Managerial Economics	S1	S2	S3	S4
Mr. Upton	S5	S6	S7	S8
Final Examination	S9	S10	L1	L2
May 12, 1998	L3	L4	S

Name:

Checking for Grades: Grades will not be available until Friday. Sometime that day (probably in the afternoon), I will revise the course log, showing both the answers to the final examination as well as your grade.

Directions: do all work on the exam itself, answering the question in the space provided. If you require extra space, use the back of the exam, indicating that you have done so. Note: as you can tell, this is a 150 point exam. Think of the extra ten points as "bonus potential".

First Part (10 Point Questions). Work nine of these ten
problems. Indicate which problem you did not work.

I did not work problem ________

1. To answer this problem, think Christmas. It is November. Wonder Toys has produced 60Wonder Toys®. It will be impossible to produce any more for the Christmas Season. Market research has determined that the demand is

Q = 100- p

This demand study as well as the fact that 60 toys have been produced, has been widely reported in the Toy Street Journal.

1. At what price can all the Wonder Toys® be sold? Show your work.

(a) The demand curve is Q = 100 - p. To sell 60, you must set the demand curve so that 60 = 100 - p. Solving, we find that p = 40.

2. In terms of narrow self interest, how many Wonder Toys® should be donated to Charity? Explain your reasoning.

(b) The profit maximizing solution is to set the quantity sold so that MR = 0. There are two ways to calculate when this happens. The first is to set R = pQ, and, substituting in from the inverse demand curve p = 100 - Q, to see that R = 100Q - Q². Differentiating, MR = 100 - 2Q, and that equals zero when Q = 50. That would mean a price equal to 50, of course. Another way to see this is to plot the MR curve. Note that for a straight-line demand curve, the MR curve hits the X-axis midpoint between the origin and where the demand curve hits the X- axis. Since the demand curve hits the X-axis at Q = 100, it is clear that the MR curve will hit the X-axis at Q = 50. There is a problem with selling 50. People will think that you will unload the other 10 at a lower price. If you donate the other 10 to charity, you will solve your problem.

3. The CEO of Wonder Toys, charitably minded, is agreeable to making a donation but modest man that he is, wants the donation kept secret. What do you think about this idea?

(c) How did this guy get to be CEO? It is vital that the donation be made public. The only reason to give the 10 away is to get credibility. If you give the 10 away in secret, then the public will still think you have them and intend to sell them later. My advice would be to have a big luncheon to announce both the donation and the CEO's resignation.

1. John Smith has a job selling shoes. Right now he works 50 hours a week, and he gets paid $20 an hour for the first 40 hours and $30 an hour for the overtime, for a total of $1100 a week. He is offered a new job selling shoes. He will be paid $22 an hour and he can work as many or as few hours as he wishes. Will he take the job? And if he does so, will he work more or fewer hours? Explain your answer using indifference curves.

He will take the job and work fewer hours. Right now he is on an indifference curve where he works 50 hours and earns $1100 a week. Given the slope of his budget line, we know his MRS between money and leisure is 30. That means he is indifferent between $30 and an extra hour's leisure. The new budget line goes through the same point, but it has a slope of 22. That means that, on the margin, he can get an additional hour's leisure for only $22. Given his preferences, that is a good deal.

2. If the price of a good falls, then - in general - there will be a decrease in demand. Explain whether you agree or disagree with this statement.

This is a double trick question. First, a fall in price usually leads to an increase in the quantity demanded. Second, it does not lead to an increase in demand but a movement along the demand curve.

3. The Elite Diner serves an all-you-can-eat buffet. It has two types of customers. Senior Citizens, who know a good meal when they see it and a number of singles, who see it as a hot date site. (Don't ask why a restaurant can appeal to both types: as Cicero long ago noted, de gustibus non est disputatum). The restaurant has calculated the consumer surplus each would get out of dining on Friday and Saturday nights as follows:

	Friday Night	Saturday Night
Senior Citizens	$12	$12
Swinging Singles	$20	$35

Assuming that it must charge all Friday diners one price and all Saturday diners one price, what price should it charge for Friday Night? For Saturday Night? (There is enough capacity that it can handle all diners and the meals are generous enough that no one is going more than once a week.). Explain your answer.

It may be a sad day when the best thing to do on a Saturday night is to go to a place which caters to senior citizens, but it is not our place to question tastes. The right solution is to charge $12 for Friday night and $27.99 for Saturday night. The Senior Citizens will then go Friday night. The Swinging Singles will see that if they go Friday night, they will get consumer surplus of $8. If they go Saturday night, they will get consumer surplus of $8.01. Thus they go Saturday night. Note that if you get greedy and raise the price for Saturday night above $28, then the Swinging Singles will simply start going Friday night and paying $12. (We will accept answers of $27 or $28).

