907ECON... P7

Question: Consider a horizontally differentiated product market in which two firms are located at any points l1 and l2 on the real line, respectively, with the notation l1 l2. Firms produce at marginal costs c. There is a continuum of consumers of mass 1 who are uniformly distributed on the unit interval. They have unit demand and have an outside utility of . A consumer located at x [0; 1] obtains indirect utility v = max (v1; v2) with v1 = r (x l1) 2 p1 if she buys one unit from firm 1 and v2 = r (l2 x) 2 p2 if she buys from firm 2. Firms have marginal costs equal to c.

a. Suppose that prices are regulated at pi = 2c. In the game in which firms simultaneously decide where to locate their product, characterize the Nash equilibrium.

b. Determine the demand function for each firm for each admissible price pair (p1; p2) given locations l1 and l2.

c. Suppose that the two firms simultaneously set prices. Determine the market equilibrium for all possible combinations of (l1; l2).

d. Suppose that the social planner chooses first-best optimal prices. Which price pairs would be socially optimal for the pair of locations l1 = 0 and l2 = 1/2?

e. Compare your results obtained in (c) and (d) for locations l1 = 0 and l2 = 1/2. Is the equilibrium socially efficient? Depending on your answer elaborate on the sources of the inefficiency or give the reason for efficiency.

Put a comment on those two post, the Professor asked us to comments to our classroom post on blackboard 1 The world is ever evolving and the technology that comes along is also evolving and adapting at a record rate. In just over the last 60 or so years, AI research and development has been able to outcompete humans in many categories. Some of these include video games where the AI can put in inputs on a controller much quicker than a human, bots to put items in carts to secure goods, and even to the "future" of self driving cars. Artificial intelligence is already being used in many businesses, including banks. Banks are using AI systems to identify potential risks and fraud. They

by running records of the recent purchases and compare them to your "typical" spending locations and prices. If a difference is identified, then an alert will be sent to not only you, but also your banker who can then help you with taking the appropriate action. Artificial Intelligence are able to analyze unstructured data which in turn saves the company time and money for financial service companies. In the bank example, the AI can lower operational, regulatory, and compliance costs as well as provide reliable credit scorings for credit decision-makers. The downside to any and all AI is the ability for it to be hacked and the consumer to be at risk. If the system is hacked, it would give the hacker access to confidential information as well as potential user names and passwords. Actions are being taken to prevent such attacks on the system, like any precautions for a regular website which includes firewalls and increased security around the weak points. 2 Artificial intelligence is probably one of the most innovative forms of technology made by mankind. It is used everywhere from our cell phones to the newest laptops and computers. It is especially useful in the use of data analytics. We all participate in data analysis most of the time without even noticing it. The amount of data mining our phones

lone is impressive. It is how advertisements that are tailored to our preferences are able to show up just for us and be right at our fingertips in seconds. Artificial intelligence is at work even when we don't realize it. It is reaching a point to where it is much more sophisticated than it used to be and can even replace basic human functions. In terms of data analysis, certain aspects such as data mining would be nowhere near as sophisticated as it is today without the use of artificial intelligence. It is also constantly getting more efficient and powerful as time goes on. There is an article I found that states that "Research in the field of artificial intelligence is aimed at developing techniques that make expert systems more efficient and provide them with greater reasoning power" (Corchado, 1998). While this may seem obvious, the key word here is reasoning power, that gives artificial intelligence the ability to make sense of data and to make it useful for us. If this gets stronger, then data mining will continue to be more effective in human data analysis.

