Columbia University



Columbia University

Graduate School of Business

Executive MBA Program

Managerial Economics

B7006

Course Assignments

Assignment #1

Piggy Bank

Please answer this case on a single, typed, sheet of paper. Put your name on a separate, attached, piece of paper. It will be discarded after you name is recorded, and before the answer is read. In short, no grade will be given to this assignment.

The year is 1974. Last Chance Savings and Loan[1] has only one real business; it borrows money from individuals who want to save, and lends the proceeds to individuals who want to spend. Years ago, the company's founder set out the standards by which all loans are now judged: loans are approved as long as (i) the borrower has the means and intent to repay the loan and (ii) the interest rate is at least 1.5% above the average cost of the funds lent. The management has hired you as a consultant because Last Chance has not been performing well relative to other Savings and Loans (earning less than one-tenth as much on its assets as the average bank) and the shareholders are starting to ask questions.

Last Chance acquires its loanable funds from three sources: checking account deposits of individuals, savings deposits of individuals, and the federal funds market (money market accounts don't exist yet). Checking deposits pay no interest, but the bank does not charge customers the full cost of servicing the accounts, either. Typically, these deposits cost the bank about 2.25% of the funds deposited. Savings accounts receive interest, and cost the bank more, roughly 4%. Last Chance has about $2 billion in customer checking accounts and $1 billion in savings accounts. Last Chance Savings and Loan's deposit account had been very stable over the years, but loan applications have been increasing (causing Last Chance to look for ways of increasing its access to loanable funds). Federal regulations prevent Last Chance from increasing the interest rates paid on customer deposits in an attempt to attract more deposits (and offering toasters with every new account doesn't seem to be increasing deposits much), so Last Chance turned to its third source, the federal funds market. The federal funds market is organized to allow banks with excess funds to loan money to other banks for short periods, sometimes as little as one day. If a bank finds itself with more deposits than loans, it lends the surplus to banks with more loans than deposits. Last Chance has become a heavy borrower in this market. In the last year, Last Chance has borrowed and re-borrowed about $2 billion. The cost of federal funds is always greater than the cost of checking and savings deposits, and can fluctuate rapidly. In the last 2 years, the federal funds rate climbed from 6 to 11 percent, and it now hovers around 10 percent.

In an effort to increase market share, Last Chance has advertised that it will reduce its standard interest rate margin from 1.5% above the average cost of funds to just 1% above the average cost of funds. As management hoped, Last Chance was flooded with loan applications shortly after the announced rate reduction. Management predicts that they will be able to increase loans by another billion dollars in this coming year.

The board of Directors has asked you to review management's strategy. Specifically, do you think that lowering loan rates to generate an additional $1 billion in loans is a profitable move? Defend your answer, using common sense, prior experience, or even something you learned in an economics course.

Assignment #2

The Chef and Ted’s Future

1. A young chef opened his own restaurant. To do so, he quit his job, which had been paying $28,000 per year; cashed in a $5,000 certificate of deposit that was paying 5% interest (to purchase equipment); and took over a building owned by his wife which had been rented out at $1000 per month. His expenses for the first year amounted to $50,000 for food, $40,000 for extra help and $4,000 for utilities.

The chef is trying to figure out whether he would have been better off not being in business last year. He knows how to calculate his revenue, but needs help with the cost side of the picture. What were the chefs total economic costs? Do you need other information to calculate these costs?

2. Like most 2nd year students, Ted was anxiously considering his future. He had just received a coveted offer from Goldman Sachs for a job in their Real Estate Finance group in New York City paying $125,000 per year, with an additional signing bonus of $25,000 and an expected first-year bonus of an additional $25,000. In his seven years of experience prior to coming to Columbia, Ted had worked for a real estate entrepreneur who had made a large fortune buying real estate loans from the Resolution Trust Corporation (RTC) in Queens and Brooklyn. This developer would foreclose on the properties, invest some money to fix them up, and then sell these properties a few years later to generate a handsome return on investment. When the RTC business dried-up, Ted decided to take a break and go to business school to improve his financial skills.

Almost two years later, the real estate market has continued to improve. A former business contact has approached Ted, saying that he knows of a plot of land that is available in a great location, and asks if Ted wants to be his partner in a joint venture. The project will require an initial investment of $500,000 from each the partner: $400,000 to buy the land plus another $600,000 to build a small 5 unit apartment building—the largest allowed by the zoning rules. The partners figure that they will be able to sell the property after one year for $1.4 million.