4. Bill Gates has a monopoly in something (Windows) that a lot of people simply must have. Therefore it is clear that the demand for Windows is inelastic.

Bill Gates does have a monopoly in Windows. But we all know that a monopolist prices in the elastic portion of his demand curve. No one makes as much money as Bill has by being stupid, so I am sure that the demand for Windows (95 or 98) is elastic.

5. (Pashigian, Chapter 5, Exercise 7). Can you explain why some restaurants guarantee to deliver lunches within a specified amount of time or why more companies are guaranteeing that they can change your oil in a certain number of minutes?

Because they recognize that the full cost of any product includes time cost. By guaranteeing on-time performance, they can assure people of the cost of a meal or oil change.

6. (Pashigian, Chapter 11, Exercise 2). The court system in Russia does not protect investors as extensively as does the court system in the United States. What does this imply about the financing of firms in the new Russian Republic.

Why invest under these terms? Principal agent problems will abound. Thus potential investors will be very uncertain about getting their money back. Investment will have to come from the managers of the firm, not from outside investors (unless they are masochists and have a desire to be fleeced).

7. (Pashigian, Chapter 9, Exercise 2). Since a monopolist equates marginal revenue to marginal cost, an upward shift in the marginal cost function will increase a monopolist's marginal revenue and marginal cost by the same amount so total profits will not be affected. Explain why you agree or disagree with this statememt.

Disagree. An upward shift in the marginal revenue function will cause the Monopolist to adjust price so that MR = MC, but it will be at a higher price and a lower quantity. The monopolist will lose in two ways. Suppose the quantity sold declines from A to B. First, he will lose the profits on the extra units (A-B) he no longer sells. Second, he will lose from the higher costs of producing B units.

8. (Pashigian, Chapter 13, Exercise 3). A monopolist wants a higher retail price so that it can increase its profits by raising the whole price. Evaluate this statement if the manufacturer is (a) a price taking competitive firm and (b) a monopolist.

If he is a price taking competitive firm, forget it. The wholesale price is set by competition. If he is a monopolist, and if the product requires special selling, there may be a case. If it does not, he can simply raise the retail price by setting the wholesale price where he wants it.

9. (Pashigian, Chapter 15, Exercise 10). Sellers of mansions often have more difficulty selling their houses than sellers of standardized tract housing. Sellers of mansions often have to reduce the initial price to sell the mansions. Can you explain why mansions take longer to sell and why the average markdown on mansions is higher than the average markdown on tract housing?

There is demand uncertainty. Who knows exactly what is the demand for a 6,000 square foot house in a particular location and with a particular set of amenities. (I once looked at a house with gold-plated doorknobs, and decided that wasn't for me. That feature may really excite someone else). Thus it is best to price high and see if anyone bites. Selling a mansion is like selling high fashion: selling a tract house is like selling the navy blue blazer.

Second Part (20 point questions)
Answer three of the four.

I have worked (check 3)

Question 1

Question 2

Question 3

Question 4

1. There is a particular product produced in a duopolistic industry. The industry demand curve is

Q = 60- P

where Q is the total quantity demanded each day and P is the price charged. To make life easy, we will assume that the product can be produced at zero marginal cost.. Given the peculiar nature of the industry, each firm must produce its output each night and then bring it to market the next day. The actual price is then set each day to clear the market.

1. Suppose initially that the two firms can collude and set price and production to maximize combined profits. What would be the total quantity produced? At what price would it sell? And, assuming that the firms split output 50-50, what would be the profits of each firm?

In this case, the firms will act as a monopoly. They will find where MR = 0. There are a number of ways you can do this, but the bottom line is that MR = 0 at q = 30. The price will be 30, and each firm will produce half of output. Thus each firm will sell 15 and get total revenues of (15)(30) = 450. Since there are no costs, this means each firm will earn profits of 450 as well.

2. Now assume that the firms cannot collude or otherwise engage in cartel-like behavior. If we assume that, when all is said and done, the two forms end up with identical production and prices, there are two Nash equilibria. The first is for each firm to produce 30. Show why this is a Nash equilibrium. (And yes, you will need to define what you mean by Nash equilibrium).

To be a Nash equilibrium, each firm must be acting rationally, and believe its actions do not impact the behavior of others. Here, price is zero. If this industry is characterized by Bertrand Equilibrium, this looks like the results of a winner take all competition.

3. A second Nash equilibrium occurs when each firm is producing 20. Show why that can be a Nash Equilibrium.

Surprise! This looks like a Cournot equilibrium.

1. As you may have read - and who has missed this story? - Pfizer Pharmaceuticals has just begun marketing VigaraÒ as a drug for treating male impotency. Suppose that, for each potential user of the product, the demand curve for pills each year is

Q = 200 - 10 p

Assume that the drug cost $200 million to develop, and $200 million to do the testing required to obtain FDA approval to sell the drug. But assume that manufacturing costs are negligible (in fact, they are pretty low and this will simply make the problem easier to handle).

