have a chance of becoming insolvent. AIG realizes that if this occurs, the United States government would then decide whether or not to bailout AIG. Suppose AIG s expected 28 payoff is $12B if they make the risky investment thinking that the government would not bail them out and $15B if they make the risky investment thinking that the government would bail them out. The United States government s expected 28 payoff from choosing a bailout if AIG becomes insolvent is minus $8B and the United States government s expected 28 payoff from choosing no bailout if AIG becomes insolvent is minus $6B. Suppose this is the game the United States government and AIG play in 28 and it is the exact same game that is played in 29 irrespective of what happens in 28. Suppose the annual interest rate is 1% for AIG as well as the United States government. a) Depict below the extensive form of the above game (include both the 28 and 29 decisions along with the payoffs). AIG Make risky investment Don t make risky investment in 28 in 28 US Gov t AIG bailout No bailout Make risky Don t make risky AIG AIG investment investment in 29 in 29 Make risky Don t Make Make risky Don t make Investment risky investment Investment risky investment in 29 in 29 in 29 in 29 US Gov t US Gov t US Gov t No No No bailout bailout bailout bailout bailout bailout AIG: 15+15/ / / / / /1.1 US: -8-8/ / /1.1 AIG: 15+12/1.1 ` 12+12/ /1.1 US: -8-6/ /1.1-6 b) What is the subgame perfect equilibrium of this game? Depict on the graph above. (You can also obtain partial credit by describing the subgame perfect equilibrium.) See above. In the end, AIG does not make the risky investment in both 28 and 29. The reason is that the US government would not bail them out if they did make the risky investment (since -8<- 6). If the US government s payoff was greater from bailing AIG out than from not bailing them out, then the US government would bail them out and AIG would then have incentive to take the risky investment since 14<15. c) Now suppose the United States government could credibly commit to either a bailout or no bailout prior to AIG s investment decision. Would the outcome of this game change and would this outcome be preferred by the United States government? Explain. (A game tree is not necessary.) The outcome of the game would not change because the US government can already credibly commit to not bailing AIG out. See the answer to part b).

4 4. (6 points) The graph below depicts the demand for MSU s full-time MBA program along with MSU s cost curves involved in operating a full-time MBA program. Assume that MSU is a profit maximizing organization. 8, 75, 7, 65, 6, 55, 5, 45, 4, 35, 3, 25, 2, 15, 1, 5, D MC ATC AVC MR a) What are MSU s maximum profits if they are unable to price discriminate? Show calculations. Profits=5,*6-35*6=9, b) Now suppose that MSU is considering hiring Mike Conlin s graduate school roommate who works for a consulting firm that specializes in optimal pricing strategies. The consulting firm guarantees to provide MSU the information that will allow MSU s full-time MBA program to perfectly price discriminate (i.e., 1 st degree price discriminate). If MSU believes the consulting firm, what is the maximum amount MSU should be willing to pay the consulting firm? Show calculations. Profits if perfectly price discriminate are.5(8-35)9+35*9-32,5*9=225k Therefore, MSU should be willing to pay a maximum of 225k-9k=135k

5 5. (12 points) 1. Consider the market for life insurance. Suppose there are three different types of individuals. Type I individuals know they will die in exactly 5 years. Type II individuals know they will die in exactly 1 years. Type III individuals know they will die in exactly 15 years. There are ten Type I individuals, ten Type II individuals and fifteen Type III individuals. Suppose for a $1, life insurance policy, Type I individuals are willing to pay $6,, Type II individuals are willing to pay $4,, and Type III individuals are willing to pay $2,. (For simplicity, assume the willingness to pay for the life insurance policy is the maximum onetime payment an individual is willing to pay right away to obtain the life insurance policy.) Assume that the life insurance industry is a monopoly in that there is only one firm in the industry. Suppose the monopolist s expected costs are the present value of the life insurance payment (where the payment is $1,) and the monopolist incurs administrative costs of $1, per individual who chooses to purchase life insurance. Finally, assume that the monopolist s annual interest rate is 15%. What price will the monopolist charge for life insurance if the monopolist cannot differentiate among the different potential customers? (Assume the monopolist chooses a price today which consumers pay immediately- a onetime payment. This is instead of some monthly payment pricing strategy.) Who will end up obtaining life insurance? SHOW ALL CALCULATIONS. Hint: To help with your calculations, (1+.15) 5 =2., (1+.15) 1 =4. and (1+.15) 15 =8.3. Type I Type II Type III Willing to pay 6k 4k 2k Marginal Cost 1k/2.+1=51, 1k/4+1=26, 1k/8.3+1=13,48 Number Profits if price at 6k 1(6k-51k) = 9, Profits if price at 4k 1(4k-51k) +1(4k-26k)= 3, Profits if price at 2k 1(2k-51k) +1(2k-26k) +15(2k-13.48k)= -265,72 Therefore, price at 6k and have only Type I s buy the life insurance.

6 6. (1 points) Suppose the demand for local telephone service in East Lansing is from two types of individuals. There are 2 type A individuals and 1 type B individuals. Each type s individual demand curve is depicted on the graphs below (where q is the number of local phone calls per month). The telephone company cannot distinguish between type A and type B individuals. The marginal cost of a local phone call is constant at $.1 and the telephone company s monthly fixed costs are $1. Suppose the telephone company charges $.4 per call and a monthly fixed fee that maximizes their profits. Type A Type B DA Maximum monthly fee Type A is willing to pay Maximum monthly fee Type B is willing to pay DB What are the telephone company s profits from this 2-part pricing scheme? If the telephone company charges $.4 per call, Type A is willing to pay a maximum monthly fixed fee of.5*(1.6-.4)*6=3.6 and Type B is willing to pay a maximum monthly fixed fee of.5*(1.2-.4)*8=3.2. Profits if monthly fixed fee is $3.2. 3*3.2+2*.4*6+1*.4*8-.1[2*6+1*8]-1 = 56. Profits if monthly fixed fee is $3.6. 2*3.6+2*.4*6-.1[2*6]-1 = 8. Therefore, profits are maximized at $56 when the monthly fixed fee is $3.2.