(a) At a production level where a firm has economies of scale, its marginal cost must be below its average cost. (b) Assume you can buy a car for $3,000 and you will be able to use it for 3 years. Afterwards it will have zero re-sale value. Alternatively you can rent a car for $1000 per year. You should be indifferent between these two options. (c) Chili-dog lovers come from far and wide to Mike's Famous Chili-Dog Fair and have identical demand for chili-dogs. (A chili-dog is a type of food.) Attendees purchase a ticket from Mike to enter the Fair but, once inside, they may purchase chili-dogs from any of a number of independent chili-dog stands. Chili-dog stands have zero fixed costs and marginal cost of $2.00 per chili-dog. Currently the stands compete aggressively so that price equals marginal cost. The standowners approach Mike with the following proposition: "This bitter price competition among the chili-dog stands is really hurting profits. If you required us to charge a higher price, we could share the extra profits with you. We would all be better off." Mike should accept the deal. 2. (250 points, 25 minutes) On the island of Wahai, apple farmers grow 200,000 apples per year. The cost of harvesting the apples is 10 cents per apple. There are no other costs. Demand for apples on Wahai is Q=240-p, with p the price per apple in cents and Q the demand in thousands of apples. Apples can also be bought or sold on the world market at a price of 50 cents per apple. (a) What is the price for apples on Wahai. How much gets imported or exported? (b) How much does total surplus change if apples bought or sold on the world market incur an extra transportation cost of 10 cents per apple? 15.010/15.011 - Sample Final 2003 p. 3 3. (200 points, 20 minutes) DSL Inc. can provide internet service at 10 Megabits per second (Mbps), but it can slow down the service to 2 Mbps at no additional cost. Consumers like faster service with values (in dollars) given by: 10 Mbps 2 Mbps Value to a business 100 30 Value to a family 40 20 Suppose there are 100 potential business consumers and 100 potential family consumers. DSL's marginal cost is zero. (a) Say that DSL can distinguish families from businesses. What speed and price should it offer businesses? What speed and price should it offer families? (b) The National Communications Commission (NCC) forces DSL to charge one price for 10 Mbps and forbids any slowdown in service. What price will DSL charge for 10 Mbps? Calculate the lost revenue due to the regulation. What is the change in consumer surplus compared to part (a)? (c) Now say that DSL cannot distinguish families from businesses and considers offering both 10 Mbps and 2 Mbps services. What price would DSL charge for each service? Should DSL offer the two services? Compare consumer surplus relative to part (b). 4. (200 points, 20 minutes) Xemico is a small island in the Pacific with demand for milk equal to Q=12-P, where P is expressed in million Petesas and Q in tons. The island has two milk producers. The marginal cost of producing milk is zero. The firms compete by choosing quantity (i.e. they are Cournot competitors). (a) How much milk will each producer produce? What will be the price? (b) By how much would total surplus change if this market were competitive? 15.010/15.011 - Sample Final 2003 p. 4 5. (270 points, 27 minutes) Harry met Sally and they decided to participate in MIT's 50K competition. They agree that if Harry puts h hours of work in the project and Sally puts s hours of work in the project, the outcome of the project will be worth: R = h s h + s . They also agree that they will split the outcome equally, receiving R/2. The cost of h units of effort for Harry is C(h) = h2 /2, and the cost of s units of effort for Sally is C(s) = s2 /2. (a) Assume that both Harry and Sally cannot observe each other's work hours and that they simultaneously decide their efforts. Find the two reaction curves, the Nash equilibrium of the game, and payoffs in equilibrium. (b) Suppose that Sally decides her number of hours first and Harry decides after knowing the number of hours chosen by Sally. Find the equilibrium of the game and payoffs in equilibrium. 6. (250 points; 25 minutes) Your company produces lawn mowers. Each lawn mower needs one engine. You produce your own engines. The market for lawn mowers is competitive and the market price is $1,100. Given the engine, there are additional costs of $900 to assemble the lawn mower. (a) Your firm has one fabrication plant for engines. Its marginal cost is MC = 10Q. There are no fixed costs. All quantities are expressed in thousands of engines or lawn mowers. What is the optimal production levels Q for your engine fabrication plant? What is the optimal transfer price for an engine? (b) Your firm has two fabrication plants for engines; their marginal cost structures are given as MC1 = 10 Q1 MC2 = 10 + 10 Q2 There are no fixed costs. All quantities are expressed in thousands of engines or lawn mowers. What are the optimal production levels Q1 and Q2 for your two engine fabrication plants? What is the optimal transfer price for an engine? (c) Take the situation of part b) but suppose that there is also a competitive outside market for engines, where engines can be purchased or sold for $ 250. What are the optimal production levels Q1 and Q2 for your two engine fabrication plants, how many lawn mowers Q should you produce, and how many engines sho

(300 points, 30 minutes) [The following is based on actual events, though details are fictionalized for simplicity.] In the early 1990s activist groups supported by Ralph Nader filed a recall petition against 10 million General Motors trucks, claiming that their fuel tanks could explode in a crash. In 1993, General Motors proposed to settle the resulting lawsuits by giving coupons to all 10 million affected owners. Each coupon allows one to receive $1000 off any new GM truck purchased in 1994. (The coupons expire at the end of 1994.) These coupons are fully transferable: if someone with a coupon gives / sells it to someone else, that person can also use it to get $1000 off a new GM truck. If the proposal goes ahead, all parties expect a competitive market to arise in which these coupons will be actively traded. GM has zero fixed costs and marginal cost of $10,000 per truck. Demand for GM trucks in 1994 is given by D(p) = 8,000,000 - 200p (a) Suppose that the judge does not allow the settlement. In this case, what price will GM charge for its trucks? What is GM's profit and what is consumer surplus? (b) Suppose now that the judge allows the settlement and that GM charges a price of $26,000 for trucks. Construct the resulting demand and supply curves in the market for coupons. What is the price at which coupons will trade? Given this price for the coupons, how many trucks will GM sell? What is GM's profit and what is consumer surplus? How much did GM's profit and consumer surplus change, relative to your answer in (a)? 8. (150 points, 15 minutes)[Short Answer; No specific calculations are necessary] Zipcar rents out cars by the hour. Originally, users paid both a per-hour and a per-mile charge. Some of its customers, however, complained that the system was too complex and clamored for a pure per-hour charge. The CFO makes the following calculation. Over the past year, Zipcars were rented for a total of 10,000 hours and driven for a total of 100,000 miles. Since the original per-mile charge was 5 cents and on average each driver drives 10 miles for each hour that he/she rents a car, the CFO concludes that eliminating the per-mile charge and raising the per-hour charge by 50 cents would be a breakeven operation (i.e. would not change the profits). Evaluate the CFO's conclusion?