1. Given this demand curve, what price should Pfizer charge for the pill? (Explain your answer)

The $400 million spent to date is simply sunk cost, and irrelevant for any decision. Don't be fooled by that.

(a) The basic idea is to set MR = MC, which is zero in this case. Total Revenue is given by R = pQ. Solving for the inverse demand function, p = 20 - 0.1Q. Thus R = 20Q - 0.1Q². Marginal revenue is thus 20 -0.2Q, so the profit maximizing quantity is Q = 100. Plugging that into the demand curve, we find the 100 = 200 - 10p, so that p = 10.

2. How much consumer surplus will each user get each year from using the drug? (Please no essays or jokes: just do the calculations).

(b) Now lets calculate consumer surplus. I've drawn the demand curve and divided it into three parts. A little plane geometry will calculate the areas as Area I = $500, Area II, the amount the consumer pays as $1000, and Area III the deadweight loss of monopoly pricing as $500. Thus users get a consumer surplus of $500. Yes, I know the graph is not to scale.

3. Assume it was possible for Pfizer to offer each customer a deal where for a fixed annual fee, he could obtain as many pills as he wanted. What price would they charge for a year's unlimited supply? Show your work.

(c) If Pfizer could price the product in this way, it would be able to get the entire consumer surplus by charging a fee of $1,999.99

4. Can you think of reasons why Pfizer might not want to adopt this pricing system?

(d) Pfizer would be foolish to offer this deal. 10, 20 or 50 people would get together. One would pay the $1,999.99 pills and order enough for him and his friends. The crucial requirement for this kind of pricing is that you be able to prevent arbitrage and it just is not possible for a product like this.

1. Used car dealers are faced with the following problem. There are two types of used cars: gems and lemons. Buyers are willing to pay $8,000 for gems and $5,000 for lemons. Sellers of lemons want $3,000, while the sellers of gems want a minimum price of $6,000. Half of the cars offered for sale are gems and half are lemons. The sellers know which cars are gems and which are lemons, but the buyers and the dealer do not.

1. Assuming that neither the dealer nor the buyers of used cars can tell a gem or lemon apart, what will gems sell for in the used car market? What will lemons sell for? (You may ignore any costs of operating the used car business beside the costs of cars offered for resale).

1. The price will be $6,500, the average of the price for Gems and Lemons.

1. A test is developed that flawlessly tells a gem from a lemon. The test, which costs nothing, is widely known. Any owner can run the test (though buyers cannot). An owner can easily offer to sell his car enclosing a certified copy of the test. The certification is an infallible sign of whether the car is a gem or a lemon. Assuming that every auto seller provides the test, what would then be the price for gems and lemons?

(b) The price will go to $8,000 for Gems and $5,000 for lemons.

2. Assume now that the test costs $50. What will happen to the price of gems and lemons?

(c) There will be no difference. Sellers will have to eat the cost.

3. Do you think there would be benefits in a law requiring all sellers to provide a copy of the test? And, if there were no such law, do you think all sellers would provide the test? (Remember that sellers know whether they have a gem or lemon. The problem is satisfying the curiosity of the buyer).

(d) As a practical matter, the law will be unnecessary and expensive. If I am offered a car without the test, I will know it is a lemon. Any owner of a Gem will voluntarily do the test. Owners of lemons will simply save the $50. If the law is passed, then they will be forced to do the test, and thus pay $50 for people to learn exactly what their silence already says.

1. The industry demand curve for widgets is given by

Q = 420 - 10 P

There is one and only one way of producing widgets. The cost varies with the number produced at each plant. Specifically, the cost of production for a given plant is:

Quantity	Total Cost
1	22
2	28
3	36
4	52
5	70

Assume initially that, by law, a firm is limited to operating one and only one plant.

1. What level of output minimizes average cost? Explain your answer.

(a) A quick calculation shows the output to be 3 per plant. LRAC is $12.

2. Assuming that the industry is competitive, what will be the price of widgets?

(b) Entry and exit will force the price to $12.

3. How many will be sold?

(c) Look at the demand curve. At a price of $12, the demand will be 300.

4. How many plants/firms will produce widgets?

(d) Since each firm will produce 3, there will be 100 firms.

5. Now assume that a firm is allowed a monopoly in the production of widgets. What price will it charge?

(e) The monopolist has a MC of 12. He must calculate MR. Revenue is pQ =
(42 - 0.1Q) Q. Differentiating, we get MR = 42 - 0.2Q. We can set that equal to MC, $12, and solve for the profit maximizing quantity of Q: 150. The price will then be $27 (substitute 150 into the demand curve and solve for P).

6. How many plants will it operate?

(f) 50. The monopolist wants to minimize cost.