Managerial Economics

Mr. Upton

Spring, 1998

Second Midterm Examination
April 7, 1998

 

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). Explain whether you agree or disagree with these statements.

1. Restricting the number of producers through licensing implies that each firm in the industry no longer behaves as a price taker.

Disagree. If the number of firms is sufficiently large, then there can still be competition and each firm acts like a competitor. If you restricted it to (say) one firm, the answer would be false, for one firm would be - and would act like - a monopolist.

2. If the government levies a per unit tax on a monopolist, the monopolist increases price and reduces the total quantity shown. Total revenue may either increase or decrease

This is a homework problem. See those answers.

3.      If both firms in a Duopoly have a dominant strategy, neither achieves maximum profits.

No. The dominant strategy could be for the two firms to cooperate.

Second Part (25 point questions)

Work any two of the following three questions. If you start a question and then change your mind about which question you want to work, please cross out the incorrect information. Also, please put check marks in two of the following boxes.

I have worked (check 2)

Question 1

 

Question 2

 

Question 3

 
  1. You have just been employed as an economic analyst by Strategic Decisions by Game Theory, Incorporated, a high powered consulting firm. On your first day on the job you are assigned to work on a rush project.

Acme Nursery is just about getting ready for spring. This is the time of year when homeowners throughout Ohio think of spending far too much money on landscaping and Acme wants to get its fair share, or perhaps more than its fair share. Acme is considering two marketing campaigns: the first is to stress professional design service. The second is to attempt to become the Wal-Mart of the flower industry, offering a profusion of flowers and shrubs for sale at low prices. Acme must choose which strategy it will follow. The strategy will dictate its seasonal ad campaign and what kind of people it hires.

Alas, for Acme, it is not the only game in town. Opal Nursery, just down the street is getting ready for spring as well. You know that Opal is still going through the same thinking about what it will do this season.

It turns out that both Acme and Opal have followed different strategies during the past four years. The Nursery Research Council of Northeast Ohio has gathered data on nursery sales on a year by year basis, and you have the following data:

Year

Acme Strategy

Opal Strategy

Acme Sales

Opal Sales

1994

Low
Prices

Low
Prices

$75

$75

1995

High Service

Low
Prices

$40

$90

1996

High Service

High Service

$40

$80

1997

Low
Prices

High Service

$45

$60

You know that, in the years Acme adopted a service strategy, its profits were half of its sales; in the years that Acme adopted a low price strategy, its profits were a third of sales. While you do not have data for Opal, it is perhaps reasonable to assume that it had the same profit margins.

What strategy do you recommend for Acme? Why?
Be sure to show your work.
Hint: Remember the name of your employer.

This is a simple problem in game theory. Construct the payoff matrix. Here, I go through two steps. First, I construct the payoff matrix in terms of sales.

 

 

Opal

 

 

Low Prices

High Service

Acme

Low Prices

so =75

sa = 75

so = 60

sa = 45

 

High Service

so = 90

sa = 40

so = 80

sa = 40

Of course, sales don't matter. Profits do. So my next step is to restate the matrix in terms of profits, and I get the following:

 

 

Opal

 

 

Low Prices

High Service

Acme

Low Prices

p o =25

p a = 25

p o = 30

p a = 15

 

High Service

p o = 30

p a = 20

p o = 40

p a = 20

From this matrix, it is clear that Opal has a dominant strategy: High Service. I assume Opal will act rationally and I therefore recommend that go with low prices, which is its right strategy if opal is going to act rationally.

2. The industry demand curve for widgets is given by

Q = 360 - 8 P

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

16 + q2

where q is the number of widgets produced by each plant.

  1. Assuming initially that only these eight firm/plants may produce widgets, determine the equilibrium price and quantity of widgets.

Each firm as a marginal cost function 2q. Each firm will therefore set p = MC = 2q. That mean each firm will supply q = p/2 to the market. Thus the total industry supply will be eight times that, or 4p. We know that supply must equal demand, so that we know that

4p = 360 - 8p

Solving, we get p = 30. Thus total quantity demanded will be 120, and each firm will supply 15.

  1. 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 eight plants. What will be the equilibrium price and quantity of widgets? How many new plants will be built?

In this case, equilibrium will occur when firms are making zero profits, so that equilibrium must be at the minimum of the average cost function. Average cost is

16/q + q,

and that is minimized when

-16/q2 + 1 = 0,

or when q = 4. Average cost is then 16/4 + 4 or 8. The price is then 8. Total quantity demanded is thus 360 - 8(8) = 296.

To determine how many plants will be build, note that each plant will be supplying four widgets. But at 4 widgets per plant, there will be 296/4 = 74 plants. Right now there are 8 plants, so another 66 will be built.

  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.

  1. 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.

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

Surpise! This looks like a Cournot equilibrium.