Managerial Economics

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Mr. Upton

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Final Examination

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Name:

 

 

 

 

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.

 

First Part (10 point questions)
Answer eight of the ten.

 

I did not work problems ________ and ________.  If you do not indicate your choice here, I will assume you did not work problems 9 and 10

1.    An increase in income will trigger a movement up the demand curve for a superior good.  Explain whether you agree or disagree with this statement.

Disagree.  An increase in income will trigger a movement of a demand curve to the right.  Only price changes cause movements along a demand curve.

2.    John Smith has the following utility as a function of wealth:

                          Wealth            Utility

                                 $60               1250

                                 $70               1400

                              $100               1550

He has $80 and is offered the chance to bet $20 on a coin toss.   Will he take the bet?  Why or why not?

No.  His marginal utility of income is decreasing.  Note that the changes in income are not equal.  He is a risk averter and will not take the bet.

3.    Joe Smith Widget Works (JSWW) makes widgets, which it sells in red, green and blue colors.  Currently it buys the paint from a paint manufacturer, at a cost of $1 a widget.  When it shops around for lower bids, this turns out to be the lowest price it can get for paint.  A new cost accountant has concluded that it can go out and buy pigments, the oil base for paint, etc, and make the paint itself for seventy-five cents.  Should JSWW make its paint or buy it?

This question comes word-for word from Lecture 7.  Therefore, the answer comes word for word from the notes.  (A shorter answer will be accepted on the exam).

With all due respect to cost accountants, my instinct is to distrust the numbers we are being given.  The paint business is a competitive business, and there are several skilled paint manufacturers.  While JSWW may know how to make widgets, it knows nothing about making paint.  How can it possibly hope to make paint at a lower cost than the market price?  The most likely conclusion is that the cost accounting is flawed, leaving out some important intangible element of cost.

If there is a case for making the paint, it must be something very special such as "This is a very special paint.  It costs a lot of money to package it and store it under very special conditions until we are ready to use it.  If we mix it on the premises, we can escape those packaging or storage costs".  Or " People really like the red color of our widget.  We have discovered a special formula for making red paint that gives it a special look.  If we contract out the manufacture, we will not be able to keep the formula secret and our competitors will begin to duplicate our color".  I might believe these arguments, but not a simple cost analysis.

4.    Joe's Barber Shop is located in a quiet Cleveland Suburb.  Joe's customers come primarily from men who work in downtown Cleveland and who are home days only on the weekends, and residents of Happy Days Retirement Home.  Joe has determined the amount each would be willing to pay for a haircut, depending on the time of week.

 

Weekdays

Saturday

Commuters

$8

$15

Denizens of Happy Days

$6

$6

`

If Joe must charge one price for weekend haircuts and another for Saturday cuts, regardless of the customer's age, what prices should Joe charge?  (Joe will be able to handle his customers whenever they come.).  Explain your answer.  Note:  Joe must price his haircuts to the nearest quarter.  Thus $2.75 is an acceptable answer; $2.73 is not.

 

$6.00 for weekday cuts and $12.75 for Saturdays

5.    The Damon’s restaurant located in Kent sent out a letter offering 20% off any lunch tab Monday through Saturday to any Kent Faculty Staff or Student with a copy of the letter. The offer expires May 12, 2000, the last day of finals week.  The letter states that this offer is made to show appreciation to the university community for its support throughout the year.  Explain what important economics lesson you think the Damon’s manager has learned.  (And if you want a copy of the letter check with the Dean’s office in the College of Business)

Methinks this is a good example of price discrimination.

6.    Smith and Jones are two old time widget manufacturers.  They essentially have the market to themselves.  Both have done studies of what happens if they price widgets at $3 and $6.  (Other prices should be considered, but let’s keep the example simple).  The overall demand for widgets is known to be

Q = 50 - 8p

where p is the lowest price charged for widgets.  If they both charge the same price, they will split the market 50-50; if one charges a higher price, he will get none of the market.  Assume widgets cost nothing to produce.  Set up the payoff matrix for both Smith and Jones and show what constitutes their optimal strategy.  That is, how much should they charge?