Ted has managed to save $200,000 from his previous job. His mother, the head of commercial lending at Chase Manhattan Bank, will arrange a loan, guaranteed by the property, with a 7% annual interest rate to fund the rest of Ted’s share. This opportunity seems to offer lots of advantages for Ted. He can spend a year wearing blue jeans instead of a suit and tie and will be his own boss. However, doing development work will require lots of time: he will probably work another 10 hours per week more than the 60 hour/week average at Goldman Sachs (i.e., he will probably work both Saturdays and Sundays). After finishing the project, Ted expects he can get the Goldman Sachs offer (or a similar offer from another investment bank) the next year.

a) If you were Ted, would you take this job? Explain your answer in detail. Be sure to identify all of the relevant economic costs.

b) Suppose that Ted’s living expenses are expected to be $2,000 per month in rent, plus another $1,000 per month in food. How does this information change your answer in part A?

Assignment #3

Decision Trees

During one of your visits to Uris Deli (a place you should avoid in general), you became friendly with a couple of PhD students from the Engineering School (people you should NOT avoid, in general). They told you that they have been working on developing high speed modems and asked for your advice about the commercial viability of a potential product. They told you that with an initial investment of $6M, they could develop a new type of high speed modem within 10 months. Although there are many companies currently working on this new generation of modems, given the cost of production and the predicted prices, they think that they have a good business idea at hand. They want your help in evaluating this potential project.

You agree to assist them if they can present you with some additional information. Here is what they gave you in your next meeting:

While there is a 10% risk that the development will fail (or will take too long to be relevant), there is a 90% chance that a good competitive product can be developed and marketed. More specifically, there is a 10% chance that the prototype will not work at all, a 60% chance that it will be classified as a standard product, and a 30% chance that it will be a highly reliable (superior) product. If they decide to go into production, it will require an additional investment of $6M for a standard product, or $10M for the superior product. The marginal costs of producing the modems are as follow: For the standard product, costs are $50 per unit up to 100,000 units per year, and an additional $50 per unit for every 100,000 increase (e.g., between 200k and 300k, the cost is $150 per unit). For the superior product the cost per unit is $100 up to 100k units and increases by $100 for every 100,000 units.

They predict that the market price of a standard product will be either $100 or $150, with equal probability. For a superior product there is a high probability (70%) that the price will be $300; however, there is a 30% chance that the price will be $200. While prices are currently uncertain, they will be known when it is time to choose output.

An alternative to going into production will be to sell the product to one of the existing large companies. The engineers predict that they will be able to sell a standard product for $5M and a superior product for $10M to such a company.

Given the high rate of technological change in this type of market, they don't expect to sell the product for more than a year. Since this is only an initial evaluation of the product, you should make the following simplifications: Ignore interest rates, assume no risk aversion, and more important, ignore the whole issue of financing this project. Do you recommend that these students proceed?

Assignment #4

The Rock Collector

An entrepreneur decides each morning whether to work as a contract consultant for her old employer, or collect rocks that she can sell to landscape artists. Her previous employer will pay her $300 a day, and has enough contract work to keep her busy every day of the year. If she collects rocks, she must pay a fixed fee of $12.50 (per day) for exclusive access to her favorite collecting spot and equipment. The variable cost of this enterprise depends on how many rocks she collects (the rocks are quite large, and the cost of transporting the each additional rock increases with the total number of rocks). The average variable cost (in dollars per rock) is 2.5 + .005Q, where Q is the total number of rocks.

1. Upon waking, the entrepreneur learns that the wholesale price (which she has no ability whatsoever to affect) is $7 per rock; how many rocks should the entrepreneur collect (if any)? What is her economic profit?

2. Suppose the next day, the wholesale price drops to $4.99 per rock. How many rocks will the entrepreneur collect on this day, and what is her economic profit?

3. Now assume the wholesale price is again $7, and expected to remain indefinitely at this level. But instead of a $12.50 daily access fee, the authorities assess a non-refundable annual access charge of $3125 payable on the first day of the year. (This annual charge is simply $12.50 multiplied by the number of workdays in the year, which is about 250.) How many rocks will the entrepreneur collect of the first day of the year, and what is her economic profit?

4. On the morning of the last day of the year and after the annual access charge has been paid, the price unexpectedly falls to $4.99. How many rocks will the entrepreneur collect that day, and what is her economic profit?