1. (250 points; 12 minutes) Decide whether each of the following statements is True, False, or Uncertain, and give a brief but clear explanation of your answer. (Most of the credit will be given for the explanation.) 1a) When an aluminum company made 100,000 cans, the last unit cost $0.02. The next year it made 500,000 cans and the last unit cost $0.04. This company does not benefit from economies of scale. 1b) A demand equation for gasoline is estimated to be: Ln Q = -0.54 - 0.40 Ln P + 0.25 Ln Income where Q is in millions of gallons per week and the price is per gallon. A refinery fire leads to a price increase from $1.00 per gallon to $1.50 per gallon. Since the above equation implies that gasoline demand is inelastic, the quantity demanded will drop by less than 1%. 2. (350 points; 18 minutes) A railroad which runs between two cities 'produces' two products: passenger and freight service. The marginal cost of carrying an extra ton of freight is $0, and the marginal cost of carrying an extra passenger is $0. There are joint, fixed costs of $19,000 per day. There is no other competitor in this market. The daily demand for passenger service is Pp = 8 - 0.005Qp with Qp the number of passengers and Pp the price of a two-way ticket. The daily demand for freight service is Pf = 10 - 0.001Qf with Qf in tons and Pf the price per ton. Currently, Pp=$5 and Pf=$8, so that Qp= 600 and Qf=2000. The revenues from passenger service are $3000 and from freight $16,000. The firm currently assigns overhead to products on the basis of their dollar share of revenues. Thus, the costs allocated to the passenger business are $3,000, while those allocated to freight are $16,000. The firm's accountants argue that prices should be raised on both products, since the firm barely breaks even. What pricing would you recommend? Evaluate the accountants' argument. Would your conclusions differ if the fixed costs were $30,000 per day?

Put a comment on those two post, the Professor asked us to comments to our classroom post on blackboard 1 The world is ever evolving and the technology that comes along is also evolving and adapting at a record rate. In just over the last 60 or so years, AI research and development has been able to outcompete humans in many categories. Some of these include video games where the AI can put in inputs on a controller much quicker than a human, bots to put items in carts to secure goods, and even to the "future" of self driving cars. Artificial intelligence is already being used in many businesses, including banks. Banks are using AI systems to identify potential risks and fraud. They

by running records of the recent purchases and compare them to your "typical" spending locations and prices. If a difference is identified, then an alert will be sent to not only you, but also your banker who can then help you with taking the appropriate action. Artificial Intelligence are able to analyze unstructured data which in turn saves the company time and money for financial service companies. In the bank example, the AI can lower operational, regulatory, and compliance costs as well as provide reliable credit scorings for credit decision-makers. The downside to any and all AI is the ability for it to be hacked and the consumer to be at risk. If the system is hacked, it would give the hacker access to confidential information as well as potential user names and passwords. Actions are being taken to prevent such attacks on the system, like any precautions for a regular website which includes firewalls and increased security around the weak points. 2 Artificial intelligence is probably one of the most innovative forms of technology made by mankind. It is used everywhere from our cell phones to the newest laptops and computers. It is especially useful in the use of data analytics. We all participate in data analysis most of the time without even noticing it. The amount of data mining our phones

lone is impressive. It is how advertisements that are tailored to our preferences are able to show up just for us and be right at our fingertips in seconds. Artificial intelligence is at work even when we don't realize it. It is reaching a point to where it is much more sophisticated than it used to be and can even replace basic human functions. In terms of data analysis, certain aspects such as data mining would be nowhere near as sophisticated as it is today without the use of artificial intelligence. It is also constantly getting more efficient and powerful as time goes on. There is an article I found that states that "Research in the field of artificial intelligence is aimed at developing techniques that make expert systems more efficient and provide them with greater reasoning power" (Corchado, 1998). While this may seem obvious, the key word here is reasoning power, that gives artificial intelligence the ability to make sense of data and to make it useful for us. If this gets stronger, then data mining will continue to be more effective in human data analysis.