I’ve written two matrices.  The first gives output given the two decisions.  The numbers in the table are (Smith, Jones)

 

 

Jones' Choices

 

 

$3

$6

 

Smith's Choices

 

$3

pJ =13

pS = 13

pJ = 0

pS = 26

 

 

$6

pJ = 26

pS = 0

pJ = 1

pS = 1

The second table, which is the one that really matters, gives revenues for the two parties.

 

 

Jones' Choices

 

 

$3

$6

 

Smith's Choices

 

$3

pJ =39

pS = 39

pJ = 0

pS = 78

 

 

$6

pJ = 78

pS = 0

pJ = 6

pS = 6

 

It is clear that both Jones and Smith have a dominant strategy: charging $3.  In one case, they are clearly better off while in the other case they are no worse off.

7.    .Web sites are notorious for dropping “cookies” on visitors to their web site.  These cookies, actually small computer files placed on the visitor’s computer, allow the sites to keep track which web sites the computer user visits.  I have noticed that after I visit a commercial web site, I suddenly get hit with ads for similar products on other web sites I visit.  Maybe this is annoying, maybe it is not.  What effect will “cookies” have on resale price maintainence?

If targeted advertising becomes cheaper, as these cookies seem to make itr the advantages of special selling become less, as does the need for retail price maintenance

8.    Ace Development has just purchased a 100-acre site around Lake Restful.  With its clear waters, quite location, and beautiful woodlands, the site calls out for development as luxury home sites.  A team of eminent econometricians has determined that the demand for home sites is Q = 110 – P, where P is the price in thousands of dollars per lot and Q is the number of lots to be developed.  Zoning requires one-acre lots.  An environmental group, Friends of Lake Restful (FLR), is petitioning that the land or at least a large part of it be set aside for a nature resort.  Show that what you have learned in this class helps you to deal with FLR.

The profit maximizing number of lots for you to develop is, of course 55.  (Set MR = 0).  But you know if you do that, you have credibility problems.  You can deal with this by giving 45 acres to FLR as their nature resort.

9.    Jones now works 40 yours a week for a salary of $400.  He would like, but cannot get, overtime, even at $10 an hour.  He is now offered a new position where he is paid entirely only on commission. Specifically, he will be paid four percent of sales.  He can work as many or as few hours as he chooses.  In checking out the new job, he comes across the following data on current employees:

Employee

Average Weekly Hours

Average Weekly Sales

Wilson

40

$10,000

Smith

50

$12,500

Brown

30

$7,500

Jones believes [and so should you] that he is no better or worse as a salesman than Wilson, Smith or Brown.  Will he take the new job?  Why or why not?

He will take the job.  Looking at the data on Wilson, Smith and Brown, it is clear that they are earning $10 an hour.  Jones is constrained.  If he had his desire, he would work more than 40 hours a week, but cannot.  This gives him the chance to do so.

10.  Monopolistic competition occurs when firms compete to become a monopolist.  Explain whether you agree or disagree with this statement.

Disagree.  Many of you missed this on the previous exam and I wanted to give you another chance..

 

 

Second Part (30 point questions)
Answer four of the five.

 

I did not work problem ________
If you do not indicate your choice here, I will assume you did not work problem 5

 

 

1               The United States Congress continues to debate proposals for reforming Medicare, medical insurance provided by the US Government to senior citizens. Without getting into the merits or lack thereof, of either of the proposals currently being considered in Washington, or indeed without getting into a discussion about the quality of the debate itself, I wish to offer my own modest proposal for reform.

While medical procedures performed on senior citizens range from open-heart surgery to a flu vaccine, it is possible to quantify procedures in terms of units of "medical service". Thus, a flu vaccine is one unit, while an open-heart operation is (say) 1867 units. The idea is that open-heart surgery is 1867 times as demanding as a flu shot and should cost 1867 times as much.