5. Explain why the answer to part (2) differs from the answer to part (4).

6. Suppose in part (4) that the fall in wholesale rock prices had occurred on the second day of the year, instead of the final day of the year. How would that have changed your responses to part (4)?

Assignment #5

Roses and Sugar

Part I: Roses

Most weeks, the demand for long-stem roses can be approximated by QD = 2400 - 50p, where QD is the total quantity demanded (in dozens) at price p (per dozen). Currently, roses are supplied by 100 identical growers, each having total costs C=0.25q2+0.5q+36, where q is the number of roses (again, in dozens) supplied by the grower. The $36 are costs that can be avoided on a daily basis.

(a) What is the supply curve for each individual grower? Describe this curve both algebraically and graphically.

(b) Derive the market supply schedule, which gives quantity supplied as a function of price.

(c) What is the equilibrium price for a dozen roses in this market? Sketch the market supply and market demand schedules.

(d) For the weeks around Valentine's Day, market demand for roses increases to QD=6150-50p. Find the new equilibrium price, assuming no change in the supply schedule.

(e) Suppose that the city government passes a law, placing a ceiling on the price of roses may at $20 per dozen. Show graphically and explain what will happen to the market for roses around Valentine's Day.

Part II: Sugar

Consider the following stylized facts: Sugar is derived from two agricultural products grown in the US, sugar cane and sugar beet. Sugar cane grows only in certain areas (mostly Hawaii and Louisiana). Suppose that there are only 20 plantations capable of growing sugar cane, and that each plantation can produce up to 5 pounds of sugar per day, at a cost of $0.05 per pound. Assume that there are no fixed costs for producing sugar from sugar cane, so the (constant) marginal cost is also the average cost. There are 100 identical potential sugar beet farms, each with daily variable costs of production (in dollars) of x2-0.9x, and a fixed cost of $1 per day. In addition, the government will give each sugar beet farmer a subsidy of $1.00 for every pound of sugar produced on a given day.

(a) What is the short run supply curve for a single sugar cane plantation? What is the short run supply curve for a single sugar beet farm? What is the industry supply curve for sugar?

(b) Daily demand for sugar in the US is given by QD=109-100p, where p is the price per pound of sugar. What is the market price for a pound of sugar? What are the profits of cane growers? of beet growers? How expensive is the subsidy program (i.e., what is the sum total of all subsidy payments to beet farmers)?

(c) Suppose that US demand for sugar increases to QD=240-100p. What is the new market price for a pound of sugar? What are the profits for each type of farmer? How expensive is the subsidy program now?

Assignment #6

The New York Taxi Industry

There are many people willing to drive taxis in New York. These workers are available to the industry (in perfectly elastic supply) at a wage of $50 per day. To put a cab on the street costs an additional $30 a day for insurance, interest payments on the car, etc., regardless of how much the car is driven. There are also maintenance, gasoline, and depreciation costs that vary with the intensity of use. These variable costs amount to r + 0.05r2, where r is the number of rides in a day. (Assume that all rides are the same, i.e., that they are all of average length.) Daily demand for taxi rides is given by a linear function D = 1,620,000 - 180,000p where p is the price of the taxi ride.

a) Graph the daily supply curve for a single cab.

b) Suppose that there is free entry into the taxi business. What would be the price of a ride? How many rides would each cab provide each day? How many taxis would operate in a long run equilibrium? If each cab operated for 300 days a year, what profit would each cab earn for its owner in a year?

(c) In fact, entry into the New York cab market is not free. Each cab operating in the city must posses a special license, known as a medallion. Licenses are issued by the city government and the total number is 12,000. (Actually, 11,787 in 1988 -- the same number as in 1937!) Also, prices are set by a regulatory commission, but we will assume that prices are set to eliminate any excess demand or supply. Given the number of medallions in existence and the cost conditions in part (b), what price clears the taxi cab market? How many riders does each cab carry each day? What profit does each cab earn in a year (again assuming 300 operating days).

(d) What could the government charge as a license fee for each medallion, if these conditions are expected to continue and the interest rate is 5%? (Note: the value of an asset yielding payments of $x per year at an interest rate of i is $x/i.)

(e) Suppose that there are currently 100 cab companies, each operating 120 cabs. The mayor proposes to increase the number of medallions by giving each cab company ten extra medallions, free of charge. Should the cab companies support this proposal? Should consumers?

Assignment #7

Hot Dogs etc.

Part 1 (Warm Up)

a) Consider the linear demand schedule Qd = 15,000 – 10p. Find the elasticity at the point where price is 1200 and quantity is 3000. What would marginal revenue be at that point for a monopolist facing this demand schedule? Why is this number less than 1200?

b) Now find the elasticity at the point where price is 500 and quantity is 10,000. What would a monopolist’s marginal revenue be at that point?

c) Now consider the linear demand schedule Qd = 27,000 – 20p. The price-quantity combination where price is 1200 and quantity is 3000 also lies on this demand schedule. What is the elasticity of demand at that point? Explain why this number differs from the number, calculated at the same point, in part (a).

d) Graph both demand schedules on a single set of axes and indicate the two points at which the elasticities were calculated.

Part 2:

There is only one hot dog vendor at Fenway Park, home of the Boston Red Sox, selling hot dogs from a variety of locations in the stadium. During a sold out Red Sox-Yankees game, the vender knows from long experience that the demand for hot dogs is given by the function Qd = 55,000 – 10,000p.

a) If the vendor’s marginal cost of cooking, fixing and providing a hot dog is always $1.50, how many hot dogs will the vendor sell and what price will the vendor charge? If its total fixed cost of serving hot dogs for the game is $500, what are its profits?

b) Suppose the vendor can expect this kind of profit at every game for the entire 81 (home) game season. If the Red Sox management understands the hot dog business, how much could it charge the vendor for the franchise?

c) Suppose the vendor has only 10,000 hot dogs to sell on a particular night, but the same marginal costs as before. How many hot dogs would the vendor sell and at what price?

And now, a tough one:

d) Suppose the mayor of Boston, as a baseball fan and populist, gets the city council to pass a law limiting the price of hot dogs at baseball games to be no greater than $3. Illustrate (in a graph) how this law affects the vendor’s marginal revenue schedule.

And now, a even further twist:

e) Return to the situation in (A). One quirky feature of Fenway Park is that the bleachers and the grandstand seats have separate entrances. Fans cannot sneak from the bleachers to the grandstand (or vice versa). Suppose the hot dog vendor at Fenway Park wanted to take advantage of this segmentation. Furthermore, suppose that the hot dog demand in the bleacher section can be approximated as QB = 21,000 - 6,000P and the hot dog demand in the grandstand can be approximated as QG = 34,000 - 4,000P. Assuming that (i) segmenting the market does not affect the cost structure and (ii) fans will not change which type of ticket that they buy based on the hot dog price, how would a profit-maximizing vendor choose quantities and prices for each section of fans? What would be the price in each section, quantity in each section, total quantity, and the vendor’s profit per game?

Assignment #8

Games

Two soft drink companies face a market in which two types of soft drinks can be produced: "bitter drink" (B), and "sweet drink" (S). Each firm has to decide whether it will produce the B or the S drink. The production of any new drink will be successful, provided that the new product is supplied by just one firm. Moreover, the B drink is a better seller than the S drink.

(a) Suppose that the firms simultaneously choose the product type to produce and that the profits resulting from each possible combination of strategies are represented by the following table (Firm X's payoffs are first):

Firm Y

S B

S 0, 0 10, 20

Firm X

B 20, 10 0, 0

Find all the Nash Equilibria of the resulting game.

b) Suppose now that firm X gets to choose the type of soft drink to produce first. Firm Y, after having observed the choice of the competitor, picks its own type of soft drink. The profits, for each possible combination of outcomes, are identical to those reported above.

(i) Represent this new situation as an extensive form game (just draw a tree!).

(ii) Indicate the strategies available to the two firms.

(iii) Find all the Nash equilibria. Which (if any) equilibria can you rule out as being not-credible?

c) Suppose now that firm Y can destroy its own capacity to produce sweet drinks. This decision is taken before firm X makes its production decision. If firm Y decides to destroy its S drink plants, the profit associated with the production of S drinks are zero for firm Y. The payoffs of firm X are, for simplicity, not affected by the plant destruction operated by firm Y.

(i) Represent this new situation as an extensive form game (just draw a tree!) and indicate the strategies available to the two firms.

(ii) Should firm Y destroy its plants to produce sweet soft drinks? Explain.

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    [1] This is a real situation; only the names have been changed.

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