The demand for units of medical services for the typical senior citizen has been estimated at

q = 300 -10p.

Currently senior citizens pay zero for services, so demand is 300.

At the same time, a study team in the economics of medical care has estimated the supply function for medical services at

p = 10 + .025 q.

To make life simple, this supply curve is stated in terms of the number of services provided per senior citizen.

My proposal is quite simple. Each recipient should be required to report on his or her tax return the number of medical units used each year and pay the government $5 for each unit of medical service.

In answering this question, do not worry about items such as the cost of administering this program, its fairness, the ease of collecting fees, its sensibility etc. Concentrate on the analysis.

The quantity demanded would fall from 300 units to 250 units. Total payments would decline to from $5,250 per senior citizen to $4,062.50 per senior citizen. The government would collect $1,250 per senior citizen. If Medicare were abolished, medical use would fall to 160  units per senior citizen.

2               A monopolist sells a product with zero marginal production cost. He has two types of customers. Half of his customers have a demand curve

Q = 12 - p

while the other half has a demand curve

Q = 18 - p

Unfortunately the monopolist cannot distinguish between the two customers. But the nature of the product ensures that there can be no arbitrage. That is, one customer cannot purchase for another.

Devise a pricing scheme that maximizes revenue per customer.

Offer the product under two plans.  The gold plan allows customers unlimited purchases for an initial fee of $89.99.  The silver plan allows you, for a membership fee of $17.99, to purchase the product at $6 a unit.  The first type of customers will find the silver plan leaves them with consumer surplus of $0.01, while the gold plan would cost them more than their entire consumer surplus.

As far as the second type of customer, we would ideally like to get their entire consumer surplus, $162.   The problem is that if we charged them that much they would simply elect the sliver plan.  Thus we must compute how much consumer surplus they would get under the silver plan ($72 minus the $17.99 membership fee, or $54.01) and leave them that much plus a penny.  That requires that we charge them $162- $54.01 –$ 0.01 = $107.98. 

 

3               Ethyl's Pizzeria is considering introducing a new style of pizzas.  She thinks the customers will prefer them to the old style.  Right now, her profits are running $2000 per week.  If she introduces the new style pizza, her profits will increase to $3000 per week, even after paying the $1000 per week rental on the new oven.  Yes, this is a very expensive pizza oven. 

While this seems like a no-brainer, there is a catch.  Ethyl competes with Vesuviuo Pizzeria, located down the street.  While both boast of the best pizza in town, the truth is that the two Pizzerias are essentially the same, with the same cost, sales and profit structure.  If Vesuviuo installs the same oven, then their situation changes.  If both have the new ovens, their profits will go down to $1000 per week, after paying for the new ovens.  If Ethyl does not install and Vesuviuo does, then her profits will rise to $2200 per week.

Ethyl asks you for advice.  She has heard you muttering about "game theory" and thinks this might be applicable to this situation.  She wants you to evaluate two strategies:

·        Doing nothing for the moment and seeing what Vesuviuo does

·        Going ahead and signing the contract for the new ovens.  The contract cannot be cancelled once signed.  If Sally does this, she is not sure whether she should make a big announcement or just wait and surprise everyone when the ovens start working.

Help her out.  Show how, with your mastery of game theory, how to answer her problem.  Explain your answer.

 

Here is the payoff matrix:

 

 

Vesuviuo

 

 

Install New Oven

Stay

 

Ethyl

Install New Oven

pV =1000

pE = 1000

pV = 2200

pE = 3000

 

Stay

pV = 3000

pE = 2200

pV = 2000

pE = 2000

 

There are actually three Nash Equilibria, involving one or both of them installing the new oven.  Once Sally has committed herself, Vesuviuo will not install and vice versa.  Sally should install and make a big splash about signing the contract.

4               In the Emerald City, public water is currently free.  Next year the projected demand for water is 100,000 gallons per household per year.  But the projected capacity of the Emerald City’s water system is only 80,000 gallons per household per year.  Two plans are proposed.  One is to build a new pumping plant, which will provide another 20,000 gallons per household per year of capacity.  The cost of building and operating that plant will be $30 per household per year; the plan is to cover the costs of the plant by billing households $30 per year for the water rights (i.e., a lump sum pricing system).  The second proposal is to begin charging households by the gallon for water they use.

Preparatory to the decision being made, a team of eminent econometricians has been engaged to estimate the demand curve for water as of next year.  The report the following demand curve:

q = 100 - 20p

where q = demand by household in thousands of gallons per year and p = price in dollars per thousand gallons.

In answering this question, you may assume that (a) all households are identical, (b) the demand curve is accurate, and (c) all households are connected to the water system.

·        One fear is that, faced with a charge for water, some citizens will elect to stop using city water and hence save the $30 charge.  Comment.  (Remember, this is a question in economics, not medicine).

·        A price of $1 per thousand gallons will reduce demand to 80,000 gallons per household per year; the annual water bill will then be $80 per household.  Assume that, if the price rationing scheme is adopted, the profits will be turned over to the city treasury (and hence available for reducing other taxes residents of the Emerald City pay).  Which scheme do you think households would prefer? Why?

·        How would your answer to the second part change if, under the second scheme, customers were to be paid a lump sum bonus of $80 per year, irrespective of how much water they used?  Explain your answer.

They will not stop using water.  The current consumer surplus is (1/2)(5)(100) = $250.  Thus, the consumer surplus exceeds the proposed tax.

The lost consumer surplus is now (1/2)(1)(20) = $10.   Citizens would clearly prefer to lose $10 in consumer surplus to paying the $30 fee for building the new pumping plant.

They would be indifferent.  This is essentially the same idea.

5               The industry demand curve for widgets is given by

Q = 240 - 10 P

Initially there are ten plants producing widgets.  Each plant belongs to a different firm.  (Indeed, there is a law restricting each firm to one plant).  Each of the ten plants has a cost function:

16 + q2

where q is the number of widgets produced by each plant.  Assuming initially that only these ten firm/plants may produce widgets, determine the equilibrium price and quantity of widgets, as well as the profits of each firm.

Now assume that other firms may open a (single) plant and produce widgets if they wish.  If they do, their cost function will be the same as the nine plants.  Determine the equilibrium price of widgets, the number of firms in the industry, the quantity of widgets produced by each firm, and the profits of each firm.

Now suppose that Acme Widgets, the owner of the first plant, is given a legal monopoly to produce widgets, but is also given the right to open as many other plants as it wishes.  Determine how many plants Acme will operate, the number of widgets it will produce at each plant, the price it will charge for widgets, and its profits. 

Now suppose that widgets are subject to a $1 tax.  What happens to Acme’s supply curve?

Each plant has a marginal cost curve equal to 2q, and sets output equal to P/2,  so with ten plants, total output is 5P.  Since demand and supply are equal, the equilibrium price is given by 240 - 10P = 5P, implying that P = 16.  Thus each firm produces q = 8.  Each firm has profits of (16)(8) - (16 + 8*8) = $48.

AC is 16/q + q, and that is minimized when q = 4.  At that level of production, LRAC = 8.  At a price of 8, total quantity demanded will be 160, and there will be 40 plants, including the first plant.  Each firm, except for the first, will earn zero profits.  Acme  will earn profits of $7.

Acme’s LRMC is of course $8.  Its revenue function is given by

R = Q(24 - 0.1Q)

so that marginal revenue equals

24 - 0.2Q. 

Profit maximization requires that MR = MC, so that total output is given by 24 - 0.2Q = 8, and that means Q = 80.  It charges a price of $16, operates 20 plants including the first.  Its profits are

(80)(16) - 8(16)  = $1,152.

This is just another way of asking about a monopolist’s supply curve..  I hope you weren’t suckered in.